40
Answer Explanations SA T ®  Practice Test #3 © 2015 The College Board. College Board, SAT, and the acorn logo are registered trademarks of the College Board. 5LSA08

PrepScholar Sat Practice Test 3 Answers

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7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 140

Answer ExplanationsSAT

reg

Practice Test 3

copy 2015 The College Board College Board SAT and the acorn logo are registered trademarks of the College Board 5LSA08

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 240

1

Answer Explanations

SAT Practice Test 3

Section 1 Reading Test

QUESTION 1

Choice B is the best answer In the passage Lady Carlotta is approachedby the ldquoimposingly attired ladyrdquo Mrs Quabarl while standing at a train sta-

tion (lines 32-35) Mrs Quabarl assumes Lady Carlotta is her new nanny

Miss Hope ldquoYou must be Miss Hope the governess Irsquove come to meetrdquo (lines

36-37) Lady Carlotta does not correct Mrs Quabarlrsquos mistake and replies

ldquoVery well i I must I mustrdquo (line 39)

Choices A C and D are incorrect because the passage is not about a woman

weighing a job choice seeking revenge on an acquaintance or disliking her

new employer

QUESTION 2

Choice C is the best answer In lines 1-3 the narrator states that Lady

Carlotta ldquostepped out on to the platorm o the small wayside station and

took a turn or two up and down its uninteresting lengthrdquo in order to ldquokill

timerdquo In this context Lady Carlotta was taking a ldquoturnrdquo or a short walk

along the platorm while waiting or the train to leave the station

Choices A B and D are incorrect because in this context ldquoturnrdquo does not

mean slight movement change in rotation or course correction While Lady

Carlotta may have had to rotate her body while moving across the station

ldquotook a turnrdquo implies that Lady Carlotta took a short walk along the plat-

ormrsquos length

QUESTION 3

Choice A is the best answer In lines 10-14 the narrator states that some o

Lady Carlottarsquos acquaintances would ofen admonish or criticize Lady Carlotta

or meddling in or openly expressing her opinion on other peoplersquos affairs

Choices B C and D are incorrect because the narrator does not suggest that

other people viewed Lady Carlotta as tactul ambitious or unriendly

7262019 PrepScholar Sat Practice Test 3 Answers

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2

QUESTION 4

Choice A is the best answer In lines 10-14 the narrator states that people

ofen criticized Lady Carlotta and suggested that she not interere in other

peoplersquos affairs which were ldquonone o her businessrdquo Te act that people

ofen were critical o Lady Carlottarsquos behavior provides evidence that Lady

Carlotta was outspoken

Choices B C and D do not provide the best evidence that Lady Carlotta was

outspoken Choices B C and D mention Lady Carlotta but do not speciy

how others view her

QUESTION 5

Choice C is the best answer Te narrator notes that Lady Carlotta decided

not to interere when one o her ldquomost eloquent exponentsrdquo was stuck in a

tree because an angry boar was nearby (lines 14-22) Tis ldquoeloquent expo-

nentrdquo was a woman who ofen criticized Lady Carlotta or interering inother peoplersquos affairs Lady Carlottarsquos decision to ldquoput the doctrine o non-

intererence into practicerdquo (to not help her emale acquaintance who was

ldquobesiegedrdquo in a tree) suggests that Lady Carlotta has a sense o humor

Choices A B and D are incorrect because the description o how she ldquoput

the doctrine o non-intererence into practicerdquo does not suggest that Lady

Carlotta is deceptive or cruel or explain a surprising change in her behavior

QUESTION 6

Choice A is the best answer Te narrator explains that Mrs Quabarl toldLady Carlotta about the ldquonature o the chargerdquo when she gave Lady Carlotta

details about the Quabarl children (line 53-61) Since Lady Carlotta is pre-

tending to be a governess the term ldquochargerdquo reers to her responsibilities or

job duties when caring or the Quabarl children

Choices B C and D are incorrect because in this context ldquochargerdquo does not

mean attack ee or expense

QUESTION 7

Choice A is the best answer Lady Carlotta learns about Mrs Quabarlrsquos chil-dren Claude Wilrid and Irene (lines 53-58) Te narrator then describes

Mrs Quabarlrsquos child Viola as ldquosomething or other else o a mould equally

commonplace among children o that class and type in the twentieth cen-

turyrdquo (lines 58-61) Tis statement about Viola implies that all o the Quabarl

children have skills typical or ldquoo a mould equally commonplacerdquo to other

peers in their social class

Choices B C and D are incorrect because the narrator does not indicate that

all o the Quabarl children are unusually creative and intelligent hostile to

the idea o having a governess or more educated than their peers

7262019 PrepScholar Sat Practice Test 3 Answers

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3

QUESTION 8

Choice B is the best answer In lines 62-69 Mrs Quabarl explains to Lady

Carlotta that she wants her children to actively participate in their education

and that Lady Carlotta should not create lessons that require her children to

simply memorize historical figures and dates Mrs Quabarl emphasizes an

education centered on active engagement when she states that her childrenshould ldquonot only be AUGH but INERESED in what they learnrdquo

Choices A C and D are incorrect because the narrator does not suggest that

Mrs Quabarl avors an education that emphasizes traditional values artistic

experimentation or actual retention

QUESTION 9

Choice B is the best answer In lines 77-82 the narrator describes Mrs

Quabarl as appearing ldquomagnificent and autocraticrdquo or outwardly domineer-

ing but easily ldquocowed and apologeticrdquo when someone challenges or defiesher authority

Choices A C and D are incorrect because the narrator does not describe

Mrs Quabarl as selfish bitter or requently imprudent

QUESTION 10

Choice D is the best answer In lines 77-82 the narrator provides evidence

that Mrs Quabarl appears imposing or autocratic but is easily defied or

opposed ldquoShe was one o those imperectly sel-assured individuals who are

magnificent and autocratic as long as they are not seriously opposed Teleast show o unexpected resistance goes a long way towards rendering them

cowed and apologeticrdquo

Choices A B and C do not provide the best evidence that Mrs Quabarl

appears imposing but is easily defied Choices A and B are incorrect because

they present Mrs Quabarlrsquos opinions on railway companies and educa-

tion and choice C is incorrect because it ocuses on Lady Carlotta not

Mrs Quabarl

QUESTION 11

Choice A is the best answer While the author predominantly supports

the use o public transportation in the third paragraph he recognizes

some limitations to the public transportation system it is a ldquodepressing

experiencerdquo (lines 25-26) and ldquounderunded ill-maintained and

ill-plannedrdquo (line 31)

Choices B C and D are incorrect because the third paragraph does not

expand upon an argument made in the first two paragraphs provide an

overview o a problem or advocate ending the use o public transportation

7262019 PrepScholar Sat Practice Test 3 Answers

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4

QUESTION 12

Choice C is the best answer Te author notes that in North America ldquohopping

in a car almost always gets you to your destination more quicklyrdquo (lines 32-34)

Tis statement suggests that speed is one advantage to driving in North America

Choices A B and D are incorrect because the author does not cite environmen-

tal impact convenience or cost as advantages o driving in North America

QUESTION 13

Choice D is the best answer In lines 32-34 the author provides evidence

that speed is one advantage to driving in North America because driving

ldquoalmost always gets you to your destination more quicklyrdquo

Choices A B and C do not provide the best evidence that speed is one

advantage to driving in North America Choices A and B are incorrect

because they offer general inormation about using public transportationChoice C is incorrect because although these lines mention North America

they ocus on the disadvantages o public transportation

QUESTION 14

Choice B is the best answer Te author argues in the ourth paragraph that

public transportation ldquocan be aster more comortable and cheaper than the

private automobilerdquo (lines 36-37) and provides examples o ast and conve-

nient public transportation systems

Choices A C and D are incorrect because they ocus on points made in theourth paragraph rather than the paragraphrsquos central idea

QUESTION 15

Choice B is the best answer In lines 35-37 the author provides evidence

that some public transportation systems are superior to driving because

public transportation ldquocan be aster more comortable and cheaper than the

private automobilerdquo

Choices A C and D do not provide the best evidence that some public

transportation systems are superior to driving as they highlight points madein the ourth paragraph rather than the paragraphrsquos central idea

QUESTION 16

Choice C is the best answer In the last paragraph the author explains the

trend that people who became adults around the end o the twentieth cen-

tury are more willing to use public transportation than people rom older

generations Te author notes ldquoI you credit the demographers this transit

trend has legsrdquo (lines 58-59) In this context ldquocreditrdquo means to believe the

demographersrsquo claims about the trend

7262019 PrepScholar Sat Practice Test 3 Answers

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5

Choices A B and D are incorrect because in this context ldquocreditrdquo does not

mean endow attribute or honor

QUESTION 17

Choice B is the best answer In lines 59-63 the author explains the trend

o people who became adults around the end o the twentieth centuryldquotend[ing] to avor cities over suburbsrdquo In this context these adults ldquoavorrdquo

or preer cities over suburbs

Choices A C and D are incorrect because in this context ldquoavorrdquo does not

mean indulge resemble or serve

QUESTION 18

Choice B is the best answer In lines 63-67 the author explains that while

riding on public transportation people can use personal electronic devices

such as ldquoiPads MP3 players Kindles and smartphonesrdquo

Choices A C and D are incorrect because they do not show that public

transportation is compatible with the use o personal electronic devices

QUESTION 19

Choice A is the best answer Figure 1 shows that 107 o public transpor-

tation passengers are students and 67 o public transportation passengers

are retirees Tus more students than retirees use public transportation

Choices B and C are incorrect because figure 1 shows that more employedthan unemployed people use public transportation and that more employed

people than homemakers use public transportation Choice D is incorrect

because figure 1 does not explain how requently passengers use public

transportation it only identifies public transportation passengers by their

primary occupation

QUESTION 20

Choice A is the best answer Figure 1 shows that 72 o public transporta-

tion passengers are ldquoemployed outside the homerdquo and figure 2 indicates that

591 o public transportation trips are or ldquoworkrdquo It can be inerred romthese figures that many public transportation passengers take public trans-

portation to their place o employment

Choices B C and D are incorrect because figure 1 and figure 2 do not

indicate that public transportation passengers primarily use the system to

run errands use their own car on weekends or are planning to purchase

a car

7262019 PrepScholar Sat Practice Test 3 Answers

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6

QUESTION 21

Choice D is the best answer Te author explains that Ken Dial created an

experiment to study the evolution o flight by observing how baby Chukars

learn to fly During the experiment Dial noticed the unusual way Chukars

use their ldquolsquowings and legs cooperativelyrsquordquo to scale hay bales (lines 38-43) and

he created ldquoa series o ingenious experimentsrdquo (line 46) to study this obser- vation Afer his additional experiments Dial determined that these baby

birds angle ldquotheir wings differently rom birds in flightrdquo (lines 49-50)

Choices A B and C are incorrect because they do not accurately reflect the

sequence o events in the passage

QUESTION 22

Choice A is the best answer In lines 6-9 the author explains that Dial was

ldquochallengedrdquo or dared by graduate students to develop ldquonew datardquo on a long-

standing scientific debate (the ldquoground-up-tree-downrdquo theory)

Choices B C and D are incorrect because in this context ldquochallengedrdquo does

not mean required disputed with or competed with

QUESTION 23

Choice A is the best answer Te author explains that Dial created his initial

experiment to try and create ldquonew data on the age-old ground-up-tree-down

debaterdquo and that he looked or ldquocluesrdquo in ldquohow baby game birds learned to

flyrdquo (lines 8-11) Te note at the beginning o the passage explains the ldquoage-

old ground-up-tree down debaterdquo and offers two different theories on howbirds evolved to fly Finally the last paragraph o the passage discusses WAIR

in an evolutionary context

Choices B C and D are incorrect because they do not identiy Dialrsquos central

assumption in setting up his research

QUESTION 24

Choice B is the best answer In lines 6-11 the author provides evidence that

Dialrsquos central assumption in setting up his research is that the acquisition o

flight in young birds is linked to the acquisition o flight in their ancestorsTe author notes that Dial created a project to ldquocome up with new data on

the age-old ground-up-tree-down debaterdquo

Choices A C and D do not provide the best evidence that Dialrsquos central

assumption in setting up his research is that the acquisition o flight in young

birds is linked to the acquisition o flight in their ancestors Choices A C

and D are incorrect because they ocus on Dialrsquos experiment and his obser-

vations on ground birds

7262019 PrepScholar Sat Practice Test 3 Answers

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7

QUESTION 25

Choice C is the best answer When a rancher observed Dialrsquos laboratory

setup he was ldquoincredulousrdquo that the Chukars were living on the ground and

he advised Dial to give the birds ldquosomething to climb onrdquo (lines 16-23) Tis

ldquokey piece o advicerdquo (line 14) led Dial to add hay bales to his laboratory

Dial later noticed that the Chukars were using their legs and wings to scalethe hay bales and this observation became the ocal point o his research

Choices A B and D are incorrect because the incident with the local rancher

did not serve to reveal Dialrsquos motivation or creating the project emphasize

differences in laboratory and field research or introduce a contributor to a

scientific theory

QUESTION 26

Choice C is the best answer Te author explains that Dialrsquos ldquoaha momentrdquo

came when he determined the Chukars used ldquotheir legs and wings coop-erativelyrdquo to scale the hay bales (lines 40-42) Dial then created additional

experiments to study how the birds dealt with gradually steeper inclines

ldquo[he filmed] the birds as they raced up textured ramps tilted at increasing

anglesrdquo (lines 46-48)

Choices A B and D are incorrect because Dialrsquos ldquoaha momentrdquo was not ol-

lowed by Dial teaching the birds to fly studying videos to find out why the

birds no longer hopped or consulting with other researchers

QUESTION 27

Choice B is the best answer Dial observed that as the Chukars raced up

steep ramps they ldquobegan to flaprdquo and ldquoaimed their flapping down and back-

ward using the orce to keep their eet firmly pressed against the ramprdquo

(lines 49-53) Dial determined that the position o their flapping wings acil-

itated the baby Chukarsrsquo traction on the steep ramps

Choices A C and D are incorrect because the passage does not indicate that

the Chukarsrsquo speed alternation o wing and oot movement or continual

hopping motions acilitated their traction on steep ramps

QUESTION 28

Choice B is the best answer In lines 61-63 the author explains that Dial

named his scientific finding ldquoWAIR or wing-assisted incline running and

went on to document it in a wide range o speciesrdquo In this context Dial

ldquodocumentedrdquo or recorded the existence o WAIR in numerous bird species

Choices A C and D are incorrect because in this context ldquodocumentrdquo does

not mean to portray publish or process

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8

QUESTION 29

Choice D is the best answer In lines 70-74 the author explains that glid-

ing animals do not use a ldquoflapping flight strokerdquo or WAIR wing-assisted

incline running Since Chukars a ground bird use WAIR to help scale steep

inclines it can be reasonably inerred that gliding animals do not use WAIR

to aid in climbing slopes

Choices A B and C are incorrect because the passage does not include

inormation on gliding animalsrsquo offspring their method o locomotion or

their eeding habits

QUESTION 30

Choice D is the best answer In lines 73-75 the author provides evidence

that ldquothe flapping flight strokerdquo is ldquosomething gliding animals donrsquot dordquo

Choices A B and C do not provide the best evidence that gliding animalsdo not use a flapping stroke to aid in climbing slopes Tese choices do not

contain inormation about gliding animals

QUESTION 31

Choice B is the best answer In lines 21-24 the authors o Passage 1 state

societyrsquos ldquocommon happinessrdquo is dependent on women never becoming

involved in politics In this context the authors o Passage 1 are sug-

gesting that all members o society can have a ldquocommonrdquo or shared

happiness

Choices A C and D are incorrect because in this context ldquocommonrdquo does

not mean average coarse or similar

QUESTION 32

Choice C is the best answer In lines 25-30 the authors o Passage 1 state

that women should seek ldquogentle occupations and the cares o the homerdquo

so they can avoid perorming difficult or ldquostrenuousrdquo and unpleasant or

ldquoonerousrdquo tasks

Choices A B and D are incorrect because the authors o Passage 1 do notsuggest that running a household and raising children are rewarding or

both sexes yield less value or society or require proessional or political

skills

QUESTION 33

Choice C is the best answer In lines 25-30 the authors o Passage 1 provide

evidence that women should run households and raise children because

these roles do not require ldquostrenuous habits and onerous dutiesrdquo

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9

Choices A B and D do not provide the best evidence that running a house-

hold and raising children entail very ew activities that are difficult or

unpleasant rather these lines offer general inormation about the differ-

ences between the sexes

QUESTION 34

Choice D is the best answer In lines 41-46 Wollstonecraf argues that i

women do not receive an education ldquoto become the companion o manrdquo or

one that is comparable to menrsquos education then society will not progress in

ldquoknowledge and virtuerdquo

Choices A B and C are incorrect because Wollstonecraf does not suggest

that society can progress only i women have happiness and financial secu-

rity ollow societal rules or replace men as figures o power

QUESTION 35

Choice C is the best answer Wollstonecraf argues that women should be

granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo

(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-

enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context

Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or

intellect and allow women to consider their role in society

Choices A B and D are incorrect because in this context ldquoreasonrdquo does not

mean motive sanity or explanation

QUESTION 36

Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws

passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to

ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf

is arguing that societyrsquos leaders grant men reedoms that are denied to women

Choices B C and D are incorrect because Wollstonecraf does not claim

that societyrsquos leaders have granted reedoms that created a general reduction

in individual virtue caused arguments about happiness or ensured equality

or all people

QUESTION 37

Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-

dence that societyrsquos leaders grant reedoms that privilege men She argues

that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-

lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to

ldquocontend or their reedomrdquo

Choices A B and C do not provide the best evidence that societyrsquos leaders

grant reedoms that privilege men over women

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10

QUESTION 38

Choice C is the best answer Wollstonecraf cites the statement made by

the authors o Passage 1 that excluding women rom political participation

is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)

Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe

abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument

by highlighting a flaw in the reasoning presented by the authors o Passage 1

Choices A B and D are incorrect because Wollstonecraf does not reer to

the statement made in Passage 1 to call into question the authorsrsquo qualifica-

tions dispute the assertion that women are excluded by their own govern-

ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on

gender roles

QUESTION 39

Choice A is the best answer Te authors o Passage 1 argue that while

restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)

this restriction is necessary or societyrsquos overall happiness (lines 13-17)

Wollstonecraf however strongly challenges this argument asking the

authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-

doms are granted to women and likening societyrsquos male leaders to tyrants as

they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in

the darkrdquo (lines 78-88)

Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2

QUESTION 40

Choice D is the best answer Te authors o Passage 1 admit that women are

ldquoexcluded by the other hal [men] rom any participation in governmentrdquo

(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws

that deny women ldquocivil and political rightsrdquo (line 86)

Choices A B and C are incorrect because the authors o both passages

would not agree that women had the same preerences as men required agood education or were as happy as men

QUESTION 41

Choice A is the best answer Wollstonecraf argues in the final paragraph

o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women

ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would

most likely argue that allowing women these rights would be ldquoa reversal o

[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos

interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as

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11

mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created

two sexes or a particular reason so while men can exercise civil and politi-

cal rights women are not naturally suited to these activities (lines 30-36)

Choices B and C are incorrect because they are not supported by inorma-

tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do

not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo

QUESTION 42

Choice C is the best answer When discussing problems with bee colo-

nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo

(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-

tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a

tentative tone and provides urther evidence that the authors believe but are

not certain that their hypothesis is correct

Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone

QUESTION 43

Choice C is the best answer In lines 24-28 the authors hypothesize that bee

colonies will be susceptible to mite inestations i they do not occasionally

eed on pyrethrum producing plants In lines 42-46 they suggest creating a

trial where a ldquosmall number o commercial honey bee colonies are offered a

number o pyrethrum producing plantsrdquo to test their hypothesis

Choices A B and D are incorrect because the authors do not hypothesize that

honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees

to develop secondary inections that beekeepers should increase their use o

insecticides or that humans are more susceptible to varroa mites

QUESTION 44

Choice D is the best answer In lines 24-28 the authors provide evidence

that a bee colony may be more resistant to mite inections i the bees eat

pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-

nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees

Choices A B and C do not describe any o the authorsrsquo hypotheses

QUESTION 45

Choice D is the best answer Te authors explain that when beekeepers

use commercially produced insecticides to fight mite inections they may

ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-

cientrdquo (lines 31-35)

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12

Choices A B and C are incorrect because the authors do not suggest that

beekeepersrsquo use o commercially produced insecticides increases mite popu-

lations kills bacteria or destroys beesrsquo primary ood source

QUESTION 46

Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-

ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo

Choices A B and D are incorrect because they do not provide the best evi-

dence that beekeepersrsquo use o commercially produced insecticides may be

harmul to bees choices A B and D ocus on mite inestationsrsquo impact on

honeybees

QUESTION 47

Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some

bees Te authors then state ldquoWe urther postulate that the proper dosage

necessary to prevent mite inestation may be better lef to the beesrdquo (lines

35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the

bees may naturally control mite inestations better than insecticides

Choices A C and D are incorrect because in this context ldquopostulaterdquo does

not mean to make an unounded assumption question a belie or theory or

conclude based on firm evidence

QUESTION 48

Choice B is the best answer In the ourth paragraph the authors propose

a trial to study i honeybeesrsquo consumption o pyrethrum producing plants

helps the honeybees deend against mite inestations In the experiment the

authors plan to offer honey bee colonies both pyrethrum producing plants

and ldquoa typical bee ood source such as cloverrdquo to determine i these different

diets affect the beesrsquo susceptibility to mite inestations

Choices A C and D are incorrect because the main purpose o the ourth

paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished

experiment

QUESTION 49

Choice A is the best answer In lines 43-45 the authors propose a scien-

tific trial in which honeybees are ldquooffered a number o pyrethrum producing

plants as well as a typical bee ood source such as cloverrdquo Since the authors

contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood

sourcerdquo it can be assumed that clover does not produce pyrethrums

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13

Choice B is incorrect because it is stated in the passage Choices C and D are

incorrect because they are not assumptions made by the authors

QUESTION 50

Choice B is the best answer Te table shows that 77 percent o the honeybee

colonies with colony collapse disorder were inected by all our pathogens

Choices A C and D are incorrect because they do not identiy the percent

o honeybee colonies with colony collapse disorder that were inected by all

our pathogens as based on data in the table

QUESTION 51

Choice D is the best answer Te table shows that 81 percent o colo-

nies without colony collapse disorder were affected by the pathogen

Nosema ceranae

Choices A B and C are incorrect because they do not identiy the pathogen

that inected the highest percentage o honeybee colonies without colony

collapse disorder as based on data in the table

QUESTION 52

Choice D is the best answer Te table discusses pathogen occurrence in

honeybee colonies but it includes no inormation as to whether these hon-

eybees were inected with mites Because the table does not suggest mites

inested the honeybee colonies no conclusions can be made as to whether

mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)

Choices A B and C are incorrect because the table provides no inormation

about whether these honeybees were inected with mites

Section 2 Writing and Language Test

QUESTION 1

Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-

ates a parallel structure within the list that begins with ldquohappierrdquo

Choices B C and D are incorrect because none creates a parallel structure

within the list o qualities

QUESTION 2

Choice B is the best answer Te ways in which exposure to natural light

affects employees is the main subject o the passage

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1540

14

Choices A C and D are incorrect because none introduces the topic dis-

cussed in the remainder o the passage

QUESTION 3

Choice C is the best answer It accurately notes that the proposed sentence

would be placed directly between the first mention o circadian rhythms andthe explanation o the term

Choices A B and D are incorrect because each misinterprets the relation-

ship between the proposed additional text and the ideas in the paragraph

QUESTION 4

Choice C is the best answer It provides the correct possessive construction

or ldquobodyrdquo which must be a singular noun when discussed in general terms

as in this sentence Choice C also provides the correct plural construction

or ldquoclocksrdquo

Choices A B and D are incorrect because each applies either a possessive or

a plural construction in a place where it doesnrsquot belong

QUESTION 5

Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular

noun ldquoabsenteeismrdquo

Choices B C and D are incorrect because each provides a verb that

either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy

QUESTION 6

Choice B is the best answer It contains a direct reerence to productivity

the topic introduced in the previous sentence

Choices A C and D are incorrect because none directly addresses employee

productivity the primary subject o the previous sentence

QUESTION 7

Choice A is the best answer It opens with a reerence to lowered worker

productivity creating a transition rom the previous paragraph and clearly

positions the high energy costs o artificial light sources as an additional

disadvantage

Choices B C and D are incorrect because none o the choices offer an ade-

quate transition rom the previous paragraph Each awkwardly inserts the

issue o lower worker productivity into a statement about the high energy

costs o artificial light sources

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1640

15

QUESTION 8

Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-

cate that the savings occurred every year

Choices A B and C are incorrect because each proposes an option that

would result in a redundancy with ldquoannualrdquo

QUESTION 9

Choice C is the best answer It provides a transitional adverb that accurately

communicates that this sentence describes an option that companies could

choose (ldquolight tubesrdquo) instead o the option described in the previous sen-

tence (ldquoull-pane windowsrdquo)

Choices A B and D are incorrect because each proposes a transitional

adverb that does not accurately reflect the relationship between this sen-

tence and the one preceding it

QUESTION 10

Choice C is the best answer It provides the correct relative pronoun to cor-

respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-

duce the definition that ollows

Choices A B and D are incorrect because each offers a pronoun inappropri-

ate or opening a dependent clause defining ldquolight tubesrdquo

QUESTION 11

Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the

noun ldquomeansrdquo particularly as a way to connect it to another noun or verb

Choices A C and D are incorrect because each results in nonstandard

phrasing with ldquomeansrdquo

QUESTION 12

Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-

responds with the plural noun ldquosettlersrdquo

Choices B C and D are incorrect because each provides either a nonstan-

dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo

QUESTION 13

Choice C is the best answer It creates a transition rom the poor ood qual-

ity mentioned in the previous sentence to the inormation about Harvey in

the remainder o the sentence

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1740

16

Choices A B and D are incorrect because none offers a transition rom the

previous sentence or a detail that corresponds precisely with the inorma-

tion in the remainder o the sentence

QUESTION 14

Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens

with a comma

Choices A B and C are incorrect because each proposes punctuation that

creates an inappropriately strong separation between the subject ldquoFred

Harveyrdquo and the verb ldquodecidedrdquo

QUESTION 15

Choice B is the best answer It provides the plural verb and plural posses-

sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo

Choices A C and D are incorrect because each either ails to provide a verb

that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide

the appropriate possessive pronoun

QUESTION 16

Choice C is the best answer It accurately echoes an earlier characterization

o the ood as being o ldquoterrible qualityrdquo while maintaining the established

tone o the passage

Choices A B and D are incorrect either because the word is less ormal than

the established tone o the passage (ldquoickyrdquo) or because it illogically attributes

agency to ood (ldquosinisterrdquo ldquosurlyrdquo)

QUESTION 17

Choice C is the best answer It accurately interprets ldquonot content to ollow

conventional business practicesrdquo as logically introducing the new practice o

ldquoemploying womenrdquo described in the ollowing sentences

Choices A B and D are incorrect because none recognizes why the sentence

is relevant to this particular location in the passage

QUESTION 18

Choice B is the best answer It is concise and ree o redundancies

Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and

ldquotremendousrdquo adjectives so close in meaning that together they present a

redundancy

7262019 PrepScholar Sat Practice Test 3 Answers

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17

QUESTION 19

Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary

reerence to ldquosuch regulationsrdquo in the previous clause

Choices A B and C are incorrect because each lacks a necessary subject

such as a pronoun or noun

QUESTION 20

Choice C is the best answer It reers directly to benefits or the restaurantsrsquo

emale employees the subject o the previous sentence

Choices A B and D are incorrect because none logically builds upon the

sentence that precedes it

QUESTION 21

Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo

Choices A B and C are incorrect because each uses the punctuation or

a dependent clause (ldquoLiving independently and demonstrating an intense

work ethicrdquo) as i it were an independent clause

QUESTION 22

Choice A is the best answer It recognizes that the new inormation sup-

ports the previous sentencersquos claim that ldquothe Harvey Girls became known as

a transormative orcerdquo

Choices B C and D are incorrect because each misinterprets the relation-

ship between the proposed text and the passage

QUESTION 23

Choice A is the best answer It opens with a clause that identifies how

1-MCP affects apples which ocuses the sentence on 1-MCP as the subject

and allows the ideas in the sentence to progress logically

Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy

QUESTION 24

Choice D is the best answer Only the comma is necessary to separate

ldquoethylenerdquo rom the appositive noun phrase that defines it

Choices A B and C are incorrect because each creates a comma splice and

or adds unnecessary words

7262019 PrepScholar Sat Practice Test 3 Answers

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18

QUESTION 25

Choice B is the best answer It offers an adjective that accurately describes

resh apples

Choices A C and D are incorrect because each proposes an adjective that

does not describe a plausible ruit texture

QUESTION 26

Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-

sponds with the plural reerent ldquoapplesrdquo

Choices B C and D are incorrect because none provides a pronoun that is

both possessive and plural

QUESTION 27

Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins

the relative clause

Choices A B and C are incorrect because each contains a pronoun that

either does not correspond with the human reerent ldquoconsumersrdquo or does

not correctly begin the relative clause

QUESTION 28

Choice B is the best answer It provides the present tense verb ldquodordquo which

corresponds to the present tense established earlier in the sentence

Choices A C and D are incorrect because each contains a verb that deviates

rom the simple present tense established in the sentence

QUESTION 29

Choice B is the best answer It provides a colon to appropriately introduce the

clause that ollows an elaboration on the preceding claim that Bartlett pears

are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo

Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically

QUESTION 30

Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-

trast with a previous idea and goes on to mention that 1-MCP can have

negative effects Sentence 1 continues the discussion o benefits o 1-MCP

and sentence 2 names the adverse effect o limiting scent production so the

most logical spot or sentence 4 is between these sentences

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040

19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240

21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340

22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440

23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540

24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640

25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740

26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840

27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040

QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 2: PrepScholar Sat Practice Test 3 Answers

7262019 PrepScholar Sat Practice Test 3 Answers

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1

Answer Explanations

SAT Practice Test 3

Section 1 Reading Test

QUESTION 1

Choice B is the best answer In the passage Lady Carlotta is approachedby the ldquoimposingly attired ladyrdquo Mrs Quabarl while standing at a train sta-

tion (lines 32-35) Mrs Quabarl assumes Lady Carlotta is her new nanny

Miss Hope ldquoYou must be Miss Hope the governess Irsquove come to meetrdquo (lines

36-37) Lady Carlotta does not correct Mrs Quabarlrsquos mistake and replies

ldquoVery well i I must I mustrdquo (line 39)

Choices A C and D are incorrect because the passage is not about a woman

weighing a job choice seeking revenge on an acquaintance or disliking her

new employer

QUESTION 2

Choice C is the best answer In lines 1-3 the narrator states that Lady

Carlotta ldquostepped out on to the platorm o the small wayside station and

took a turn or two up and down its uninteresting lengthrdquo in order to ldquokill

timerdquo In this context Lady Carlotta was taking a ldquoturnrdquo or a short walk

along the platorm while waiting or the train to leave the station

Choices A B and D are incorrect because in this context ldquoturnrdquo does not

mean slight movement change in rotation or course correction While Lady

Carlotta may have had to rotate her body while moving across the station

ldquotook a turnrdquo implies that Lady Carlotta took a short walk along the plat-

ormrsquos length

QUESTION 3

Choice A is the best answer In lines 10-14 the narrator states that some o

Lady Carlottarsquos acquaintances would ofen admonish or criticize Lady Carlotta

or meddling in or openly expressing her opinion on other peoplersquos affairs

Choices B C and D are incorrect because the narrator does not suggest that

other people viewed Lady Carlotta as tactul ambitious or unriendly

7262019 PrepScholar Sat Practice Test 3 Answers

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2

QUESTION 4

Choice A is the best answer In lines 10-14 the narrator states that people

ofen criticized Lady Carlotta and suggested that she not interere in other

peoplersquos affairs which were ldquonone o her businessrdquo Te act that people

ofen were critical o Lady Carlottarsquos behavior provides evidence that Lady

Carlotta was outspoken

Choices B C and D do not provide the best evidence that Lady Carlotta was

outspoken Choices B C and D mention Lady Carlotta but do not speciy

how others view her

QUESTION 5

Choice C is the best answer Te narrator notes that Lady Carlotta decided

not to interere when one o her ldquomost eloquent exponentsrdquo was stuck in a

tree because an angry boar was nearby (lines 14-22) Tis ldquoeloquent expo-

nentrdquo was a woman who ofen criticized Lady Carlotta or interering inother peoplersquos affairs Lady Carlottarsquos decision to ldquoput the doctrine o non-

intererence into practicerdquo (to not help her emale acquaintance who was

ldquobesiegedrdquo in a tree) suggests that Lady Carlotta has a sense o humor

Choices A B and D are incorrect because the description o how she ldquoput

the doctrine o non-intererence into practicerdquo does not suggest that Lady

Carlotta is deceptive or cruel or explain a surprising change in her behavior

QUESTION 6

Choice A is the best answer Te narrator explains that Mrs Quabarl toldLady Carlotta about the ldquonature o the chargerdquo when she gave Lady Carlotta

details about the Quabarl children (line 53-61) Since Lady Carlotta is pre-

tending to be a governess the term ldquochargerdquo reers to her responsibilities or

job duties when caring or the Quabarl children

Choices B C and D are incorrect because in this context ldquochargerdquo does not

mean attack ee or expense

QUESTION 7

Choice A is the best answer Lady Carlotta learns about Mrs Quabarlrsquos chil-dren Claude Wilrid and Irene (lines 53-58) Te narrator then describes

Mrs Quabarlrsquos child Viola as ldquosomething or other else o a mould equally

commonplace among children o that class and type in the twentieth cen-

turyrdquo (lines 58-61) Tis statement about Viola implies that all o the Quabarl

children have skills typical or ldquoo a mould equally commonplacerdquo to other

peers in their social class

Choices B C and D are incorrect because the narrator does not indicate that

all o the Quabarl children are unusually creative and intelligent hostile to

the idea o having a governess or more educated than their peers

7262019 PrepScholar Sat Practice Test 3 Answers

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3

QUESTION 8

Choice B is the best answer In lines 62-69 Mrs Quabarl explains to Lady

Carlotta that she wants her children to actively participate in their education

and that Lady Carlotta should not create lessons that require her children to

simply memorize historical figures and dates Mrs Quabarl emphasizes an

education centered on active engagement when she states that her childrenshould ldquonot only be AUGH but INERESED in what they learnrdquo

Choices A C and D are incorrect because the narrator does not suggest that

Mrs Quabarl avors an education that emphasizes traditional values artistic

experimentation or actual retention

QUESTION 9

Choice B is the best answer In lines 77-82 the narrator describes Mrs

Quabarl as appearing ldquomagnificent and autocraticrdquo or outwardly domineer-

ing but easily ldquocowed and apologeticrdquo when someone challenges or defiesher authority

Choices A C and D are incorrect because the narrator does not describe

Mrs Quabarl as selfish bitter or requently imprudent

QUESTION 10

Choice D is the best answer In lines 77-82 the narrator provides evidence

that Mrs Quabarl appears imposing or autocratic but is easily defied or

opposed ldquoShe was one o those imperectly sel-assured individuals who are

magnificent and autocratic as long as they are not seriously opposed Teleast show o unexpected resistance goes a long way towards rendering them

cowed and apologeticrdquo

Choices A B and C do not provide the best evidence that Mrs Quabarl

appears imposing but is easily defied Choices A and B are incorrect because

they present Mrs Quabarlrsquos opinions on railway companies and educa-

tion and choice C is incorrect because it ocuses on Lady Carlotta not

Mrs Quabarl

QUESTION 11

Choice A is the best answer While the author predominantly supports

the use o public transportation in the third paragraph he recognizes

some limitations to the public transportation system it is a ldquodepressing

experiencerdquo (lines 25-26) and ldquounderunded ill-maintained and

ill-plannedrdquo (line 31)

Choices B C and D are incorrect because the third paragraph does not

expand upon an argument made in the first two paragraphs provide an

overview o a problem or advocate ending the use o public transportation

7262019 PrepScholar Sat Practice Test 3 Answers

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4

QUESTION 12

Choice C is the best answer Te author notes that in North America ldquohopping

in a car almost always gets you to your destination more quicklyrdquo (lines 32-34)

Tis statement suggests that speed is one advantage to driving in North America

Choices A B and D are incorrect because the author does not cite environmen-

tal impact convenience or cost as advantages o driving in North America

QUESTION 13

Choice D is the best answer In lines 32-34 the author provides evidence

that speed is one advantage to driving in North America because driving

ldquoalmost always gets you to your destination more quicklyrdquo

Choices A B and C do not provide the best evidence that speed is one

advantage to driving in North America Choices A and B are incorrect

because they offer general inormation about using public transportationChoice C is incorrect because although these lines mention North America

they ocus on the disadvantages o public transportation

QUESTION 14

Choice B is the best answer Te author argues in the ourth paragraph that

public transportation ldquocan be aster more comortable and cheaper than the

private automobilerdquo (lines 36-37) and provides examples o ast and conve-

nient public transportation systems

Choices A C and D are incorrect because they ocus on points made in theourth paragraph rather than the paragraphrsquos central idea

QUESTION 15

Choice B is the best answer In lines 35-37 the author provides evidence

that some public transportation systems are superior to driving because

public transportation ldquocan be aster more comortable and cheaper than the

private automobilerdquo

Choices A C and D do not provide the best evidence that some public

transportation systems are superior to driving as they highlight points madein the ourth paragraph rather than the paragraphrsquos central idea

QUESTION 16

Choice C is the best answer In the last paragraph the author explains the

trend that people who became adults around the end o the twentieth cen-

tury are more willing to use public transportation than people rom older

generations Te author notes ldquoI you credit the demographers this transit

trend has legsrdquo (lines 58-59) In this context ldquocreditrdquo means to believe the

demographersrsquo claims about the trend

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 640

5

Choices A B and D are incorrect because in this context ldquocreditrdquo does not

mean endow attribute or honor

QUESTION 17

Choice B is the best answer In lines 59-63 the author explains the trend

o people who became adults around the end o the twentieth centuryldquotend[ing] to avor cities over suburbsrdquo In this context these adults ldquoavorrdquo

or preer cities over suburbs

Choices A C and D are incorrect because in this context ldquoavorrdquo does not

mean indulge resemble or serve

QUESTION 18

Choice B is the best answer In lines 63-67 the author explains that while

riding on public transportation people can use personal electronic devices

such as ldquoiPads MP3 players Kindles and smartphonesrdquo

Choices A C and D are incorrect because they do not show that public

transportation is compatible with the use o personal electronic devices

QUESTION 19

Choice A is the best answer Figure 1 shows that 107 o public transpor-

tation passengers are students and 67 o public transportation passengers

are retirees Tus more students than retirees use public transportation

Choices B and C are incorrect because figure 1 shows that more employedthan unemployed people use public transportation and that more employed

people than homemakers use public transportation Choice D is incorrect

because figure 1 does not explain how requently passengers use public

transportation it only identifies public transportation passengers by their

primary occupation

QUESTION 20

Choice A is the best answer Figure 1 shows that 72 o public transporta-

tion passengers are ldquoemployed outside the homerdquo and figure 2 indicates that

591 o public transportation trips are or ldquoworkrdquo It can be inerred romthese figures that many public transportation passengers take public trans-

portation to their place o employment

Choices B C and D are incorrect because figure 1 and figure 2 do not

indicate that public transportation passengers primarily use the system to

run errands use their own car on weekends or are planning to purchase

a car

7262019 PrepScholar Sat Practice Test 3 Answers

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6

QUESTION 21

Choice D is the best answer Te author explains that Ken Dial created an

experiment to study the evolution o flight by observing how baby Chukars

learn to fly During the experiment Dial noticed the unusual way Chukars

use their ldquolsquowings and legs cooperativelyrsquordquo to scale hay bales (lines 38-43) and

he created ldquoa series o ingenious experimentsrdquo (line 46) to study this obser- vation Afer his additional experiments Dial determined that these baby

birds angle ldquotheir wings differently rom birds in flightrdquo (lines 49-50)

Choices A B and C are incorrect because they do not accurately reflect the

sequence o events in the passage

QUESTION 22

Choice A is the best answer In lines 6-9 the author explains that Dial was

ldquochallengedrdquo or dared by graduate students to develop ldquonew datardquo on a long-

standing scientific debate (the ldquoground-up-tree-downrdquo theory)

Choices B C and D are incorrect because in this context ldquochallengedrdquo does

not mean required disputed with or competed with

QUESTION 23

Choice A is the best answer Te author explains that Dial created his initial

experiment to try and create ldquonew data on the age-old ground-up-tree-down

debaterdquo and that he looked or ldquocluesrdquo in ldquohow baby game birds learned to

flyrdquo (lines 8-11) Te note at the beginning o the passage explains the ldquoage-

old ground-up-tree down debaterdquo and offers two different theories on howbirds evolved to fly Finally the last paragraph o the passage discusses WAIR

in an evolutionary context

Choices B C and D are incorrect because they do not identiy Dialrsquos central

assumption in setting up his research

QUESTION 24

Choice B is the best answer In lines 6-11 the author provides evidence that

Dialrsquos central assumption in setting up his research is that the acquisition o

flight in young birds is linked to the acquisition o flight in their ancestorsTe author notes that Dial created a project to ldquocome up with new data on

the age-old ground-up-tree-down debaterdquo

Choices A C and D do not provide the best evidence that Dialrsquos central

assumption in setting up his research is that the acquisition o flight in young

birds is linked to the acquisition o flight in their ancestors Choices A C

and D are incorrect because they ocus on Dialrsquos experiment and his obser-

vations on ground birds

7262019 PrepScholar Sat Practice Test 3 Answers

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7

QUESTION 25

Choice C is the best answer When a rancher observed Dialrsquos laboratory

setup he was ldquoincredulousrdquo that the Chukars were living on the ground and

he advised Dial to give the birds ldquosomething to climb onrdquo (lines 16-23) Tis

ldquokey piece o advicerdquo (line 14) led Dial to add hay bales to his laboratory

Dial later noticed that the Chukars were using their legs and wings to scalethe hay bales and this observation became the ocal point o his research

Choices A B and D are incorrect because the incident with the local rancher

did not serve to reveal Dialrsquos motivation or creating the project emphasize

differences in laboratory and field research or introduce a contributor to a

scientific theory

QUESTION 26

Choice C is the best answer Te author explains that Dialrsquos ldquoaha momentrdquo

came when he determined the Chukars used ldquotheir legs and wings coop-erativelyrdquo to scale the hay bales (lines 40-42) Dial then created additional

experiments to study how the birds dealt with gradually steeper inclines

ldquo[he filmed] the birds as they raced up textured ramps tilted at increasing

anglesrdquo (lines 46-48)

Choices A B and D are incorrect because Dialrsquos ldquoaha momentrdquo was not ol-

lowed by Dial teaching the birds to fly studying videos to find out why the

birds no longer hopped or consulting with other researchers

QUESTION 27

Choice B is the best answer Dial observed that as the Chukars raced up

steep ramps they ldquobegan to flaprdquo and ldquoaimed their flapping down and back-

ward using the orce to keep their eet firmly pressed against the ramprdquo

(lines 49-53) Dial determined that the position o their flapping wings acil-

itated the baby Chukarsrsquo traction on the steep ramps

Choices A C and D are incorrect because the passage does not indicate that

the Chukarsrsquo speed alternation o wing and oot movement or continual

hopping motions acilitated their traction on steep ramps

QUESTION 28

Choice B is the best answer In lines 61-63 the author explains that Dial

named his scientific finding ldquoWAIR or wing-assisted incline running and

went on to document it in a wide range o speciesrdquo In this context Dial

ldquodocumentedrdquo or recorded the existence o WAIR in numerous bird species

Choices A C and D are incorrect because in this context ldquodocumentrdquo does

not mean to portray publish or process

7262019 PrepScholar Sat Practice Test 3 Answers

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8

QUESTION 29

Choice D is the best answer In lines 70-74 the author explains that glid-

ing animals do not use a ldquoflapping flight strokerdquo or WAIR wing-assisted

incline running Since Chukars a ground bird use WAIR to help scale steep

inclines it can be reasonably inerred that gliding animals do not use WAIR

to aid in climbing slopes

Choices A B and C are incorrect because the passage does not include

inormation on gliding animalsrsquo offspring their method o locomotion or

their eeding habits

QUESTION 30

Choice D is the best answer In lines 73-75 the author provides evidence

that ldquothe flapping flight strokerdquo is ldquosomething gliding animals donrsquot dordquo

Choices A B and C do not provide the best evidence that gliding animalsdo not use a flapping stroke to aid in climbing slopes Tese choices do not

contain inormation about gliding animals

QUESTION 31

Choice B is the best answer In lines 21-24 the authors o Passage 1 state

societyrsquos ldquocommon happinessrdquo is dependent on women never becoming

involved in politics In this context the authors o Passage 1 are sug-

gesting that all members o society can have a ldquocommonrdquo or shared

happiness

Choices A C and D are incorrect because in this context ldquocommonrdquo does

not mean average coarse or similar

QUESTION 32

Choice C is the best answer In lines 25-30 the authors o Passage 1 state

that women should seek ldquogentle occupations and the cares o the homerdquo

so they can avoid perorming difficult or ldquostrenuousrdquo and unpleasant or

ldquoonerousrdquo tasks

Choices A B and D are incorrect because the authors o Passage 1 do notsuggest that running a household and raising children are rewarding or

both sexes yield less value or society or require proessional or political

skills

QUESTION 33

Choice C is the best answer In lines 25-30 the authors o Passage 1 provide

evidence that women should run households and raise children because

these roles do not require ldquostrenuous habits and onerous dutiesrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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9

Choices A B and D do not provide the best evidence that running a house-

hold and raising children entail very ew activities that are difficult or

unpleasant rather these lines offer general inormation about the differ-

ences between the sexes

QUESTION 34

Choice D is the best answer In lines 41-46 Wollstonecraf argues that i

women do not receive an education ldquoto become the companion o manrdquo or

one that is comparable to menrsquos education then society will not progress in

ldquoknowledge and virtuerdquo

Choices A B and C are incorrect because Wollstonecraf does not suggest

that society can progress only i women have happiness and financial secu-

rity ollow societal rules or replace men as figures o power

QUESTION 35

Choice C is the best answer Wollstonecraf argues that women should be

granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo

(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-

enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context

Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or

intellect and allow women to consider their role in society

Choices A B and D are incorrect because in this context ldquoreasonrdquo does not

mean motive sanity or explanation

QUESTION 36

Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws

passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to

ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf

is arguing that societyrsquos leaders grant men reedoms that are denied to women

Choices B C and D are incorrect because Wollstonecraf does not claim

that societyrsquos leaders have granted reedoms that created a general reduction

in individual virtue caused arguments about happiness or ensured equality

or all people

QUESTION 37

Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-

dence that societyrsquos leaders grant reedoms that privilege men She argues

that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-

lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to

ldquocontend or their reedomrdquo

Choices A B and C do not provide the best evidence that societyrsquos leaders

grant reedoms that privilege men over women

7262019 PrepScholar Sat Practice Test 3 Answers

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10

QUESTION 38

Choice C is the best answer Wollstonecraf cites the statement made by

the authors o Passage 1 that excluding women rom political participation

is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)

Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe

abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument

by highlighting a flaw in the reasoning presented by the authors o Passage 1

Choices A B and D are incorrect because Wollstonecraf does not reer to

the statement made in Passage 1 to call into question the authorsrsquo qualifica-

tions dispute the assertion that women are excluded by their own govern-

ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on

gender roles

QUESTION 39

Choice A is the best answer Te authors o Passage 1 argue that while

restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)

this restriction is necessary or societyrsquos overall happiness (lines 13-17)

Wollstonecraf however strongly challenges this argument asking the

authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-

doms are granted to women and likening societyrsquos male leaders to tyrants as

they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in

the darkrdquo (lines 78-88)

Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2

QUESTION 40

Choice D is the best answer Te authors o Passage 1 admit that women are

ldquoexcluded by the other hal [men] rom any participation in governmentrdquo

(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws

that deny women ldquocivil and political rightsrdquo (line 86)

Choices A B and C are incorrect because the authors o both passages

would not agree that women had the same preerences as men required agood education or were as happy as men

QUESTION 41

Choice A is the best answer Wollstonecraf argues in the final paragraph

o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women

ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would

most likely argue that allowing women these rights would be ldquoa reversal o

[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos

interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as

7262019 PrepScholar Sat Practice Test 3 Answers

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11

mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created

two sexes or a particular reason so while men can exercise civil and politi-

cal rights women are not naturally suited to these activities (lines 30-36)

Choices B and C are incorrect because they are not supported by inorma-

tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do

not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo

QUESTION 42

Choice C is the best answer When discussing problems with bee colo-

nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo

(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-

tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a

tentative tone and provides urther evidence that the authors believe but are

not certain that their hypothesis is correct

Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone

QUESTION 43

Choice C is the best answer In lines 24-28 the authors hypothesize that bee

colonies will be susceptible to mite inestations i they do not occasionally

eed on pyrethrum producing plants In lines 42-46 they suggest creating a

trial where a ldquosmall number o commercial honey bee colonies are offered a

number o pyrethrum producing plantsrdquo to test their hypothesis

Choices A B and D are incorrect because the authors do not hypothesize that

honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees

to develop secondary inections that beekeepers should increase their use o

insecticides or that humans are more susceptible to varroa mites

QUESTION 44

Choice D is the best answer In lines 24-28 the authors provide evidence

that a bee colony may be more resistant to mite inections i the bees eat

pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-

nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees

Choices A B and C do not describe any o the authorsrsquo hypotheses

QUESTION 45

Choice D is the best answer Te authors explain that when beekeepers

use commercially produced insecticides to fight mite inections they may

ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-

cientrdquo (lines 31-35)

7262019 PrepScholar Sat Practice Test 3 Answers

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12

Choices A B and C are incorrect because the authors do not suggest that

beekeepersrsquo use o commercially produced insecticides increases mite popu-

lations kills bacteria or destroys beesrsquo primary ood source

QUESTION 46

Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-

ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo

Choices A B and D are incorrect because they do not provide the best evi-

dence that beekeepersrsquo use o commercially produced insecticides may be

harmul to bees choices A B and D ocus on mite inestationsrsquo impact on

honeybees

QUESTION 47

Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some

bees Te authors then state ldquoWe urther postulate that the proper dosage

necessary to prevent mite inestation may be better lef to the beesrdquo (lines

35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the

bees may naturally control mite inestations better than insecticides

Choices A C and D are incorrect because in this context ldquopostulaterdquo does

not mean to make an unounded assumption question a belie or theory or

conclude based on firm evidence

QUESTION 48

Choice B is the best answer In the ourth paragraph the authors propose

a trial to study i honeybeesrsquo consumption o pyrethrum producing plants

helps the honeybees deend against mite inestations In the experiment the

authors plan to offer honey bee colonies both pyrethrum producing plants

and ldquoa typical bee ood source such as cloverrdquo to determine i these different

diets affect the beesrsquo susceptibility to mite inestations

Choices A C and D are incorrect because the main purpose o the ourth

paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished

experiment

QUESTION 49

Choice A is the best answer In lines 43-45 the authors propose a scien-

tific trial in which honeybees are ldquooffered a number o pyrethrum producing

plants as well as a typical bee ood source such as cloverrdquo Since the authors

contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood

sourcerdquo it can be assumed that clover does not produce pyrethrums

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1440

13

Choice B is incorrect because it is stated in the passage Choices C and D are

incorrect because they are not assumptions made by the authors

QUESTION 50

Choice B is the best answer Te table shows that 77 percent o the honeybee

colonies with colony collapse disorder were inected by all our pathogens

Choices A C and D are incorrect because they do not identiy the percent

o honeybee colonies with colony collapse disorder that were inected by all

our pathogens as based on data in the table

QUESTION 51

Choice D is the best answer Te table shows that 81 percent o colo-

nies without colony collapse disorder were affected by the pathogen

Nosema ceranae

Choices A B and C are incorrect because they do not identiy the pathogen

that inected the highest percentage o honeybee colonies without colony

collapse disorder as based on data in the table

QUESTION 52

Choice D is the best answer Te table discusses pathogen occurrence in

honeybee colonies but it includes no inormation as to whether these hon-

eybees were inected with mites Because the table does not suggest mites

inested the honeybee colonies no conclusions can be made as to whether

mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)

Choices A B and C are incorrect because the table provides no inormation

about whether these honeybees were inected with mites

Section 2 Writing and Language Test

QUESTION 1

Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-

ates a parallel structure within the list that begins with ldquohappierrdquo

Choices B C and D are incorrect because none creates a parallel structure

within the list o qualities

QUESTION 2

Choice B is the best answer Te ways in which exposure to natural light

affects employees is the main subject o the passage

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1540

14

Choices A C and D are incorrect because none introduces the topic dis-

cussed in the remainder o the passage

QUESTION 3

Choice C is the best answer It accurately notes that the proposed sentence

would be placed directly between the first mention o circadian rhythms andthe explanation o the term

Choices A B and D are incorrect because each misinterprets the relation-

ship between the proposed additional text and the ideas in the paragraph

QUESTION 4

Choice C is the best answer It provides the correct possessive construction

or ldquobodyrdquo which must be a singular noun when discussed in general terms

as in this sentence Choice C also provides the correct plural construction

or ldquoclocksrdquo

Choices A B and D are incorrect because each applies either a possessive or

a plural construction in a place where it doesnrsquot belong

QUESTION 5

Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular

noun ldquoabsenteeismrdquo

Choices B C and D are incorrect because each provides a verb that

either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy

QUESTION 6

Choice B is the best answer It contains a direct reerence to productivity

the topic introduced in the previous sentence

Choices A C and D are incorrect because none directly addresses employee

productivity the primary subject o the previous sentence

QUESTION 7

Choice A is the best answer It opens with a reerence to lowered worker

productivity creating a transition rom the previous paragraph and clearly

positions the high energy costs o artificial light sources as an additional

disadvantage

Choices B C and D are incorrect because none o the choices offer an ade-

quate transition rom the previous paragraph Each awkwardly inserts the

issue o lower worker productivity into a statement about the high energy

costs o artificial light sources

7262019 PrepScholar Sat Practice Test 3 Answers

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15

QUESTION 8

Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-

cate that the savings occurred every year

Choices A B and C are incorrect because each proposes an option that

would result in a redundancy with ldquoannualrdquo

QUESTION 9

Choice C is the best answer It provides a transitional adverb that accurately

communicates that this sentence describes an option that companies could

choose (ldquolight tubesrdquo) instead o the option described in the previous sen-

tence (ldquoull-pane windowsrdquo)

Choices A B and D are incorrect because each proposes a transitional

adverb that does not accurately reflect the relationship between this sen-

tence and the one preceding it

QUESTION 10

Choice C is the best answer It provides the correct relative pronoun to cor-

respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-

duce the definition that ollows

Choices A B and D are incorrect because each offers a pronoun inappropri-

ate or opening a dependent clause defining ldquolight tubesrdquo

QUESTION 11

Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the

noun ldquomeansrdquo particularly as a way to connect it to another noun or verb

Choices A C and D are incorrect because each results in nonstandard

phrasing with ldquomeansrdquo

QUESTION 12

Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-

responds with the plural noun ldquosettlersrdquo

Choices B C and D are incorrect because each provides either a nonstan-

dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo

QUESTION 13

Choice C is the best answer It creates a transition rom the poor ood qual-

ity mentioned in the previous sentence to the inormation about Harvey in

the remainder o the sentence

7262019 PrepScholar Sat Practice Test 3 Answers

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16

Choices A B and D are incorrect because none offers a transition rom the

previous sentence or a detail that corresponds precisely with the inorma-

tion in the remainder o the sentence

QUESTION 14

Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens

with a comma

Choices A B and C are incorrect because each proposes punctuation that

creates an inappropriately strong separation between the subject ldquoFred

Harveyrdquo and the verb ldquodecidedrdquo

QUESTION 15

Choice B is the best answer It provides the plural verb and plural posses-

sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo

Choices A C and D are incorrect because each either ails to provide a verb

that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide

the appropriate possessive pronoun

QUESTION 16

Choice C is the best answer It accurately echoes an earlier characterization

o the ood as being o ldquoterrible qualityrdquo while maintaining the established

tone o the passage

Choices A B and D are incorrect either because the word is less ormal than

the established tone o the passage (ldquoickyrdquo) or because it illogically attributes

agency to ood (ldquosinisterrdquo ldquosurlyrdquo)

QUESTION 17

Choice C is the best answer It accurately interprets ldquonot content to ollow

conventional business practicesrdquo as logically introducing the new practice o

ldquoemploying womenrdquo described in the ollowing sentences

Choices A B and D are incorrect because none recognizes why the sentence

is relevant to this particular location in the passage

QUESTION 18

Choice B is the best answer It is concise and ree o redundancies

Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and

ldquotremendousrdquo adjectives so close in meaning that together they present a

redundancy

7262019 PrepScholar Sat Practice Test 3 Answers

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17

QUESTION 19

Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary

reerence to ldquosuch regulationsrdquo in the previous clause

Choices A B and C are incorrect because each lacks a necessary subject

such as a pronoun or noun

QUESTION 20

Choice C is the best answer It reers directly to benefits or the restaurantsrsquo

emale employees the subject o the previous sentence

Choices A B and D are incorrect because none logically builds upon the

sentence that precedes it

QUESTION 21

Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo

Choices A B and C are incorrect because each uses the punctuation or

a dependent clause (ldquoLiving independently and demonstrating an intense

work ethicrdquo) as i it were an independent clause

QUESTION 22

Choice A is the best answer It recognizes that the new inormation sup-

ports the previous sentencersquos claim that ldquothe Harvey Girls became known as

a transormative orcerdquo

Choices B C and D are incorrect because each misinterprets the relation-

ship between the proposed text and the passage

QUESTION 23

Choice A is the best answer It opens with a clause that identifies how

1-MCP affects apples which ocuses the sentence on 1-MCP as the subject

and allows the ideas in the sentence to progress logically

Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy

QUESTION 24

Choice D is the best answer Only the comma is necessary to separate

ldquoethylenerdquo rom the appositive noun phrase that defines it

Choices A B and C are incorrect because each creates a comma splice and

or adds unnecessary words

7262019 PrepScholar Sat Practice Test 3 Answers

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18

QUESTION 25

Choice B is the best answer It offers an adjective that accurately describes

resh apples

Choices A C and D are incorrect because each proposes an adjective that

does not describe a plausible ruit texture

QUESTION 26

Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-

sponds with the plural reerent ldquoapplesrdquo

Choices B C and D are incorrect because none provides a pronoun that is

both possessive and plural

QUESTION 27

Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins

the relative clause

Choices A B and C are incorrect because each contains a pronoun that

either does not correspond with the human reerent ldquoconsumersrdquo or does

not correctly begin the relative clause

QUESTION 28

Choice B is the best answer It provides the present tense verb ldquodordquo which

corresponds to the present tense established earlier in the sentence

Choices A C and D are incorrect because each contains a verb that deviates

rom the simple present tense established in the sentence

QUESTION 29

Choice B is the best answer It provides a colon to appropriately introduce the

clause that ollows an elaboration on the preceding claim that Bartlett pears

are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo

Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically

QUESTION 30

Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-

trast with a previous idea and goes on to mention that 1-MCP can have

negative effects Sentence 1 continues the discussion o benefits o 1-MCP

and sentence 2 names the adverse effect o limiting scent production so the

most logical spot or sentence 4 is between these sentences

7262019 PrepScholar Sat Practice Test 3 Answers

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19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

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22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540

24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

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25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740

26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

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27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3940

38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040

QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 3: PrepScholar Sat Practice Test 3 Answers

7262019 PrepScholar Sat Practice Test 3 Answers

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2

QUESTION 4

Choice A is the best answer In lines 10-14 the narrator states that people

ofen criticized Lady Carlotta and suggested that she not interere in other

peoplersquos affairs which were ldquonone o her businessrdquo Te act that people

ofen were critical o Lady Carlottarsquos behavior provides evidence that Lady

Carlotta was outspoken

Choices B C and D do not provide the best evidence that Lady Carlotta was

outspoken Choices B C and D mention Lady Carlotta but do not speciy

how others view her

QUESTION 5

Choice C is the best answer Te narrator notes that Lady Carlotta decided

not to interere when one o her ldquomost eloquent exponentsrdquo was stuck in a

tree because an angry boar was nearby (lines 14-22) Tis ldquoeloquent expo-

nentrdquo was a woman who ofen criticized Lady Carlotta or interering inother peoplersquos affairs Lady Carlottarsquos decision to ldquoput the doctrine o non-

intererence into practicerdquo (to not help her emale acquaintance who was

ldquobesiegedrdquo in a tree) suggests that Lady Carlotta has a sense o humor

Choices A B and D are incorrect because the description o how she ldquoput

the doctrine o non-intererence into practicerdquo does not suggest that Lady

Carlotta is deceptive or cruel or explain a surprising change in her behavior

QUESTION 6

Choice A is the best answer Te narrator explains that Mrs Quabarl toldLady Carlotta about the ldquonature o the chargerdquo when she gave Lady Carlotta

details about the Quabarl children (line 53-61) Since Lady Carlotta is pre-

tending to be a governess the term ldquochargerdquo reers to her responsibilities or

job duties when caring or the Quabarl children

Choices B C and D are incorrect because in this context ldquochargerdquo does not

mean attack ee or expense

QUESTION 7

Choice A is the best answer Lady Carlotta learns about Mrs Quabarlrsquos chil-dren Claude Wilrid and Irene (lines 53-58) Te narrator then describes

Mrs Quabarlrsquos child Viola as ldquosomething or other else o a mould equally

commonplace among children o that class and type in the twentieth cen-

turyrdquo (lines 58-61) Tis statement about Viola implies that all o the Quabarl

children have skills typical or ldquoo a mould equally commonplacerdquo to other

peers in their social class

Choices B C and D are incorrect because the narrator does not indicate that

all o the Quabarl children are unusually creative and intelligent hostile to

the idea o having a governess or more educated than their peers

7262019 PrepScholar Sat Practice Test 3 Answers

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3

QUESTION 8

Choice B is the best answer In lines 62-69 Mrs Quabarl explains to Lady

Carlotta that she wants her children to actively participate in their education

and that Lady Carlotta should not create lessons that require her children to

simply memorize historical figures and dates Mrs Quabarl emphasizes an

education centered on active engagement when she states that her childrenshould ldquonot only be AUGH but INERESED in what they learnrdquo

Choices A C and D are incorrect because the narrator does not suggest that

Mrs Quabarl avors an education that emphasizes traditional values artistic

experimentation or actual retention

QUESTION 9

Choice B is the best answer In lines 77-82 the narrator describes Mrs

Quabarl as appearing ldquomagnificent and autocraticrdquo or outwardly domineer-

ing but easily ldquocowed and apologeticrdquo when someone challenges or defiesher authority

Choices A C and D are incorrect because the narrator does not describe

Mrs Quabarl as selfish bitter or requently imprudent

QUESTION 10

Choice D is the best answer In lines 77-82 the narrator provides evidence

that Mrs Quabarl appears imposing or autocratic but is easily defied or

opposed ldquoShe was one o those imperectly sel-assured individuals who are

magnificent and autocratic as long as they are not seriously opposed Teleast show o unexpected resistance goes a long way towards rendering them

cowed and apologeticrdquo

Choices A B and C do not provide the best evidence that Mrs Quabarl

appears imposing but is easily defied Choices A and B are incorrect because

they present Mrs Quabarlrsquos opinions on railway companies and educa-

tion and choice C is incorrect because it ocuses on Lady Carlotta not

Mrs Quabarl

QUESTION 11

Choice A is the best answer While the author predominantly supports

the use o public transportation in the third paragraph he recognizes

some limitations to the public transportation system it is a ldquodepressing

experiencerdquo (lines 25-26) and ldquounderunded ill-maintained and

ill-plannedrdquo (line 31)

Choices B C and D are incorrect because the third paragraph does not

expand upon an argument made in the first two paragraphs provide an

overview o a problem or advocate ending the use o public transportation

7262019 PrepScholar Sat Practice Test 3 Answers

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4

QUESTION 12

Choice C is the best answer Te author notes that in North America ldquohopping

in a car almost always gets you to your destination more quicklyrdquo (lines 32-34)

Tis statement suggests that speed is one advantage to driving in North America

Choices A B and D are incorrect because the author does not cite environmen-

tal impact convenience or cost as advantages o driving in North America

QUESTION 13

Choice D is the best answer In lines 32-34 the author provides evidence

that speed is one advantage to driving in North America because driving

ldquoalmost always gets you to your destination more quicklyrdquo

Choices A B and C do not provide the best evidence that speed is one

advantage to driving in North America Choices A and B are incorrect

because they offer general inormation about using public transportationChoice C is incorrect because although these lines mention North America

they ocus on the disadvantages o public transportation

QUESTION 14

Choice B is the best answer Te author argues in the ourth paragraph that

public transportation ldquocan be aster more comortable and cheaper than the

private automobilerdquo (lines 36-37) and provides examples o ast and conve-

nient public transportation systems

Choices A C and D are incorrect because they ocus on points made in theourth paragraph rather than the paragraphrsquos central idea

QUESTION 15

Choice B is the best answer In lines 35-37 the author provides evidence

that some public transportation systems are superior to driving because

public transportation ldquocan be aster more comortable and cheaper than the

private automobilerdquo

Choices A C and D do not provide the best evidence that some public

transportation systems are superior to driving as they highlight points madein the ourth paragraph rather than the paragraphrsquos central idea

QUESTION 16

Choice C is the best answer In the last paragraph the author explains the

trend that people who became adults around the end o the twentieth cen-

tury are more willing to use public transportation than people rom older

generations Te author notes ldquoI you credit the demographers this transit

trend has legsrdquo (lines 58-59) In this context ldquocreditrdquo means to believe the

demographersrsquo claims about the trend

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 640

5

Choices A B and D are incorrect because in this context ldquocreditrdquo does not

mean endow attribute or honor

QUESTION 17

Choice B is the best answer In lines 59-63 the author explains the trend

o people who became adults around the end o the twentieth centuryldquotend[ing] to avor cities over suburbsrdquo In this context these adults ldquoavorrdquo

or preer cities over suburbs

Choices A C and D are incorrect because in this context ldquoavorrdquo does not

mean indulge resemble or serve

QUESTION 18

Choice B is the best answer In lines 63-67 the author explains that while

riding on public transportation people can use personal electronic devices

such as ldquoiPads MP3 players Kindles and smartphonesrdquo

Choices A C and D are incorrect because they do not show that public

transportation is compatible with the use o personal electronic devices

QUESTION 19

Choice A is the best answer Figure 1 shows that 107 o public transpor-

tation passengers are students and 67 o public transportation passengers

are retirees Tus more students than retirees use public transportation

Choices B and C are incorrect because figure 1 shows that more employedthan unemployed people use public transportation and that more employed

people than homemakers use public transportation Choice D is incorrect

because figure 1 does not explain how requently passengers use public

transportation it only identifies public transportation passengers by their

primary occupation

QUESTION 20

Choice A is the best answer Figure 1 shows that 72 o public transporta-

tion passengers are ldquoemployed outside the homerdquo and figure 2 indicates that

591 o public transportation trips are or ldquoworkrdquo It can be inerred romthese figures that many public transportation passengers take public trans-

portation to their place o employment

Choices B C and D are incorrect because figure 1 and figure 2 do not

indicate that public transportation passengers primarily use the system to

run errands use their own car on weekends or are planning to purchase

a car

7262019 PrepScholar Sat Practice Test 3 Answers

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6

QUESTION 21

Choice D is the best answer Te author explains that Ken Dial created an

experiment to study the evolution o flight by observing how baby Chukars

learn to fly During the experiment Dial noticed the unusual way Chukars

use their ldquolsquowings and legs cooperativelyrsquordquo to scale hay bales (lines 38-43) and

he created ldquoa series o ingenious experimentsrdquo (line 46) to study this obser- vation Afer his additional experiments Dial determined that these baby

birds angle ldquotheir wings differently rom birds in flightrdquo (lines 49-50)

Choices A B and C are incorrect because they do not accurately reflect the

sequence o events in the passage

QUESTION 22

Choice A is the best answer In lines 6-9 the author explains that Dial was

ldquochallengedrdquo or dared by graduate students to develop ldquonew datardquo on a long-

standing scientific debate (the ldquoground-up-tree-downrdquo theory)

Choices B C and D are incorrect because in this context ldquochallengedrdquo does

not mean required disputed with or competed with

QUESTION 23

Choice A is the best answer Te author explains that Dial created his initial

experiment to try and create ldquonew data on the age-old ground-up-tree-down

debaterdquo and that he looked or ldquocluesrdquo in ldquohow baby game birds learned to

flyrdquo (lines 8-11) Te note at the beginning o the passage explains the ldquoage-

old ground-up-tree down debaterdquo and offers two different theories on howbirds evolved to fly Finally the last paragraph o the passage discusses WAIR

in an evolutionary context

Choices B C and D are incorrect because they do not identiy Dialrsquos central

assumption in setting up his research

QUESTION 24

Choice B is the best answer In lines 6-11 the author provides evidence that

Dialrsquos central assumption in setting up his research is that the acquisition o

flight in young birds is linked to the acquisition o flight in their ancestorsTe author notes that Dial created a project to ldquocome up with new data on

the age-old ground-up-tree-down debaterdquo

Choices A C and D do not provide the best evidence that Dialrsquos central

assumption in setting up his research is that the acquisition o flight in young

birds is linked to the acquisition o flight in their ancestors Choices A C

and D are incorrect because they ocus on Dialrsquos experiment and his obser-

vations on ground birds

7262019 PrepScholar Sat Practice Test 3 Answers

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7

QUESTION 25

Choice C is the best answer When a rancher observed Dialrsquos laboratory

setup he was ldquoincredulousrdquo that the Chukars were living on the ground and

he advised Dial to give the birds ldquosomething to climb onrdquo (lines 16-23) Tis

ldquokey piece o advicerdquo (line 14) led Dial to add hay bales to his laboratory

Dial later noticed that the Chukars were using their legs and wings to scalethe hay bales and this observation became the ocal point o his research

Choices A B and D are incorrect because the incident with the local rancher

did not serve to reveal Dialrsquos motivation or creating the project emphasize

differences in laboratory and field research or introduce a contributor to a

scientific theory

QUESTION 26

Choice C is the best answer Te author explains that Dialrsquos ldquoaha momentrdquo

came when he determined the Chukars used ldquotheir legs and wings coop-erativelyrdquo to scale the hay bales (lines 40-42) Dial then created additional

experiments to study how the birds dealt with gradually steeper inclines

ldquo[he filmed] the birds as they raced up textured ramps tilted at increasing

anglesrdquo (lines 46-48)

Choices A B and D are incorrect because Dialrsquos ldquoaha momentrdquo was not ol-

lowed by Dial teaching the birds to fly studying videos to find out why the

birds no longer hopped or consulting with other researchers

QUESTION 27

Choice B is the best answer Dial observed that as the Chukars raced up

steep ramps they ldquobegan to flaprdquo and ldquoaimed their flapping down and back-

ward using the orce to keep their eet firmly pressed against the ramprdquo

(lines 49-53) Dial determined that the position o their flapping wings acil-

itated the baby Chukarsrsquo traction on the steep ramps

Choices A C and D are incorrect because the passage does not indicate that

the Chukarsrsquo speed alternation o wing and oot movement or continual

hopping motions acilitated their traction on steep ramps

QUESTION 28

Choice B is the best answer In lines 61-63 the author explains that Dial

named his scientific finding ldquoWAIR or wing-assisted incline running and

went on to document it in a wide range o speciesrdquo In this context Dial

ldquodocumentedrdquo or recorded the existence o WAIR in numerous bird species

Choices A C and D are incorrect because in this context ldquodocumentrdquo does

not mean to portray publish or process

7262019 PrepScholar Sat Practice Test 3 Answers

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8

QUESTION 29

Choice D is the best answer In lines 70-74 the author explains that glid-

ing animals do not use a ldquoflapping flight strokerdquo or WAIR wing-assisted

incline running Since Chukars a ground bird use WAIR to help scale steep

inclines it can be reasonably inerred that gliding animals do not use WAIR

to aid in climbing slopes

Choices A B and C are incorrect because the passage does not include

inormation on gliding animalsrsquo offspring their method o locomotion or

their eeding habits

QUESTION 30

Choice D is the best answer In lines 73-75 the author provides evidence

that ldquothe flapping flight strokerdquo is ldquosomething gliding animals donrsquot dordquo

Choices A B and C do not provide the best evidence that gliding animalsdo not use a flapping stroke to aid in climbing slopes Tese choices do not

contain inormation about gliding animals

QUESTION 31

Choice B is the best answer In lines 21-24 the authors o Passage 1 state

societyrsquos ldquocommon happinessrdquo is dependent on women never becoming

involved in politics In this context the authors o Passage 1 are sug-

gesting that all members o society can have a ldquocommonrdquo or shared

happiness

Choices A C and D are incorrect because in this context ldquocommonrdquo does

not mean average coarse or similar

QUESTION 32

Choice C is the best answer In lines 25-30 the authors o Passage 1 state

that women should seek ldquogentle occupations and the cares o the homerdquo

so they can avoid perorming difficult or ldquostrenuousrdquo and unpleasant or

ldquoonerousrdquo tasks

Choices A B and D are incorrect because the authors o Passage 1 do notsuggest that running a household and raising children are rewarding or

both sexes yield less value or society or require proessional or political

skills

QUESTION 33

Choice C is the best answer In lines 25-30 the authors o Passage 1 provide

evidence that women should run households and raise children because

these roles do not require ldquostrenuous habits and onerous dutiesrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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9

Choices A B and D do not provide the best evidence that running a house-

hold and raising children entail very ew activities that are difficult or

unpleasant rather these lines offer general inormation about the differ-

ences between the sexes

QUESTION 34

Choice D is the best answer In lines 41-46 Wollstonecraf argues that i

women do not receive an education ldquoto become the companion o manrdquo or

one that is comparable to menrsquos education then society will not progress in

ldquoknowledge and virtuerdquo

Choices A B and C are incorrect because Wollstonecraf does not suggest

that society can progress only i women have happiness and financial secu-

rity ollow societal rules or replace men as figures o power

QUESTION 35

Choice C is the best answer Wollstonecraf argues that women should be

granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo

(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-

enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context

Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or

intellect and allow women to consider their role in society

Choices A B and D are incorrect because in this context ldquoreasonrdquo does not

mean motive sanity or explanation

QUESTION 36

Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws

passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to

ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf

is arguing that societyrsquos leaders grant men reedoms that are denied to women

Choices B C and D are incorrect because Wollstonecraf does not claim

that societyrsquos leaders have granted reedoms that created a general reduction

in individual virtue caused arguments about happiness or ensured equality

or all people

QUESTION 37

Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-

dence that societyrsquos leaders grant reedoms that privilege men She argues

that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-

lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to

ldquocontend or their reedomrdquo

Choices A B and C do not provide the best evidence that societyrsquos leaders

grant reedoms that privilege men over women

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1140

10

QUESTION 38

Choice C is the best answer Wollstonecraf cites the statement made by

the authors o Passage 1 that excluding women rom political participation

is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)

Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe

abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument

by highlighting a flaw in the reasoning presented by the authors o Passage 1

Choices A B and D are incorrect because Wollstonecraf does not reer to

the statement made in Passage 1 to call into question the authorsrsquo qualifica-

tions dispute the assertion that women are excluded by their own govern-

ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on

gender roles

QUESTION 39

Choice A is the best answer Te authors o Passage 1 argue that while

restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)

this restriction is necessary or societyrsquos overall happiness (lines 13-17)

Wollstonecraf however strongly challenges this argument asking the

authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-

doms are granted to women and likening societyrsquos male leaders to tyrants as

they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in

the darkrdquo (lines 78-88)

Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2

QUESTION 40

Choice D is the best answer Te authors o Passage 1 admit that women are

ldquoexcluded by the other hal [men] rom any participation in governmentrdquo

(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws

that deny women ldquocivil and political rightsrdquo (line 86)

Choices A B and C are incorrect because the authors o both passages

would not agree that women had the same preerences as men required agood education or were as happy as men

QUESTION 41

Choice A is the best answer Wollstonecraf argues in the final paragraph

o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women

ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would

most likely argue that allowing women these rights would be ldquoa reversal o

[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos

interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as

7262019 PrepScholar Sat Practice Test 3 Answers

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11

mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created

two sexes or a particular reason so while men can exercise civil and politi-

cal rights women are not naturally suited to these activities (lines 30-36)

Choices B and C are incorrect because they are not supported by inorma-

tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do

not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo

QUESTION 42

Choice C is the best answer When discussing problems with bee colo-

nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo

(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-

tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a

tentative tone and provides urther evidence that the authors believe but are

not certain that their hypothesis is correct

Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone

QUESTION 43

Choice C is the best answer In lines 24-28 the authors hypothesize that bee

colonies will be susceptible to mite inestations i they do not occasionally

eed on pyrethrum producing plants In lines 42-46 they suggest creating a

trial where a ldquosmall number o commercial honey bee colonies are offered a

number o pyrethrum producing plantsrdquo to test their hypothesis

Choices A B and D are incorrect because the authors do not hypothesize that

honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees

to develop secondary inections that beekeepers should increase their use o

insecticides or that humans are more susceptible to varroa mites

QUESTION 44

Choice D is the best answer In lines 24-28 the authors provide evidence

that a bee colony may be more resistant to mite inections i the bees eat

pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-

nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees

Choices A B and C do not describe any o the authorsrsquo hypotheses

QUESTION 45

Choice D is the best answer Te authors explain that when beekeepers

use commercially produced insecticides to fight mite inections they may

ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-

cientrdquo (lines 31-35)

7262019 PrepScholar Sat Practice Test 3 Answers

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12

Choices A B and C are incorrect because the authors do not suggest that

beekeepersrsquo use o commercially produced insecticides increases mite popu-

lations kills bacteria or destroys beesrsquo primary ood source

QUESTION 46

Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-

ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo

Choices A B and D are incorrect because they do not provide the best evi-

dence that beekeepersrsquo use o commercially produced insecticides may be

harmul to bees choices A B and D ocus on mite inestationsrsquo impact on

honeybees

QUESTION 47

Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some

bees Te authors then state ldquoWe urther postulate that the proper dosage

necessary to prevent mite inestation may be better lef to the beesrdquo (lines

35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the

bees may naturally control mite inestations better than insecticides

Choices A C and D are incorrect because in this context ldquopostulaterdquo does

not mean to make an unounded assumption question a belie or theory or

conclude based on firm evidence

QUESTION 48

Choice B is the best answer In the ourth paragraph the authors propose

a trial to study i honeybeesrsquo consumption o pyrethrum producing plants

helps the honeybees deend against mite inestations In the experiment the

authors plan to offer honey bee colonies both pyrethrum producing plants

and ldquoa typical bee ood source such as cloverrdquo to determine i these different

diets affect the beesrsquo susceptibility to mite inestations

Choices A C and D are incorrect because the main purpose o the ourth

paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished

experiment

QUESTION 49

Choice A is the best answer In lines 43-45 the authors propose a scien-

tific trial in which honeybees are ldquooffered a number o pyrethrum producing

plants as well as a typical bee ood source such as cloverrdquo Since the authors

contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood

sourcerdquo it can be assumed that clover does not produce pyrethrums

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1440

13

Choice B is incorrect because it is stated in the passage Choices C and D are

incorrect because they are not assumptions made by the authors

QUESTION 50

Choice B is the best answer Te table shows that 77 percent o the honeybee

colonies with colony collapse disorder were inected by all our pathogens

Choices A C and D are incorrect because they do not identiy the percent

o honeybee colonies with colony collapse disorder that were inected by all

our pathogens as based on data in the table

QUESTION 51

Choice D is the best answer Te table shows that 81 percent o colo-

nies without colony collapse disorder were affected by the pathogen

Nosema ceranae

Choices A B and C are incorrect because they do not identiy the pathogen

that inected the highest percentage o honeybee colonies without colony

collapse disorder as based on data in the table

QUESTION 52

Choice D is the best answer Te table discusses pathogen occurrence in

honeybee colonies but it includes no inormation as to whether these hon-

eybees were inected with mites Because the table does not suggest mites

inested the honeybee colonies no conclusions can be made as to whether

mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)

Choices A B and C are incorrect because the table provides no inormation

about whether these honeybees were inected with mites

Section 2 Writing and Language Test

QUESTION 1

Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-

ates a parallel structure within the list that begins with ldquohappierrdquo

Choices B C and D are incorrect because none creates a parallel structure

within the list o qualities

QUESTION 2

Choice B is the best answer Te ways in which exposure to natural light

affects employees is the main subject o the passage

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1540

14

Choices A C and D are incorrect because none introduces the topic dis-

cussed in the remainder o the passage

QUESTION 3

Choice C is the best answer It accurately notes that the proposed sentence

would be placed directly between the first mention o circadian rhythms andthe explanation o the term

Choices A B and D are incorrect because each misinterprets the relation-

ship between the proposed additional text and the ideas in the paragraph

QUESTION 4

Choice C is the best answer It provides the correct possessive construction

or ldquobodyrdquo which must be a singular noun when discussed in general terms

as in this sentence Choice C also provides the correct plural construction

or ldquoclocksrdquo

Choices A B and D are incorrect because each applies either a possessive or

a plural construction in a place where it doesnrsquot belong

QUESTION 5

Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular

noun ldquoabsenteeismrdquo

Choices B C and D are incorrect because each provides a verb that

either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy

QUESTION 6

Choice B is the best answer It contains a direct reerence to productivity

the topic introduced in the previous sentence

Choices A C and D are incorrect because none directly addresses employee

productivity the primary subject o the previous sentence

QUESTION 7

Choice A is the best answer It opens with a reerence to lowered worker

productivity creating a transition rom the previous paragraph and clearly

positions the high energy costs o artificial light sources as an additional

disadvantage

Choices B C and D are incorrect because none o the choices offer an ade-

quate transition rom the previous paragraph Each awkwardly inserts the

issue o lower worker productivity into a statement about the high energy

costs o artificial light sources

7262019 PrepScholar Sat Practice Test 3 Answers

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15

QUESTION 8

Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-

cate that the savings occurred every year

Choices A B and C are incorrect because each proposes an option that

would result in a redundancy with ldquoannualrdquo

QUESTION 9

Choice C is the best answer It provides a transitional adverb that accurately

communicates that this sentence describes an option that companies could

choose (ldquolight tubesrdquo) instead o the option described in the previous sen-

tence (ldquoull-pane windowsrdquo)

Choices A B and D are incorrect because each proposes a transitional

adverb that does not accurately reflect the relationship between this sen-

tence and the one preceding it

QUESTION 10

Choice C is the best answer It provides the correct relative pronoun to cor-

respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-

duce the definition that ollows

Choices A B and D are incorrect because each offers a pronoun inappropri-

ate or opening a dependent clause defining ldquolight tubesrdquo

QUESTION 11

Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the

noun ldquomeansrdquo particularly as a way to connect it to another noun or verb

Choices A C and D are incorrect because each results in nonstandard

phrasing with ldquomeansrdquo

QUESTION 12

Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-

responds with the plural noun ldquosettlersrdquo

Choices B C and D are incorrect because each provides either a nonstan-

dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo

QUESTION 13

Choice C is the best answer It creates a transition rom the poor ood qual-

ity mentioned in the previous sentence to the inormation about Harvey in

the remainder o the sentence

7262019 PrepScholar Sat Practice Test 3 Answers

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16

Choices A B and D are incorrect because none offers a transition rom the

previous sentence or a detail that corresponds precisely with the inorma-

tion in the remainder o the sentence

QUESTION 14

Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens

with a comma

Choices A B and C are incorrect because each proposes punctuation that

creates an inappropriately strong separation between the subject ldquoFred

Harveyrdquo and the verb ldquodecidedrdquo

QUESTION 15

Choice B is the best answer It provides the plural verb and plural posses-

sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo

Choices A C and D are incorrect because each either ails to provide a verb

that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide

the appropriate possessive pronoun

QUESTION 16

Choice C is the best answer It accurately echoes an earlier characterization

o the ood as being o ldquoterrible qualityrdquo while maintaining the established

tone o the passage

Choices A B and D are incorrect either because the word is less ormal than

the established tone o the passage (ldquoickyrdquo) or because it illogically attributes

agency to ood (ldquosinisterrdquo ldquosurlyrdquo)

QUESTION 17

Choice C is the best answer It accurately interprets ldquonot content to ollow

conventional business practicesrdquo as logically introducing the new practice o

ldquoemploying womenrdquo described in the ollowing sentences

Choices A B and D are incorrect because none recognizes why the sentence

is relevant to this particular location in the passage

QUESTION 18

Choice B is the best answer It is concise and ree o redundancies

Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and

ldquotremendousrdquo adjectives so close in meaning that together they present a

redundancy

7262019 PrepScholar Sat Practice Test 3 Answers

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17

QUESTION 19

Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary

reerence to ldquosuch regulationsrdquo in the previous clause

Choices A B and C are incorrect because each lacks a necessary subject

such as a pronoun or noun

QUESTION 20

Choice C is the best answer It reers directly to benefits or the restaurantsrsquo

emale employees the subject o the previous sentence

Choices A B and D are incorrect because none logically builds upon the

sentence that precedes it

QUESTION 21

Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo

Choices A B and C are incorrect because each uses the punctuation or

a dependent clause (ldquoLiving independently and demonstrating an intense

work ethicrdquo) as i it were an independent clause

QUESTION 22

Choice A is the best answer It recognizes that the new inormation sup-

ports the previous sentencersquos claim that ldquothe Harvey Girls became known as

a transormative orcerdquo

Choices B C and D are incorrect because each misinterprets the relation-

ship between the proposed text and the passage

QUESTION 23

Choice A is the best answer It opens with a clause that identifies how

1-MCP affects apples which ocuses the sentence on 1-MCP as the subject

and allows the ideas in the sentence to progress logically

Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy

QUESTION 24

Choice D is the best answer Only the comma is necessary to separate

ldquoethylenerdquo rom the appositive noun phrase that defines it

Choices A B and C are incorrect because each creates a comma splice and

or adds unnecessary words

7262019 PrepScholar Sat Practice Test 3 Answers

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18

QUESTION 25

Choice B is the best answer It offers an adjective that accurately describes

resh apples

Choices A C and D are incorrect because each proposes an adjective that

does not describe a plausible ruit texture

QUESTION 26

Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-

sponds with the plural reerent ldquoapplesrdquo

Choices B C and D are incorrect because none provides a pronoun that is

both possessive and plural

QUESTION 27

Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins

the relative clause

Choices A B and C are incorrect because each contains a pronoun that

either does not correspond with the human reerent ldquoconsumersrdquo or does

not correctly begin the relative clause

QUESTION 28

Choice B is the best answer It provides the present tense verb ldquodordquo which

corresponds to the present tense established earlier in the sentence

Choices A C and D are incorrect because each contains a verb that deviates

rom the simple present tense established in the sentence

QUESTION 29

Choice B is the best answer It provides a colon to appropriately introduce the

clause that ollows an elaboration on the preceding claim that Bartlett pears

are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo

Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically

QUESTION 30

Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-

trast with a previous idea and goes on to mention that 1-MCP can have

negative effects Sentence 1 continues the discussion o benefits o 1-MCP

and sentence 2 names the adverse effect o limiting scent production so the

most logical spot or sentence 4 is between these sentences

7262019 PrepScholar Sat Practice Test 3 Answers

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19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

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22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540

24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640

25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740

26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

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27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3940

38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040

QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 4: PrepScholar Sat Practice Test 3 Answers

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3

QUESTION 8

Choice B is the best answer In lines 62-69 Mrs Quabarl explains to Lady

Carlotta that she wants her children to actively participate in their education

and that Lady Carlotta should not create lessons that require her children to

simply memorize historical figures and dates Mrs Quabarl emphasizes an

education centered on active engagement when she states that her childrenshould ldquonot only be AUGH but INERESED in what they learnrdquo

Choices A C and D are incorrect because the narrator does not suggest that

Mrs Quabarl avors an education that emphasizes traditional values artistic

experimentation or actual retention

QUESTION 9

Choice B is the best answer In lines 77-82 the narrator describes Mrs

Quabarl as appearing ldquomagnificent and autocraticrdquo or outwardly domineer-

ing but easily ldquocowed and apologeticrdquo when someone challenges or defiesher authority

Choices A C and D are incorrect because the narrator does not describe

Mrs Quabarl as selfish bitter or requently imprudent

QUESTION 10

Choice D is the best answer In lines 77-82 the narrator provides evidence

that Mrs Quabarl appears imposing or autocratic but is easily defied or

opposed ldquoShe was one o those imperectly sel-assured individuals who are

magnificent and autocratic as long as they are not seriously opposed Teleast show o unexpected resistance goes a long way towards rendering them

cowed and apologeticrdquo

Choices A B and C do not provide the best evidence that Mrs Quabarl

appears imposing but is easily defied Choices A and B are incorrect because

they present Mrs Quabarlrsquos opinions on railway companies and educa-

tion and choice C is incorrect because it ocuses on Lady Carlotta not

Mrs Quabarl

QUESTION 11

Choice A is the best answer While the author predominantly supports

the use o public transportation in the third paragraph he recognizes

some limitations to the public transportation system it is a ldquodepressing

experiencerdquo (lines 25-26) and ldquounderunded ill-maintained and

ill-plannedrdquo (line 31)

Choices B C and D are incorrect because the third paragraph does not

expand upon an argument made in the first two paragraphs provide an

overview o a problem or advocate ending the use o public transportation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 540

4

QUESTION 12

Choice C is the best answer Te author notes that in North America ldquohopping

in a car almost always gets you to your destination more quicklyrdquo (lines 32-34)

Tis statement suggests that speed is one advantage to driving in North America

Choices A B and D are incorrect because the author does not cite environmen-

tal impact convenience or cost as advantages o driving in North America

QUESTION 13

Choice D is the best answer In lines 32-34 the author provides evidence

that speed is one advantage to driving in North America because driving

ldquoalmost always gets you to your destination more quicklyrdquo

Choices A B and C do not provide the best evidence that speed is one

advantage to driving in North America Choices A and B are incorrect

because they offer general inormation about using public transportationChoice C is incorrect because although these lines mention North America

they ocus on the disadvantages o public transportation

QUESTION 14

Choice B is the best answer Te author argues in the ourth paragraph that

public transportation ldquocan be aster more comortable and cheaper than the

private automobilerdquo (lines 36-37) and provides examples o ast and conve-

nient public transportation systems

Choices A C and D are incorrect because they ocus on points made in theourth paragraph rather than the paragraphrsquos central idea

QUESTION 15

Choice B is the best answer In lines 35-37 the author provides evidence

that some public transportation systems are superior to driving because

public transportation ldquocan be aster more comortable and cheaper than the

private automobilerdquo

Choices A C and D do not provide the best evidence that some public

transportation systems are superior to driving as they highlight points madein the ourth paragraph rather than the paragraphrsquos central idea

QUESTION 16

Choice C is the best answer In the last paragraph the author explains the

trend that people who became adults around the end o the twentieth cen-

tury are more willing to use public transportation than people rom older

generations Te author notes ldquoI you credit the demographers this transit

trend has legsrdquo (lines 58-59) In this context ldquocreditrdquo means to believe the

demographersrsquo claims about the trend

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 640

5

Choices A B and D are incorrect because in this context ldquocreditrdquo does not

mean endow attribute or honor

QUESTION 17

Choice B is the best answer In lines 59-63 the author explains the trend

o people who became adults around the end o the twentieth centuryldquotend[ing] to avor cities over suburbsrdquo In this context these adults ldquoavorrdquo

or preer cities over suburbs

Choices A C and D are incorrect because in this context ldquoavorrdquo does not

mean indulge resemble or serve

QUESTION 18

Choice B is the best answer In lines 63-67 the author explains that while

riding on public transportation people can use personal electronic devices

such as ldquoiPads MP3 players Kindles and smartphonesrdquo

Choices A C and D are incorrect because they do not show that public

transportation is compatible with the use o personal electronic devices

QUESTION 19

Choice A is the best answer Figure 1 shows that 107 o public transpor-

tation passengers are students and 67 o public transportation passengers

are retirees Tus more students than retirees use public transportation

Choices B and C are incorrect because figure 1 shows that more employedthan unemployed people use public transportation and that more employed

people than homemakers use public transportation Choice D is incorrect

because figure 1 does not explain how requently passengers use public

transportation it only identifies public transportation passengers by their

primary occupation

QUESTION 20

Choice A is the best answer Figure 1 shows that 72 o public transporta-

tion passengers are ldquoemployed outside the homerdquo and figure 2 indicates that

591 o public transportation trips are or ldquoworkrdquo It can be inerred romthese figures that many public transportation passengers take public trans-

portation to their place o employment

Choices B C and D are incorrect because figure 1 and figure 2 do not

indicate that public transportation passengers primarily use the system to

run errands use their own car on weekends or are planning to purchase

a car

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 740

6

QUESTION 21

Choice D is the best answer Te author explains that Ken Dial created an

experiment to study the evolution o flight by observing how baby Chukars

learn to fly During the experiment Dial noticed the unusual way Chukars

use their ldquolsquowings and legs cooperativelyrsquordquo to scale hay bales (lines 38-43) and

he created ldquoa series o ingenious experimentsrdquo (line 46) to study this obser- vation Afer his additional experiments Dial determined that these baby

birds angle ldquotheir wings differently rom birds in flightrdquo (lines 49-50)

Choices A B and C are incorrect because they do not accurately reflect the

sequence o events in the passage

QUESTION 22

Choice A is the best answer In lines 6-9 the author explains that Dial was

ldquochallengedrdquo or dared by graduate students to develop ldquonew datardquo on a long-

standing scientific debate (the ldquoground-up-tree-downrdquo theory)

Choices B C and D are incorrect because in this context ldquochallengedrdquo does

not mean required disputed with or competed with

QUESTION 23

Choice A is the best answer Te author explains that Dial created his initial

experiment to try and create ldquonew data on the age-old ground-up-tree-down

debaterdquo and that he looked or ldquocluesrdquo in ldquohow baby game birds learned to

flyrdquo (lines 8-11) Te note at the beginning o the passage explains the ldquoage-

old ground-up-tree down debaterdquo and offers two different theories on howbirds evolved to fly Finally the last paragraph o the passage discusses WAIR

in an evolutionary context

Choices B C and D are incorrect because they do not identiy Dialrsquos central

assumption in setting up his research

QUESTION 24

Choice B is the best answer In lines 6-11 the author provides evidence that

Dialrsquos central assumption in setting up his research is that the acquisition o

flight in young birds is linked to the acquisition o flight in their ancestorsTe author notes that Dial created a project to ldquocome up with new data on

the age-old ground-up-tree-down debaterdquo

Choices A C and D do not provide the best evidence that Dialrsquos central

assumption in setting up his research is that the acquisition o flight in young

birds is linked to the acquisition o flight in their ancestors Choices A C

and D are incorrect because they ocus on Dialrsquos experiment and his obser-

vations on ground birds

7262019 PrepScholar Sat Practice Test 3 Answers

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7

QUESTION 25

Choice C is the best answer When a rancher observed Dialrsquos laboratory

setup he was ldquoincredulousrdquo that the Chukars were living on the ground and

he advised Dial to give the birds ldquosomething to climb onrdquo (lines 16-23) Tis

ldquokey piece o advicerdquo (line 14) led Dial to add hay bales to his laboratory

Dial later noticed that the Chukars were using their legs and wings to scalethe hay bales and this observation became the ocal point o his research

Choices A B and D are incorrect because the incident with the local rancher

did not serve to reveal Dialrsquos motivation or creating the project emphasize

differences in laboratory and field research or introduce a contributor to a

scientific theory

QUESTION 26

Choice C is the best answer Te author explains that Dialrsquos ldquoaha momentrdquo

came when he determined the Chukars used ldquotheir legs and wings coop-erativelyrdquo to scale the hay bales (lines 40-42) Dial then created additional

experiments to study how the birds dealt with gradually steeper inclines

ldquo[he filmed] the birds as they raced up textured ramps tilted at increasing

anglesrdquo (lines 46-48)

Choices A B and D are incorrect because Dialrsquos ldquoaha momentrdquo was not ol-

lowed by Dial teaching the birds to fly studying videos to find out why the

birds no longer hopped or consulting with other researchers

QUESTION 27

Choice B is the best answer Dial observed that as the Chukars raced up

steep ramps they ldquobegan to flaprdquo and ldquoaimed their flapping down and back-

ward using the orce to keep their eet firmly pressed against the ramprdquo

(lines 49-53) Dial determined that the position o their flapping wings acil-

itated the baby Chukarsrsquo traction on the steep ramps

Choices A C and D are incorrect because the passage does not indicate that

the Chukarsrsquo speed alternation o wing and oot movement or continual

hopping motions acilitated their traction on steep ramps

QUESTION 28

Choice B is the best answer In lines 61-63 the author explains that Dial

named his scientific finding ldquoWAIR or wing-assisted incline running and

went on to document it in a wide range o speciesrdquo In this context Dial

ldquodocumentedrdquo or recorded the existence o WAIR in numerous bird species

Choices A C and D are incorrect because in this context ldquodocumentrdquo does

not mean to portray publish or process

7262019 PrepScholar Sat Practice Test 3 Answers

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8

QUESTION 29

Choice D is the best answer In lines 70-74 the author explains that glid-

ing animals do not use a ldquoflapping flight strokerdquo or WAIR wing-assisted

incline running Since Chukars a ground bird use WAIR to help scale steep

inclines it can be reasonably inerred that gliding animals do not use WAIR

to aid in climbing slopes

Choices A B and C are incorrect because the passage does not include

inormation on gliding animalsrsquo offspring their method o locomotion or

their eeding habits

QUESTION 30

Choice D is the best answer In lines 73-75 the author provides evidence

that ldquothe flapping flight strokerdquo is ldquosomething gliding animals donrsquot dordquo

Choices A B and C do not provide the best evidence that gliding animalsdo not use a flapping stroke to aid in climbing slopes Tese choices do not

contain inormation about gliding animals

QUESTION 31

Choice B is the best answer In lines 21-24 the authors o Passage 1 state

societyrsquos ldquocommon happinessrdquo is dependent on women never becoming

involved in politics In this context the authors o Passage 1 are sug-

gesting that all members o society can have a ldquocommonrdquo or shared

happiness

Choices A C and D are incorrect because in this context ldquocommonrdquo does

not mean average coarse or similar

QUESTION 32

Choice C is the best answer In lines 25-30 the authors o Passage 1 state

that women should seek ldquogentle occupations and the cares o the homerdquo

so they can avoid perorming difficult or ldquostrenuousrdquo and unpleasant or

ldquoonerousrdquo tasks

Choices A B and D are incorrect because the authors o Passage 1 do notsuggest that running a household and raising children are rewarding or

both sexes yield less value or society or require proessional or political

skills

QUESTION 33

Choice C is the best answer In lines 25-30 the authors o Passage 1 provide

evidence that women should run households and raise children because

these roles do not require ldquostrenuous habits and onerous dutiesrdquo

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9

Choices A B and D do not provide the best evidence that running a house-

hold and raising children entail very ew activities that are difficult or

unpleasant rather these lines offer general inormation about the differ-

ences between the sexes

QUESTION 34

Choice D is the best answer In lines 41-46 Wollstonecraf argues that i

women do not receive an education ldquoto become the companion o manrdquo or

one that is comparable to menrsquos education then society will not progress in

ldquoknowledge and virtuerdquo

Choices A B and C are incorrect because Wollstonecraf does not suggest

that society can progress only i women have happiness and financial secu-

rity ollow societal rules or replace men as figures o power

QUESTION 35

Choice C is the best answer Wollstonecraf argues that women should be

granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo

(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-

enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context

Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or

intellect and allow women to consider their role in society

Choices A B and D are incorrect because in this context ldquoreasonrdquo does not

mean motive sanity or explanation

QUESTION 36

Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws

passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to

ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf

is arguing that societyrsquos leaders grant men reedoms that are denied to women

Choices B C and D are incorrect because Wollstonecraf does not claim

that societyrsquos leaders have granted reedoms that created a general reduction

in individual virtue caused arguments about happiness or ensured equality

or all people

QUESTION 37

Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-

dence that societyrsquos leaders grant reedoms that privilege men She argues

that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-

lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to

ldquocontend or their reedomrdquo

Choices A B and C do not provide the best evidence that societyrsquos leaders

grant reedoms that privilege men over women

7262019 PrepScholar Sat Practice Test 3 Answers

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10

QUESTION 38

Choice C is the best answer Wollstonecraf cites the statement made by

the authors o Passage 1 that excluding women rom political participation

is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)

Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe

abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument

by highlighting a flaw in the reasoning presented by the authors o Passage 1

Choices A B and D are incorrect because Wollstonecraf does not reer to

the statement made in Passage 1 to call into question the authorsrsquo qualifica-

tions dispute the assertion that women are excluded by their own govern-

ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on

gender roles

QUESTION 39

Choice A is the best answer Te authors o Passage 1 argue that while

restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)

this restriction is necessary or societyrsquos overall happiness (lines 13-17)

Wollstonecraf however strongly challenges this argument asking the

authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-

doms are granted to women and likening societyrsquos male leaders to tyrants as

they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in

the darkrdquo (lines 78-88)

Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2

QUESTION 40

Choice D is the best answer Te authors o Passage 1 admit that women are

ldquoexcluded by the other hal [men] rom any participation in governmentrdquo

(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws

that deny women ldquocivil and political rightsrdquo (line 86)

Choices A B and C are incorrect because the authors o both passages

would not agree that women had the same preerences as men required agood education or were as happy as men

QUESTION 41

Choice A is the best answer Wollstonecraf argues in the final paragraph

o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women

ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would

most likely argue that allowing women these rights would be ldquoa reversal o

[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos

interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as

7262019 PrepScholar Sat Practice Test 3 Answers

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11

mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created

two sexes or a particular reason so while men can exercise civil and politi-

cal rights women are not naturally suited to these activities (lines 30-36)

Choices B and C are incorrect because they are not supported by inorma-

tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do

not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo

QUESTION 42

Choice C is the best answer When discussing problems with bee colo-

nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo

(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-

tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a

tentative tone and provides urther evidence that the authors believe but are

not certain that their hypothesis is correct

Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone

QUESTION 43

Choice C is the best answer In lines 24-28 the authors hypothesize that bee

colonies will be susceptible to mite inestations i they do not occasionally

eed on pyrethrum producing plants In lines 42-46 they suggest creating a

trial where a ldquosmall number o commercial honey bee colonies are offered a

number o pyrethrum producing plantsrdquo to test their hypothesis

Choices A B and D are incorrect because the authors do not hypothesize that

honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees

to develop secondary inections that beekeepers should increase their use o

insecticides or that humans are more susceptible to varroa mites

QUESTION 44

Choice D is the best answer In lines 24-28 the authors provide evidence

that a bee colony may be more resistant to mite inections i the bees eat

pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-

nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees

Choices A B and C do not describe any o the authorsrsquo hypotheses

QUESTION 45

Choice D is the best answer Te authors explain that when beekeepers

use commercially produced insecticides to fight mite inections they may

ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-

cientrdquo (lines 31-35)

7262019 PrepScholar Sat Practice Test 3 Answers

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12

Choices A B and C are incorrect because the authors do not suggest that

beekeepersrsquo use o commercially produced insecticides increases mite popu-

lations kills bacteria or destroys beesrsquo primary ood source

QUESTION 46

Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-

ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo

Choices A B and D are incorrect because they do not provide the best evi-

dence that beekeepersrsquo use o commercially produced insecticides may be

harmul to bees choices A B and D ocus on mite inestationsrsquo impact on

honeybees

QUESTION 47

Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some

bees Te authors then state ldquoWe urther postulate that the proper dosage

necessary to prevent mite inestation may be better lef to the beesrdquo (lines

35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the

bees may naturally control mite inestations better than insecticides

Choices A C and D are incorrect because in this context ldquopostulaterdquo does

not mean to make an unounded assumption question a belie or theory or

conclude based on firm evidence

QUESTION 48

Choice B is the best answer In the ourth paragraph the authors propose

a trial to study i honeybeesrsquo consumption o pyrethrum producing plants

helps the honeybees deend against mite inestations In the experiment the

authors plan to offer honey bee colonies both pyrethrum producing plants

and ldquoa typical bee ood source such as cloverrdquo to determine i these different

diets affect the beesrsquo susceptibility to mite inestations

Choices A C and D are incorrect because the main purpose o the ourth

paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished

experiment

QUESTION 49

Choice A is the best answer In lines 43-45 the authors propose a scien-

tific trial in which honeybees are ldquooffered a number o pyrethrum producing

plants as well as a typical bee ood source such as cloverrdquo Since the authors

contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood

sourcerdquo it can be assumed that clover does not produce pyrethrums

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1440

13

Choice B is incorrect because it is stated in the passage Choices C and D are

incorrect because they are not assumptions made by the authors

QUESTION 50

Choice B is the best answer Te table shows that 77 percent o the honeybee

colonies with colony collapse disorder were inected by all our pathogens

Choices A C and D are incorrect because they do not identiy the percent

o honeybee colonies with colony collapse disorder that were inected by all

our pathogens as based on data in the table

QUESTION 51

Choice D is the best answer Te table shows that 81 percent o colo-

nies without colony collapse disorder were affected by the pathogen

Nosema ceranae

Choices A B and C are incorrect because they do not identiy the pathogen

that inected the highest percentage o honeybee colonies without colony

collapse disorder as based on data in the table

QUESTION 52

Choice D is the best answer Te table discusses pathogen occurrence in

honeybee colonies but it includes no inormation as to whether these hon-

eybees were inected with mites Because the table does not suggest mites

inested the honeybee colonies no conclusions can be made as to whether

mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)

Choices A B and C are incorrect because the table provides no inormation

about whether these honeybees were inected with mites

Section 2 Writing and Language Test

QUESTION 1

Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-

ates a parallel structure within the list that begins with ldquohappierrdquo

Choices B C and D are incorrect because none creates a parallel structure

within the list o qualities

QUESTION 2

Choice B is the best answer Te ways in which exposure to natural light

affects employees is the main subject o the passage

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1540

14

Choices A C and D are incorrect because none introduces the topic dis-

cussed in the remainder o the passage

QUESTION 3

Choice C is the best answer It accurately notes that the proposed sentence

would be placed directly between the first mention o circadian rhythms andthe explanation o the term

Choices A B and D are incorrect because each misinterprets the relation-

ship between the proposed additional text and the ideas in the paragraph

QUESTION 4

Choice C is the best answer It provides the correct possessive construction

or ldquobodyrdquo which must be a singular noun when discussed in general terms

as in this sentence Choice C also provides the correct plural construction

or ldquoclocksrdquo

Choices A B and D are incorrect because each applies either a possessive or

a plural construction in a place where it doesnrsquot belong

QUESTION 5

Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular

noun ldquoabsenteeismrdquo

Choices B C and D are incorrect because each provides a verb that

either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy

QUESTION 6

Choice B is the best answer It contains a direct reerence to productivity

the topic introduced in the previous sentence

Choices A C and D are incorrect because none directly addresses employee

productivity the primary subject o the previous sentence

QUESTION 7

Choice A is the best answer It opens with a reerence to lowered worker

productivity creating a transition rom the previous paragraph and clearly

positions the high energy costs o artificial light sources as an additional

disadvantage

Choices B C and D are incorrect because none o the choices offer an ade-

quate transition rom the previous paragraph Each awkwardly inserts the

issue o lower worker productivity into a statement about the high energy

costs o artificial light sources

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1640

15

QUESTION 8

Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-

cate that the savings occurred every year

Choices A B and C are incorrect because each proposes an option that

would result in a redundancy with ldquoannualrdquo

QUESTION 9

Choice C is the best answer It provides a transitional adverb that accurately

communicates that this sentence describes an option that companies could

choose (ldquolight tubesrdquo) instead o the option described in the previous sen-

tence (ldquoull-pane windowsrdquo)

Choices A B and D are incorrect because each proposes a transitional

adverb that does not accurately reflect the relationship between this sen-

tence and the one preceding it

QUESTION 10

Choice C is the best answer It provides the correct relative pronoun to cor-

respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-

duce the definition that ollows

Choices A B and D are incorrect because each offers a pronoun inappropri-

ate or opening a dependent clause defining ldquolight tubesrdquo

QUESTION 11

Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the

noun ldquomeansrdquo particularly as a way to connect it to another noun or verb

Choices A C and D are incorrect because each results in nonstandard

phrasing with ldquomeansrdquo

QUESTION 12

Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-

responds with the plural noun ldquosettlersrdquo

Choices B C and D are incorrect because each provides either a nonstan-

dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo

QUESTION 13

Choice C is the best answer It creates a transition rom the poor ood qual-

ity mentioned in the previous sentence to the inormation about Harvey in

the remainder o the sentence

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1740

16

Choices A B and D are incorrect because none offers a transition rom the

previous sentence or a detail that corresponds precisely with the inorma-

tion in the remainder o the sentence

QUESTION 14

Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens

with a comma

Choices A B and C are incorrect because each proposes punctuation that

creates an inappropriately strong separation between the subject ldquoFred

Harveyrdquo and the verb ldquodecidedrdquo

QUESTION 15

Choice B is the best answer It provides the plural verb and plural posses-

sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo

Choices A C and D are incorrect because each either ails to provide a verb

that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide

the appropriate possessive pronoun

QUESTION 16

Choice C is the best answer It accurately echoes an earlier characterization

o the ood as being o ldquoterrible qualityrdquo while maintaining the established

tone o the passage

Choices A B and D are incorrect either because the word is less ormal than

the established tone o the passage (ldquoickyrdquo) or because it illogically attributes

agency to ood (ldquosinisterrdquo ldquosurlyrdquo)

QUESTION 17

Choice C is the best answer It accurately interprets ldquonot content to ollow

conventional business practicesrdquo as logically introducing the new practice o

ldquoemploying womenrdquo described in the ollowing sentences

Choices A B and D are incorrect because none recognizes why the sentence

is relevant to this particular location in the passage

QUESTION 18

Choice B is the best answer It is concise and ree o redundancies

Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and

ldquotremendousrdquo adjectives so close in meaning that together they present a

redundancy

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1840

17

QUESTION 19

Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary

reerence to ldquosuch regulationsrdquo in the previous clause

Choices A B and C are incorrect because each lacks a necessary subject

such as a pronoun or noun

QUESTION 20

Choice C is the best answer It reers directly to benefits or the restaurantsrsquo

emale employees the subject o the previous sentence

Choices A B and D are incorrect because none logically builds upon the

sentence that precedes it

QUESTION 21

Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo

Choices A B and C are incorrect because each uses the punctuation or

a dependent clause (ldquoLiving independently and demonstrating an intense

work ethicrdquo) as i it were an independent clause

QUESTION 22

Choice A is the best answer It recognizes that the new inormation sup-

ports the previous sentencersquos claim that ldquothe Harvey Girls became known as

a transormative orcerdquo

Choices B C and D are incorrect because each misinterprets the relation-

ship between the proposed text and the passage

QUESTION 23

Choice A is the best answer It opens with a clause that identifies how

1-MCP affects apples which ocuses the sentence on 1-MCP as the subject

and allows the ideas in the sentence to progress logically

Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy

QUESTION 24

Choice D is the best answer Only the comma is necessary to separate

ldquoethylenerdquo rom the appositive noun phrase that defines it

Choices A B and C are incorrect because each creates a comma splice and

or adds unnecessary words

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1940

18

QUESTION 25

Choice B is the best answer It offers an adjective that accurately describes

resh apples

Choices A C and D are incorrect because each proposes an adjective that

does not describe a plausible ruit texture

QUESTION 26

Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-

sponds with the plural reerent ldquoapplesrdquo

Choices B C and D are incorrect because none provides a pronoun that is

both possessive and plural

QUESTION 27

Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins

the relative clause

Choices A B and C are incorrect because each contains a pronoun that

either does not correspond with the human reerent ldquoconsumersrdquo or does

not correctly begin the relative clause

QUESTION 28

Choice B is the best answer It provides the present tense verb ldquodordquo which

corresponds to the present tense established earlier in the sentence

Choices A C and D are incorrect because each contains a verb that deviates

rom the simple present tense established in the sentence

QUESTION 29

Choice B is the best answer It provides a colon to appropriately introduce the

clause that ollows an elaboration on the preceding claim that Bartlett pears

are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo

Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically

QUESTION 30

Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-

trast with a previous idea and goes on to mention that 1-MCP can have

negative effects Sentence 1 continues the discussion o benefits o 1-MCP

and sentence 2 names the adverse effect o limiting scent production so the

most logical spot or sentence 4 is between these sentences

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040

19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2140

20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240

21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340

22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440

23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540

24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640

25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740

26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840

27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 5: PrepScholar Sat Practice Test 3 Answers

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4

QUESTION 12

Choice C is the best answer Te author notes that in North America ldquohopping

in a car almost always gets you to your destination more quicklyrdquo (lines 32-34)

Tis statement suggests that speed is one advantage to driving in North America

Choices A B and D are incorrect because the author does not cite environmen-

tal impact convenience or cost as advantages o driving in North America

QUESTION 13

Choice D is the best answer In lines 32-34 the author provides evidence

that speed is one advantage to driving in North America because driving

ldquoalmost always gets you to your destination more quicklyrdquo

Choices A B and C do not provide the best evidence that speed is one

advantage to driving in North America Choices A and B are incorrect

because they offer general inormation about using public transportationChoice C is incorrect because although these lines mention North America

they ocus on the disadvantages o public transportation

QUESTION 14

Choice B is the best answer Te author argues in the ourth paragraph that

public transportation ldquocan be aster more comortable and cheaper than the

private automobilerdquo (lines 36-37) and provides examples o ast and conve-

nient public transportation systems

Choices A C and D are incorrect because they ocus on points made in theourth paragraph rather than the paragraphrsquos central idea

QUESTION 15

Choice B is the best answer In lines 35-37 the author provides evidence

that some public transportation systems are superior to driving because

public transportation ldquocan be aster more comortable and cheaper than the

private automobilerdquo

Choices A C and D do not provide the best evidence that some public

transportation systems are superior to driving as they highlight points madein the ourth paragraph rather than the paragraphrsquos central idea

QUESTION 16

Choice C is the best answer In the last paragraph the author explains the

trend that people who became adults around the end o the twentieth cen-

tury are more willing to use public transportation than people rom older

generations Te author notes ldquoI you credit the demographers this transit

trend has legsrdquo (lines 58-59) In this context ldquocreditrdquo means to believe the

demographersrsquo claims about the trend

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 640

5

Choices A B and D are incorrect because in this context ldquocreditrdquo does not

mean endow attribute or honor

QUESTION 17

Choice B is the best answer In lines 59-63 the author explains the trend

o people who became adults around the end o the twentieth centuryldquotend[ing] to avor cities over suburbsrdquo In this context these adults ldquoavorrdquo

or preer cities over suburbs

Choices A C and D are incorrect because in this context ldquoavorrdquo does not

mean indulge resemble or serve

QUESTION 18

Choice B is the best answer In lines 63-67 the author explains that while

riding on public transportation people can use personal electronic devices

such as ldquoiPads MP3 players Kindles and smartphonesrdquo

Choices A C and D are incorrect because they do not show that public

transportation is compatible with the use o personal electronic devices

QUESTION 19

Choice A is the best answer Figure 1 shows that 107 o public transpor-

tation passengers are students and 67 o public transportation passengers

are retirees Tus more students than retirees use public transportation

Choices B and C are incorrect because figure 1 shows that more employedthan unemployed people use public transportation and that more employed

people than homemakers use public transportation Choice D is incorrect

because figure 1 does not explain how requently passengers use public

transportation it only identifies public transportation passengers by their

primary occupation

QUESTION 20

Choice A is the best answer Figure 1 shows that 72 o public transporta-

tion passengers are ldquoemployed outside the homerdquo and figure 2 indicates that

591 o public transportation trips are or ldquoworkrdquo It can be inerred romthese figures that many public transportation passengers take public trans-

portation to their place o employment

Choices B C and D are incorrect because figure 1 and figure 2 do not

indicate that public transportation passengers primarily use the system to

run errands use their own car on weekends or are planning to purchase

a car

7262019 PrepScholar Sat Practice Test 3 Answers

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6

QUESTION 21

Choice D is the best answer Te author explains that Ken Dial created an

experiment to study the evolution o flight by observing how baby Chukars

learn to fly During the experiment Dial noticed the unusual way Chukars

use their ldquolsquowings and legs cooperativelyrsquordquo to scale hay bales (lines 38-43) and

he created ldquoa series o ingenious experimentsrdquo (line 46) to study this obser- vation Afer his additional experiments Dial determined that these baby

birds angle ldquotheir wings differently rom birds in flightrdquo (lines 49-50)

Choices A B and C are incorrect because they do not accurately reflect the

sequence o events in the passage

QUESTION 22

Choice A is the best answer In lines 6-9 the author explains that Dial was

ldquochallengedrdquo or dared by graduate students to develop ldquonew datardquo on a long-

standing scientific debate (the ldquoground-up-tree-downrdquo theory)

Choices B C and D are incorrect because in this context ldquochallengedrdquo does

not mean required disputed with or competed with

QUESTION 23

Choice A is the best answer Te author explains that Dial created his initial

experiment to try and create ldquonew data on the age-old ground-up-tree-down

debaterdquo and that he looked or ldquocluesrdquo in ldquohow baby game birds learned to

flyrdquo (lines 8-11) Te note at the beginning o the passage explains the ldquoage-

old ground-up-tree down debaterdquo and offers two different theories on howbirds evolved to fly Finally the last paragraph o the passage discusses WAIR

in an evolutionary context

Choices B C and D are incorrect because they do not identiy Dialrsquos central

assumption in setting up his research

QUESTION 24

Choice B is the best answer In lines 6-11 the author provides evidence that

Dialrsquos central assumption in setting up his research is that the acquisition o

flight in young birds is linked to the acquisition o flight in their ancestorsTe author notes that Dial created a project to ldquocome up with new data on

the age-old ground-up-tree-down debaterdquo

Choices A C and D do not provide the best evidence that Dialrsquos central

assumption in setting up his research is that the acquisition o flight in young

birds is linked to the acquisition o flight in their ancestors Choices A C

and D are incorrect because they ocus on Dialrsquos experiment and his obser-

vations on ground birds

7262019 PrepScholar Sat Practice Test 3 Answers

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7

QUESTION 25

Choice C is the best answer When a rancher observed Dialrsquos laboratory

setup he was ldquoincredulousrdquo that the Chukars were living on the ground and

he advised Dial to give the birds ldquosomething to climb onrdquo (lines 16-23) Tis

ldquokey piece o advicerdquo (line 14) led Dial to add hay bales to his laboratory

Dial later noticed that the Chukars were using their legs and wings to scalethe hay bales and this observation became the ocal point o his research

Choices A B and D are incorrect because the incident with the local rancher

did not serve to reveal Dialrsquos motivation or creating the project emphasize

differences in laboratory and field research or introduce a contributor to a

scientific theory

QUESTION 26

Choice C is the best answer Te author explains that Dialrsquos ldquoaha momentrdquo

came when he determined the Chukars used ldquotheir legs and wings coop-erativelyrdquo to scale the hay bales (lines 40-42) Dial then created additional

experiments to study how the birds dealt with gradually steeper inclines

ldquo[he filmed] the birds as they raced up textured ramps tilted at increasing

anglesrdquo (lines 46-48)

Choices A B and D are incorrect because Dialrsquos ldquoaha momentrdquo was not ol-

lowed by Dial teaching the birds to fly studying videos to find out why the

birds no longer hopped or consulting with other researchers

QUESTION 27

Choice B is the best answer Dial observed that as the Chukars raced up

steep ramps they ldquobegan to flaprdquo and ldquoaimed their flapping down and back-

ward using the orce to keep their eet firmly pressed against the ramprdquo

(lines 49-53) Dial determined that the position o their flapping wings acil-

itated the baby Chukarsrsquo traction on the steep ramps

Choices A C and D are incorrect because the passage does not indicate that

the Chukarsrsquo speed alternation o wing and oot movement or continual

hopping motions acilitated their traction on steep ramps

QUESTION 28

Choice B is the best answer In lines 61-63 the author explains that Dial

named his scientific finding ldquoWAIR or wing-assisted incline running and

went on to document it in a wide range o speciesrdquo In this context Dial

ldquodocumentedrdquo or recorded the existence o WAIR in numerous bird species

Choices A C and D are incorrect because in this context ldquodocumentrdquo does

not mean to portray publish or process

7262019 PrepScholar Sat Practice Test 3 Answers

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8

QUESTION 29

Choice D is the best answer In lines 70-74 the author explains that glid-

ing animals do not use a ldquoflapping flight strokerdquo or WAIR wing-assisted

incline running Since Chukars a ground bird use WAIR to help scale steep

inclines it can be reasonably inerred that gliding animals do not use WAIR

to aid in climbing slopes

Choices A B and C are incorrect because the passage does not include

inormation on gliding animalsrsquo offspring their method o locomotion or

their eeding habits

QUESTION 30

Choice D is the best answer In lines 73-75 the author provides evidence

that ldquothe flapping flight strokerdquo is ldquosomething gliding animals donrsquot dordquo

Choices A B and C do not provide the best evidence that gliding animalsdo not use a flapping stroke to aid in climbing slopes Tese choices do not

contain inormation about gliding animals

QUESTION 31

Choice B is the best answer In lines 21-24 the authors o Passage 1 state

societyrsquos ldquocommon happinessrdquo is dependent on women never becoming

involved in politics In this context the authors o Passage 1 are sug-

gesting that all members o society can have a ldquocommonrdquo or shared

happiness

Choices A C and D are incorrect because in this context ldquocommonrdquo does

not mean average coarse or similar

QUESTION 32

Choice C is the best answer In lines 25-30 the authors o Passage 1 state

that women should seek ldquogentle occupations and the cares o the homerdquo

so they can avoid perorming difficult or ldquostrenuousrdquo and unpleasant or

ldquoonerousrdquo tasks

Choices A B and D are incorrect because the authors o Passage 1 do notsuggest that running a household and raising children are rewarding or

both sexes yield less value or society or require proessional or political

skills

QUESTION 33

Choice C is the best answer In lines 25-30 the authors o Passage 1 provide

evidence that women should run households and raise children because

these roles do not require ldquostrenuous habits and onerous dutiesrdquo

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9

Choices A B and D do not provide the best evidence that running a house-

hold and raising children entail very ew activities that are difficult or

unpleasant rather these lines offer general inormation about the differ-

ences between the sexes

QUESTION 34

Choice D is the best answer In lines 41-46 Wollstonecraf argues that i

women do not receive an education ldquoto become the companion o manrdquo or

one that is comparable to menrsquos education then society will not progress in

ldquoknowledge and virtuerdquo

Choices A B and C are incorrect because Wollstonecraf does not suggest

that society can progress only i women have happiness and financial secu-

rity ollow societal rules or replace men as figures o power

QUESTION 35

Choice C is the best answer Wollstonecraf argues that women should be

granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo

(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-

enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context

Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or

intellect and allow women to consider their role in society

Choices A B and D are incorrect because in this context ldquoreasonrdquo does not

mean motive sanity or explanation

QUESTION 36

Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws

passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to

ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf

is arguing that societyrsquos leaders grant men reedoms that are denied to women

Choices B C and D are incorrect because Wollstonecraf does not claim

that societyrsquos leaders have granted reedoms that created a general reduction

in individual virtue caused arguments about happiness or ensured equality

or all people

QUESTION 37

Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-

dence that societyrsquos leaders grant reedoms that privilege men She argues

that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-

lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to

ldquocontend or their reedomrdquo

Choices A B and C do not provide the best evidence that societyrsquos leaders

grant reedoms that privilege men over women

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10

QUESTION 38

Choice C is the best answer Wollstonecraf cites the statement made by

the authors o Passage 1 that excluding women rom political participation

is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)

Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe

abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument

by highlighting a flaw in the reasoning presented by the authors o Passage 1

Choices A B and D are incorrect because Wollstonecraf does not reer to

the statement made in Passage 1 to call into question the authorsrsquo qualifica-

tions dispute the assertion that women are excluded by their own govern-

ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on

gender roles

QUESTION 39

Choice A is the best answer Te authors o Passage 1 argue that while

restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)

this restriction is necessary or societyrsquos overall happiness (lines 13-17)

Wollstonecraf however strongly challenges this argument asking the

authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-

doms are granted to women and likening societyrsquos male leaders to tyrants as

they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in

the darkrdquo (lines 78-88)

Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2

QUESTION 40

Choice D is the best answer Te authors o Passage 1 admit that women are

ldquoexcluded by the other hal [men] rom any participation in governmentrdquo

(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws

that deny women ldquocivil and political rightsrdquo (line 86)

Choices A B and C are incorrect because the authors o both passages

would not agree that women had the same preerences as men required agood education or were as happy as men

QUESTION 41

Choice A is the best answer Wollstonecraf argues in the final paragraph

o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women

ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would

most likely argue that allowing women these rights would be ldquoa reversal o

[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos

interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as

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11

mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created

two sexes or a particular reason so while men can exercise civil and politi-

cal rights women are not naturally suited to these activities (lines 30-36)

Choices B and C are incorrect because they are not supported by inorma-

tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do

not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo

QUESTION 42

Choice C is the best answer When discussing problems with bee colo-

nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo

(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-

tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a

tentative tone and provides urther evidence that the authors believe but are

not certain that their hypothesis is correct

Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone

QUESTION 43

Choice C is the best answer In lines 24-28 the authors hypothesize that bee

colonies will be susceptible to mite inestations i they do not occasionally

eed on pyrethrum producing plants In lines 42-46 they suggest creating a

trial where a ldquosmall number o commercial honey bee colonies are offered a

number o pyrethrum producing plantsrdquo to test their hypothesis

Choices A B and D are incorrect because the authors do not hypothesize that

honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees

to develop secondary inections that beekeepers should increase their use o

insecticides or that humans are more susceptible to varroa mites

QUESTION 44

Choice D is the best answer In lines 24-28 the authors provide evidence

that a bee colony may be more resistant to mite inections i the bees eat

pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-

nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees

Choices A B and C do not describe any o the authorsrsquo hypotheses

QUESTION 45

Choice D is the best answer Te authors explain that when beekeepers

use commercially produced insecticides to fight mite inections they may

ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-

cientrdquo (lines 31-35)

7262019 PrepScholar Sat Practice Test 3 Answers

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12

Choices A B and C are incorrect because the authors do not suggest that

beekeepersrsquo use o commercially produced insecticides increases mite popu-

lations kills bacteria or destroys beesrsquo primary ood source

QUESTION 46

Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-

ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo

Choices A B and D are incorrect because they do not provide the best evi-

dence that beekeepersrsquo use o commercially produced insecticides may be

harmul to bees choices A B and D ocus on mite inestationsrsquo impact on

honeybees

QUESTION 47

Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some

bees Te authors then state ldquoWe urther postulate that the proper dosage

necessary to prevent mite inestation may be better lef to the beesrdquo (lines

35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the

bees may naturally control mite inestations better than insecticides

Choices A C and D are incorrect because in this context ldquopostulaterdquo does

not mean to make an unounded assumption question a belie or theory or

conclude based on firm evidence

QUESTION 48

Choice B is the best answer In the ourth paragraph the authors propose

a trial to study i honeybeesrsquo consumption o pyrethrum producing plants

helps the honeybees deend against mite inestations In the experiment the

authors plan to offer honey bee colonies both pyrethrum producing plants

and ldquoa typical bee ood source such as cloverrdquo to determine i these different

diets affect the beesrsquo susceptibility to mite inestations

Choices A C and D are incorrect because the main purpose o the ourth

paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished

experiment

QUESTION 49

Choice A is the best answer In lines 43-45 the authors propose a scien-

tific trial in which honeybees are ldquooffered a number o pyrethrum producing

plants as well as a typical bee ood source such as cloverrdquo Since the authors

contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood

sourcerdquo it can be assumed that clover does not produce pyrethrums

7262019 PrepScholar Sat Practice Test 3 Answers

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13

Choice B is incorrect because it is stated in the passage Choices C and D are

incorrect because they are not assumptions made by the authors

QUESTION 50

Choice B is the best answer Te table shows that 77 percent o the honeybee

colonies with colony collapse disorder were inected by all our pathogens

Choices A C and D are incorrect because they do not identiy the percent

o honeybee colonies with colony collapse disorder that were inected by all

our pathogens as based on data in the table

QUESTION 51

Choice D is the best answer Te table shows that 81 percent o colo-

nies without colony collapse disorder were affected by the pathogen

Nosema ceranae

Choices A B and C are incorrect because they do not identiy the pathogen

that inected the highest percentage o honeybee colonies without colony

collapse disorder as based on data in the table

QUESTION 52

Choice D is the best answer Te table discusses pathogen occurrence in

honeybee colonies but it includes no inormation as to whether these hon-

eybees were inected with mites Because the table does not suggest mites

inested the honeybee colonies no conclusions can be made as to whether

mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)

Choices A B and C are incorrect because the table provides no inormation

about whether these honeybees were inected with mites

Section 2 Writing and Language Test

QUESTION 1

Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-

ates a parallel structure within the list that begins with ldquohappierrdquo

Choices B C and D are incorrect because none creates a parallel structure

within the list o qualities

QUESTION 2

Choice B is the best answer Te ways in which exposure to natural light

affects employees is the main subject o the passage

7262019 PrepScholar Sat Practice Test 3 Answers

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14

Choices A C and D are incorrect because none introduces the topic dis-

cussed in the remainder o the passage

QUESTION 3

Choice C is the best answer It accurately notes that the proposed sentence

would be placed directly between the first mention o circadian rhythms andthe explanation o the term

Choices A B and D are incorrect because each misinterprets the relation-

ship between the proposed additional text and the ideas in the paragraph

QUESTION 4

Choice C is the best answer It provides the correct possessive construction

or ldquobodyrdquo which must be a singular noun when discussed in general terms

as in this sentence Choice C also provides the correct plural construction

or ldquoclocksrdquo

Choices A B and D are incorrect because each applies either a possessive or

a plural construction in a place where it doesnrsquot belong

QUESTION 5

Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular

noun ldquoabsenteeismrdquo

Choices B C and D are incorrect because each provides a verb that

either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy

QUESTION 6

Choice B is the best answer It contains a direct reerence to productivity

the topic introduced in the previous sentence

Choices A C and D are incorrect because none directly addresses employee

productivity the primary subject o the previous sentence

QUESTION 7

Choice A is the best answer It opens with a reerence to lowered worker

productivity creating a transition rom the previous paragraph and clearly

positions the high energy costs o artificial light sources as an additional

disadvantage

Choices B C and D are incorrect because none o the choices offer an ade-

quate transition rom the previous paragraph Each awkwardly inserts the

issue o lower worker productivity into a statement about the high energy

costs o artificial light sources

7262019 PrepScholar Sat Practice Test 3 Answers

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15

QUESTION 8

Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-

cate that the savings occurred every year

Choices A B and C are incorrect because each proposes an option that

would result in a redundancy with ldquoannualrdquo

QUESTION 9

Choice C is the best answer It provides a transitional adverb that accurately

communicates that this sentence describes an option that companies could

choose (ldquolight tubesrdquo) instead o the option described in the previous sen-

tence (ldquoull-pane windowsrdquo)

Choices A B and D are incorrect because each proposes a transitional

adverb that does not accurately reflect the relationship between this sen-

tence and the one preceding it

QUESTION 10

Choice C is the best answer It provides the correct relative pronoun to cor-

respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-

duce the definition that ollows

Choices A B and D are incorrect because each offers a pronoun inappropri-

ate or opening a dependent clause defining ldquolight tubesrdquo

QUESTION 11

Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the

noun ldquomeansrdquo particularly as a way to connect it to another noun or verb

Choices A C and D are incorrect because each results in nonstandard

phrasing with ldquomeansrdquo

QUESTION 12

Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-

responds with the plural noun ldquosettlersrdquo

Choices B C and D are incorrect because each provides either a nonstan-

dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo

QUESTION 13

Choice C is the best answer It creates a transition rom the poor ood qual-

ity mentioned in the previous sentence to the inormation about Harvey in

the remainder o the sentence

7262019 PrepScholar Sat Practice Test 3 Answers

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16

Choices A B and D are incorrect because none offers a transition rom the

previous sentence or a detail that corresponds precisely with the inorma-

tion in the remainder o the sentence

QUESTION 14

Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens

with a comma

Choices A B and C are incorrect because each proposes punctuation that

creates an inappropriately strong separation between the subject ldquoFred

Harveyrdquo and the verb ldquodecidedrdquo

QUESTION 15

Choice B is the best answer It provides the plural verb and plural posses-

sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo

Choices A C and D are incorrect because each either ails to provide a verb

that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide

the appropriate possessive pronoun

QUESTION 16

Choice C is the best answer It accurately echoes an earlier characterization

o the ood as being o ldquoterrible qualityrdquo while maintaining the established

tone o the passage

Choices A B and D are incorrect either because the word is less ormal than

the established tone o the passage (ldquoickyrdquo) or because it illogically attributes

agency to ood (ldquosinisterrdquo ldquosurlyrdquo)

QUESTION 17

Choice C is the best answer It accurately interprets ldquonot content to ollow

conventional business practicesrdquo as logically introducing the new practice o

ldquoemploying womenrdquo described in the ollowing sentences

Choices A B and D are incorrect because none recognizes why the sentence

is relevant to this particular location in the passage

QUESTION 18

Choice B is the best answer It is concise and ree o redundancies

Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and

ldquotremendousrdquo adjectives so close in meaning that together they present a

redundancy

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1840

17

QUESTION 19

Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary

reerence to ldquosuch regulationsrdquo in the previous clause

Choices A B and C are incorrect because each lacks a necessary subject

such as a pronoun or noun

QUESTION 20

Choice C is the best answer It reers directly to benefits or the restaurantsrsquo

emale employees the subject o the previous sentence

Choices A B and D are incorrect because none logically builds upon the

sentence that precedes it

QUESTION 21

Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo

Choices A B and C are incorrect because each uses the punctuation or

a dependent clause (ldquoLiving independently and demonstrating an intense

work ethicrdquo) as i it were an independent clause

QUESTION 22

Choice A is the best answer It recognizes that the new inormation sup-

ports the previous sentencersquos claim that ldquothe Harvey Girls became known as

a transormative orcerdquo

Choices B C and D are incorrect because each misinterprets the relation-

ship between the proposed text and the passage

QUESTION 23

Choice A is the best answer It opens with a clause that identifies how

1-MCP affects apples which ocuses the sentence on 1-MCP as the subject

and allows the ideas in the sentence to progress logically

Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy

QUESTION 24

Choice D is the best answer Only the comma is necessary to separate

ldquoethylenerdquo rom the appositive noun phrase that defines it

Choices A B and C are incorrect because each creates a comma splice and

or adds unnecessary words

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1940

18

QUESTION 25

Choice B is the best answer It offers an adjective that accurately describes

resh apples

Choices A C and D are incorrect because each proposes an adjective that

does not describe a plausible ruit texture

QUESTION 26

Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-

sponds with the plural reerent ldquoapplesrdquo

Choices B C and D are incorrect because none provides a pronoun that is

both possessive and plural

QUESTION 27

Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins

the relative clause

Choices A B and C are incorrect because each contains a pronoun that

either does not correspond with the human reerent ldquoconsumersrdquo or does

not correctly begin the relative clause

QUESTION 28

Choice B is the best answer It provides the present tense verb ldquodordquo which

corresponds to the present tense established earlier in the sentence

Choices A C and D are incorrect because each contains a verb that deviates

rom the simple present tense established in the sentence

QUESTION 29

Choice B is the best answer It provides a colon to appropriately introduce the

clause that ollows an elaboration on the preceding claim that Bartlett pears

are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo

Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically

QUESTION 30

Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-

trast with a previous idea and goes on to mention that 1-MCP can have

negative effects Sentence 1 continues the discussion o benefits o 1-MCP

and sentence 2 names the adverse effect o limiting scent production so the

most logical spot or sentence 4 is between these sentences

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040

19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2140

20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240

21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340

22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440

23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540

24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640

25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740

26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840

27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940

28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040

29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 6: PrepScholar Sat Practice Test 3 Answers

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5

Choices A B and D are incorrect because in this context ldquocreditrdquo does not

mean endow attribute or honor

QUESTION 17

Choice B is the best answer In lines 59-63 the author explains the trend

o people who became adults around the end o the twentieth centuryldquotend[ing] to avor cities over suburbsrdquo In this context these adults ldquoavorrdquo

or preer cities over suburbs

Choices A C and D are incorrect because in this context ldquoavorrdquo does not

mean indulge resemble or serve

QUESTION 18

Choice B is the best answer In lines 63-67 the author explains that while

riding on public transportation people can use personal electronic devices

such as ldquoiPads MP3 players Kindles and smartphonesrdquo

Choices A C and D are incorrect because they do not show that public

transportation is compatible with the use o personal electronic devices

QUESTION 19

Choice A is the best answer Figure 1 shows that 107 o public transpor-

tation passengers are students and 67 o public transportation passengers

are retirees Tus more students than retirees use public transportation

Choices B and C are incorrect because figure 1 shows that more employedthan unemployed people use public transportation and that more employed

people than homemakers use public transportation Choice D is incorrect

because figure 1 does not explain how requently passengers use public

transportation it only identifies public transportation passengers by their

primary occupation

QUESTION 20

Choice A is the best answer Figure 1 shows that 72 o public transporta-

tion passengers are ldquoemployed outside the homerdquo and figure 2 indicates that

591 o public transportation trips are or ldquoworkrdquo It can be inerred romthese figures that many public transportation passengers take public trans-

portation to their place o employment

Choices B C and D are incorrect because figure 1 and figure 2 do not

indicate that public transportation passengers primarily use the system to

run errands use their own car on weekends or are planning to purchase

a car

7262019 PrepScholar Sat Practice Test 3 Answers

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6

QUESTION 21

Choice D is the best answer Te author explains that Ken Dial created an

experiment to study the evolution o flight by observing how baby Chukars

learn to fly During the experiment Dial noticed the unusual way Chukars

use their ldquolsquowings and legs cooperativelyrsquordquo to scale hay bales (lines 38-43) and

he created ldquoa series o ingenious experimentsrdquo (line 46) to study this obser- vation Afer his additional experiments Dial determined that these baby

birds angle ldquotheir wings differently rom birds in flightrdquo (lines 49-50)

Choices A B and C are incorrect because they do not accurately reflect the

sequence o events in the passage

QUESTION 22

Choice A is the best answer In lines 6-9 the author explains that Dial was

ldquochallengedrdquo or dared by graduate students to develop ldquonew datardquo on a long-

standing scientific debate (the ldquoground-up-tree-downrdquo theory)

Choices B C and D are incorrect because in this context ldquochallengedrdquo does

not mean required disputed with or competed with

QUESTION 23

Choice A is the best answer Te author explains that Dial created his initial

experiment to try and create ldquonew data on the age-old ground-up-tree-down

debaterdquo and that he looked or ldquocluesrdquo in ldquohow baby game birds learned to

flyrdquo (lines 8-11) Te note at the beginning o the passage explains the ldquoage-

old ground-up-tree down debaterdquo and offers two different theories on howbirds evolved to fly Finally the last paragraph o the passage discusses WAIR

in an evolutionary context

Choices B C and D are incorrect because they do not identiy Dialrsquos central

assumption in setting up his research

QUESTION 24

Choice B is the best answer In lines 6-11 the author provides evidence that

Dialrsquos central assumption in setting up his research is that the acquisition o

flight in young birds is linked to the acquisition o flight in their ancestorsTe author notes that Dial created a project to ldquocome up with new data on

the age-old ground-up-tree-down debaterdquo

Choices A C and D do not provide the best evidence that Dialrsquos central

assumption in setting up his research is that the acquisition o flight in young

birds is linked to the acquisition o flight in their ancestors Choices A C

and D are incorrect because they ocus on Dialrsquos experiment and his obser-

vations on ground birds

7262019 PrepScholar Sat Practice Test 3 Answers

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7

QUESTION 25

Choice C is the best answer When a rancher observed Dialrsquos laboratory

setup he was ldquoincredulousrdquo that the Chukars were living on the ground and

he advised Dial to give the birds ldquosomething to climb onrdquo (lines 16-23) Tis

ldquokey piece o advicerdquo (line 14) led Dial to add hay bales to his laboratory

Dial later noticed that the Chukars were using their legs and wings to scalethe hay bales and this observation became the ocal point o his research

Choices A B and D are incorrect because the incident with the local rancher

did not serve to reveal Dialrsquos motivation or creating the project emphasize

differences in laboratory and field research or introduce a contributor to a

scientific theory

QUESTION 26

Choice C is the best answer Te author explains that Dialrsquos ldquoaha momentrdquo

came when he determined the Chukars used ldquotheir legs and wings coop-erativelyrdquo to scale the hay bales (lines 40-42) Dial then created additional

experiments to study how the birds dealt with gradually steeper inclines

ldquo[he filmed] the birds as they raced up textured ramps tilted at increasing

anglesrdquo (lines 46-48)

Choices A B and D are incorrect because Dialrsquos ldquoaha momentrdquo was not ol-

lowed by Dial teaching the birds to fly studying videos to find out why the

birds no longer hopped or consulting with other researchers

QUESTION 27

Choice B is the best answer Dial observed that as the Chukars raced up

steep ramps they ldquobegan to flaprdquo and ldquoaimed their flapping down and back-

ward using the orce to keep their eet firmly pressed against the ramprdquo

(lines 49-53) Dial determined that the position o their flapping wings acil-

itated the baby Chukarsrsquo traction on the steep ramps

Choices A C and D are incorrect because the passage does not indicate that

the Chukarsrsquo speed alternation o wing and oot movement or continual

hopping motions acilitated their traction on steep ramps

QUESTION 28

Choice B is the best answer In lines 61-63 the author explains that Dial

named his scientific finding ldquoWAIR or wing-assisted incline running and

went on to document it in a wide range o speciesrdquo In this context Dial

ldquodocumentedrdquo or recorded the existence o WAIR in numerous bird species

Choices A C and D are incorrect because in this context ldquodocumentrdquo does

not mean to portray publish or process

7262019 PrepScholar Sat Practice Test 3 Answers

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8

QUESTION 29

Choice D is the best answer In lines 70-74 the author explains that glid-

ing animals do not use a ldquoflapping flight strokerdquo or WAIR wing-assisted

incline running Since Chukars a ground bird use WAIR to help scale steep

inclines it can be reasonably inerred that gliding animals do not use WAIR

to aid in climbing slopes

Choices A B and C are incorrect because the passage does not include

inormation on gliding animalsrsquo offspring their method o locomotion or

their eeding habits

QUESTION 30

Choice D is the best answer In lines 73-75 the author provides evidence

that ldquothe flapping flight strokerdquo is ldquosomething gliding animals donrsquot dordquo

Choices A B and C do not provide the best evidence that gliding animalsdo not use a flapping stroke to aid in climbing slopes Tese choices do not

contain inormation about gliding animals

QUESTION 31

Choice B is the best answer In lines 21-24 the authors o Passage 1 state

societyrsquos ldquocommon happinessrdquo is dependent on women never becoming

involved in politics In this context the authors o Passage 1 are sug-

gesting that all members o society can have a ldquocommonrdquo or shared

happiness

Choices A C and D are incorrect because in this context ldquocommonrdquo does

not mean average coarse or similar

QUESTION 32

Choice C is the best answer In lines 25-30 the authors o Passage 1 state

that women should seek ldquogentle occupations and the cares o the homerdquo

so they can avoid perorming difficult or ldquostrenuousrdquo and unpleasant or

ldquoonerousrdquo tasks

Choices A B and D are incorrect because the authors o Passage 1 do notsuggest that running a household and raising children are rewarding or

both sexes yield less value or society or require proessional or political

skills

QUESTION 33

Choice C is the best answer In lines 25-30 the authors o Passage 1 provide

evidence that women should run households and raise children because

these roles do not require ldquostrenuous habits and onerous dutiesrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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9

Choices A B and D do not provide the best evidence that running a house-

hold and raising children entail very ew activities that are difficult or

unpleasant rather these lines offer general inormation about the differ-

ences between the sexes

QUESTION 34

Choice D is the best answer In lines 41-46 Wollstonecraf argues that i

women do not receive an education ldquoto become the companion o manrdquo or

one that is comparable to menrsquos education then society will not progress in

ldquoknowledge and virtuerdquo

Choices A B and C are incorrect because Wollstonecraf does not suggest

that society can progress only i women have happiness and financial secu-

rity ollow societal rules or replace men as figures o power

QUESTION 35

Choice C is the best answer Wollstonecraf argues that women should be

granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo

(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-

enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context

Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or

intellect and allow women to consider their role in society

Choices A B and D are incorrect because in this context ldquoreasonrdquo does not

mean motive sanity or explanation

QUESTION 36

Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws

passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to

ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf

is arguing that societyrsquos leaders grant men reedoms that are denied to women

Choices B C and D are incorrect because Wollstonecraf does not claim

that societyrsquos leaders have granted reedoms that created a general reduction

in individual virtue caused arguments about happiness or ensured equality

or all people

QUESTION 37

Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-

dence that societyrsquos leaders grant reedoms that privilege men She argues

that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-

lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to

ldquocontend or their reedomrdquo

Choices A B and C do not provide the best evidence that societyrsquos leaders

grant reedoms that privilege men over women

7262019 PrepScholar Sat Practice Test 3 Answers

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10

QUESTION 38

Choice C is the best answer Wollstonecraf cites the statement made by

the authors o Passage 1 that excluding women rom political participation

is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)

Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe

abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument

by highlighting a flaw in the reasoning presented by the authors o Passage 1

Choices A B and D are incorrect because Wollstonecraf does not reer to

the statement made in Passage 1 to call into question the authorsrsquo qualifica-

tions dispute the assertion that women are excluded by their own govern-

ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on

gender roles

QUESTION 39

Choice A is the best answer Te authors o Passage 1 argue that while

restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)

this restriction is necessary or societyrsquos overall happiness (lines 13-17)

Wollstonecraf however strongly challenges this argument asking the

authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-

doms are granted to women and likening societyrsquos male leaders to tyrants as

they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in

the darkrdquo (lines 78-88)

Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2

QUESTION 40

Choice D is the best answer Te authors o Passage 1 admit that women are

ldquoexcluded by the other hal [men] rom any participation in governmentrdquo

(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws

that deny women ldquocivil and political rightsrdquo (line 86)

Choices A B and C are incorrect because the authors o both passages

would not agree that women had the same preerences as men required agood education or were as happy as men

QUESTION 41

Choice A is the best answer Wollstonecraf argues in the final paragraph

o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women

ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would

most likely argue that allowing women these rights would be ldquoa reversal o

[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos

interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as

7262019 PrepScholar Sat Practice Test 3 Answers

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11

mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created

two sexes or a particular reason so while men can exercise civil and politi-

cal rights women are not naturally suited to these activities (lines 30-36)

Choices B and C are incorrect because they are not supported by inorma-

tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do

not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo

QUESTION 42

Choice C is the best answer When discussing problems with bee colo-

nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo

(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-

tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a

tentative tone and provides urther evidence that the authors believe but are

not certain that their hypothesis is correct

Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone

QUESTION 43

Choice C is the best answer In lines 24-28 the authors hypothesize that bee

colonies will be susceptible to mite inestations i they do not occasionally

eed on pyrethrum producing plants In lines 42-46 they suggest creating a

trial where a ldquosmall number o commercial honey bee colonies are offered a

number o pyrethrum producing plantsrdquo to test their hypothesis

Choices A B and D are incorrect because the authors do not hypothesize that

honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees

to develop secondary inections that beekeepers should increase their use o

insecticides or that humans are more susceptible to varroa mites

QUESTION 44

Choice D is the best answer In lines 24-28 the authors provide evidence

that a bee colony may be more resistant to mite inections i the bees eat

pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-

nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees

Choices A B and C do not describe any o the authorsrsquo hypotheses

QUESTION 45

Choice D is the best answer Te authors explain that when beekeepers

use commercially produced insecticides to fight mite inections they may

ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-

cientrdquo (lines 31-35)

7262019 PrepScholar Sat Practice Test 3 Answers

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12

Choices A B and C are incorrect because the authors do not suggest that

beekeepersrsquo use o commercially produced insecticides increases mite popu-

lations kills bacteria or destroys beesrsquo primary ood source

QUESTION 46

Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-

ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo

Choices A B and D are incorrect because they do not provide the best evi-

dence that beekeepersrsquo use o commercially produced insecticides may be

harmul to bees choices A B and D ocus on mite inestationsrsquo impact on

honeybees

QUESTION 47

Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some

bees Te authors then state ldquoWe urther postulate that the proper dosage

necessary to prevent mite inestation may be better lef to the beesrdquo (lines

35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the

bees may naturally control mite inestations better than insecticides

Choices A C and D are incorrect because in this context ldquopostulaterdquo does

not mean to make an unounded assumption question a belie or theory or

conclude based on firm evidence

QUESTION 48

Choice B is the best answer In the ourth paragraph the authors propose

a trial to study i honeybeesrsquo consumption o pyrethrum producing plants

helps the honeybees deend against mite inestations In the experiment the

authors plan to offer honey bee colonies both pyrethrum producing plants

and ldquoa typical bee ood source such as cloverrdquo to determine i these different

diets affect the beesrsquo susceptibility to mite inestations

Choices A C and D are incorrect because the main purpose o the ourth

paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished

experiment

QUESTION 49

Choice A is the best answer In lines 43-45 the authors propose a scien-

tific trial in which honeybees are ldquooffered a number o pyrethrum producing

plants as well as a typical bee ood source such as cloverrdquo Since the authors

contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood

sourcerdquo it can be assumed that clover does not produce pyrethrums

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13

Choice B is incorrect because it is stated in the passage Choices C and D are

incorrect because they are not assumptions made by the authors

QUESTION 50

Choice B is the best answer Te table shows that 77 percent o the honeybee

colonies with colony collapse disorder were inected by all our pathogens

Choices A C and D are incorrect because they do not identiy the percent

o honeybee colonies with colony collapse disorder that were inected by all

our pathogens as based on data in the table

QUESTION 51

Choice D is the best answer Te table shows that 81 percent o colo-

nies without colony collapse disorder were affected by the pathogen

Nosema ceranae

Choices A B and C are incorrect because they do not identiy the pathogen

that inected the highest percentage o honeybee colonies without colony

collapse disorder as based on data in the table

QUESTION 52

Choice D is the best answer Te table discusses pathogen occurrence in

honeybee colonies but it includes no inormation as to whether these hon-

eybees were inected with mites Because the table does not suggest mites

inested the honeybee colonies no conclusions can be made as to whether

mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)

Choices A B and C are incorrect because the table provides no inormation

about whether these honeybees were inected with mites

Section 2 Writing and Language Test

QUESTION 1

Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-

ates a parallel structure within the list that begins with ldquohappierrdquo

Choices B C and D are incorrect because none creates a parallel structure

within the list o qualities

QUESTION 2

Choice B is the best answer Te ways in which exposure to natural light

affects employees is the main subject o the passage

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14

Choices A C and D are incorrect because none introduces the topic dis-

cussed in the remainder o the passage

QUESTION 3

Choice C is the best answer It accurately notes that the proposed sentence

would be placed directly between the first mention o circadian rhythms andthe explanation o the term

Choices A B and D are incorrect because each misinterprets the relation-

ship between the proposed additional text and the ideas in the paragraph

QUESTION 4

Choice C is the best answer It provides the correct possessive construction

or ldquobodyrdquo which must be a singular noun when discussed in general terms

as in this sentence Choice C also provides the correct plural construction

or ldquoclocksrdquo

Choices A B and D are incorrect because each applies either a possessive or

a plural construction in a place where it doesnrsquot belong

QUESTION 5

Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular

noun ldquoabsenteeismrdquo

Choices B C and D are incorrect because each provides a verb that

either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy

QUESTION 6

Choice B is the best answer It contains a direct reerence to productivity

the topic introduced in the previous sentence

Choices A C and D are incorrect because none directly addresses employee

productivity the primary subject o the previous sentence

QUESTION 7

Choice A is the best answer It opens with a reerence to lowered worker

productivity creating a transition rom the previous paragraph and clearly

positions the high energy costs o artificial light sources as an additional

disadvantage

Choices B C and D are incorrect because none o the choices offer an ade-

quate transition rom the previous paragraph Each awkwardly inserts the

issue o lower worker productivity into a statement about the high energy

costs o artificial light sources

7262019 PrepScholar Sat Practice Test 3 Answers

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15

QUESTION 8

Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-

cate that the savings occurred every year

Choices A B and C are incorrect because each proposes an option that

would result in a redundancy with ldquoannualrdquo

QUESTION 9

Choice C is the best answer It provides a transitional adverb that accurately

communicates that this sentence describes an option that companies could

choose (ldquolight tubesrdquo) instead o the option described in the previous sen-

tence (ldquoull-pane windowsrdquo)

Choices A B and D are incorrect because each proposes a transitional

adverb that does not accurately reflect the relationship between this sen-

tence and the one preceding it

QUESTION 10

Choice C is the best answer It provides the correct relative pronoun to cor-

respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-

duce the definition that ollows

Choices A B and D are incorrect because each offers a pronoun inappropri-

ate or opening a dependent clause defining ldquolight tubesrdquo

QUESTION 11

Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the

noun ldquomeansrdquo particularly as a way to connect it to another noun or verb

Choices A C and D are incorrect because each results in nonstandard

phrasing with ldquomeansrdquo

QUESTION 12

Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-

responds with the plural noun ldquosettlersrdquo

Choices B C and D are incorrect because each provides either a nonstan-

dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo

QUESTION 13

Choice C is the best answer It creates a transition rom the poor ood qual-

ity mentioned in the previous sentence to the inormation about Harvey in

the remainder o the sentence

7262019 PrepScholar Sat Practice Test 3 Answers

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16

Choices A B and D are incorrect because none offers a transition rom the

previous sentence or a detail that corresponds precisely with the inorma-

tion in the remainder o the sentence

QUESTION 14

Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens

with a comma

Choices A B and C are incorrect because each proposes punctuation that

creates an inappropriately strong separation between the subject ldquoFred

Harveyrdquo and the verb ldquodecidedrdquo

QUESTION 15

Choice B is the best answer It provides the plural verb and plural posses-

sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo

Choices A C and D are incorrect because each either ails to provide a verb

that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide

the appropriate possessive pronoun

QUESTION 16

Choice C is the best answer It accurately echoes an earlier characterization

o the ood as being o ldquoterrible qualityrdquo while maintaining the established

tone o the passage

Choices A B and D are incorrect either because the word is less ormal than

the established tone o the passage (ldquoickyrdquo) or because it illogically attributes

agency to ood (ldquosinisterrdquo ldquosurlyrdquo)

QUESTION 17

Choice C is the best answer It accurately interprets ldquonot content to ollow

conventional business practicesrdquo as logically introducing the new practice o

ldquoemploying womenrdquo described in the ollowing sentences

Choices A B and D are incorrect because none recognizes why the sentence

is relevant to this particular location in the passage

QUESTION 18

Choice B is the best answer It is concise and ree o redundancies

Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and

ldquotremendousrdquo adjectives so close in meaning that together they present a

redundancy

7262019 PrepScholar Sat Practice Test 3 Answers

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17

QUESTION 19

Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary

reerence to ldquosuch regulationsrdquo in the previous clause

Choices A B and C are incorrect because each lacks a necessary subject

such as a pronoun or noun

QUESTION 20

Choice C is the best answer It reers directly to benefits or the restaurantsrsquo

emale employees the subject o the previous sentence

Choices A B and D are incorrect because none logically builds upon the

sentence that precedes it

QUESTION 21

Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo

Choices A B and C are incorrect because each uses the punctuation or

a dependent clause (ldquoLiving independently and demonstrating an intense

work ethicrdquo) as i it were an independent clause

QUESTION 22

Choice A is the best answer It recognizes that the new inormation sup-

ports the previous sentencersquos claim that ldquothe Harvey Girls became known as

a transormative orcerdquo

Choices B C and D are incorrect because each misinterprets the relation-

ship between the proposed text and the passage

QUESTION 23

Choice A is the best answer It opens with a clause that identifies how

1-MCP affects apples which ocuses the sentence on 1-MCP as the subject

and allows the ideas in the sentence to progress logically

Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy

QUESTION 24

Choice D is the best answer Only the comma is necessary to separate

ldquoethylenerdquo rom the appositive noun phrase that defines it

Choices A B and C are incorrect because each creates a comma splice and

or adds unnecessary words

7262019 PrepScholar Sat Practice Test 3 Answers

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18

QUESTION 25

Choice B is the best answer It offers an adjective that accurately describes

resh apples

Choices A C and D are incorrect because each proposes an adjective that

does not describe a plausible ruit texture

QUESTION 26

Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-

sponds with the plural reerent ldquoapplesrdquo

Choices B C and D are incorrect because none provides a pronoun that is

both possessive and plural

QUESTION 27

Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins

the relative clause

Choices A B and C are incorrect because each contains a pronoun that

either does not correspond with the human reerent ldquoconsumersrdquo or does

not correctly begin the relative clause

QUESTION 28

Choice B is the best answer It provides the present tense verb ldquodordquo which

corresponds to the present tense established earlier in the sentence

Choices A C and D are incorrect because each contains a verb that deviates

rom the simple present tense established in the sentence

QUESTION 29

Choice B is the best answer It provides a colon to appropriately introduce the

clause that ollows an elaboration on the preceding claim that Bartlett pears

are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo

Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically

QUESTION 30

Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-

trast with a previous idea and goes on to mention that 1-MCP can have

negative effects Sentence 1 continues the discussion o benefits o 1-MCP

and sentence 2 names the adverse effect o limiting scent production so the

most logical spot or sentence 4 is between these sentences

7262019 PrepScholar Sat Practice Test 3 Answers

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19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240

21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340

22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440

23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540

24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

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25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

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26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

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27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040

29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3140

30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3440

33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640

35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 7: PrepScholar Sat Practice Test 3 Answers

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6

QUESTION 21

Choice D is the best answer Te author explains that Ken Dial created an

experiment to study the evolution o flight by observing how baby Chukars

learn to fly During the experiment Dial noticed the unusual way Chukars

use their ldquolsquowings and legs cooperativelyrsquordquo to scale hay bales (lines 38-43) and

he created ldquoa series o ingenious experimentsrdquo (line 46) to study this obser- vation Afer his additional experiments Dial determined that these baby

birds angle ldquotheir wings differently rom birds in flightrdquo (lines 49-50)

Choices A B and C are incorrect because they do not accurately reflect the

sequence o events in the passage

QUESTION 22

Choice A is the best answer In lines 6-9 the author explains that Dial was

ldquochallengedrdquo or dared by graduate students to develop ldquonew datardquo on a long-

standing scientific debate (the ldquoground-up-tree-downrdquo theory)

Choices B C and D are incorrect because in this context ldquochallengedrdquo does

not mean required disputed with or competed with

QUESTION 23

Choice A is the best answer Te author explains that Dial created his initial

experiment to try and create ldquonew data on the age-old ground-up-tree-down

debaterdquo and that he looked or ldquocluesrdquo in ldquohow baby game birds learned to

flyrdquo (lines 8-11) Te note at the beginning o the passage explains the ldquoage-

old ground-up-tree down debaterdquo and offers two different theories on howbirds evolved to fly Finally the last paragraph o the passage discusses WAIR

in an evolutionary context

Choices B C and D are incorrect because they do not identiy Dialrsquos central

assumption in setting up his research

QUESTION 24

Choice B is the best answer In lines 6-11 the author provides evidence that

Dialrsquos central assumption in setting up his research is that the acquisition o

flight in young birds is linked to the acquisition o flight in their ancestorsTe author notes that Dial created a project to ldquocome up with new data on

the age-old ground-up-tree-down debaterdquo

Choices A C and D do not provide the best evidence that Dialrsquos central

assumption in setting up his research is that the acquisition o flight in young

birds is linked to the acquisition o flight in their ancestors Choices A C

and D are incorrect because they ocus on Dialrsquos experiment and his obser-

vations on ground birds

7262019 PrepScholar Sat Practice Test 3 Answers

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7

QUESTION 25

Choice C is the best answer When a rancher observed Dialrsquos laboratory

setup he was ldquoincredulousrdquo that the Chukars were living on the ground and

he advised Dial to give the birds ldquosomething to climb onrdquo (lines 16-23) Tis

ldquokey piece o advicerdquo (line 14) led Dial to add hay bales to his laboratory

Dial later noticed that the Chukars were using their legs and wings to scalethe hay bales and this observation became the ocal point o his research

Choices A B and D are incorrect because the incident with the local rancher

did not serve to reveal Dialrsquos motivation or creating the project emphasize

differences in laboratory and field research or introduce a contributor to a

scientific theory

QUESTION 26

Choice C is the best answer Te author explains that Dialrsquos ldquoaha momentrdquo

came when he determined the Chukars used ldquotheir legs and wings coop-erativelyrdquo to scale the hay bales (lines 40-42) Dial then created additional

experiments to study how the birds dealt with gradually steeper inclines

ldquo[he filmed] the birds as they raced up textured ramps tilted at increasing

anglesrdquo (lines 46-48)

Choices A B and D are incorrect because Dialrsquos ldquoaha momentrdquo was not ol-

lowed by Dial teaching the birds to fly studying videos to find out why the

birds no longer hopped or consulting with other researchers

QUESTION 27

Choice B is the best answer Dial observed that as the Chukars raced up

steep ramps they ldquobegan to flaprdquo and ldquoaimed their flapping down and back-

ward using the orce to keep their eet firmly pressed against the ramprdquo

(lines 49-53) Dial determined that the position o their flapping wings acil-

itated the baby Chukarsrsquo traction on the steep ramps

Choices A C and D are incorrect because the passage does not indicate that

the Chukarsrsquo speed alternation o wing and oot movement or continual

hopping motions acilitated their traction on steep ramps

QUESTION 28

Choice B is the best answer In lines 61-63 the author explains that Dial

named his scientific finding ldquoWAIR or wing-assisted incline running and

went on to document it in a wide range o speciesrdquo In this context Dial

ldquodocumentedrdquo or recorded the existence o WAIR in numerous bird species

Choices A C and D are incorrect because in this context ldquodocumentrdquo does

not mean to portray publish or process

7262019 PrepScholar Sat Practice Test 3 Answers

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8

QUESTION 29

Choice D is the best answer In lines 70-74 the author explains that glid-

ing animals do not use a ldquoflapping flight strokerdquo or WAIR wing-assisted

incline running Since Chukars a ground bird use WAIR to help scale steep

inclines it can be reasonably inerred that gliding animals do not use WAIR

to aid in climbing slopes

Choices A B and C are incorrect because the passage does not include

inormation on gliding animalsrsquo offspring their method o locomotion or

their eeding habits

QUESTION 30

Choice D is the best answer In lines 73-75 the author provides evidence

that ldquothe flapping flight strokerdquo is ldquosomething gliding animals donrsquot dordquo

Choices A B and C do not provide the best evidence that gliding animalsdo not use a flapping stroke to aid in climbing slopes Tese choices do not

contain inormation about gliding animals

QUESTION 31

Choice B is the best answer In lines 21-24 the authors o Passage 1 state

societyrsquos ldquocommon happinessrdquo is dependent on women never becoming

involved in politics In this context the authors o Passage 1 are sug-

gesting that all members o society can have a ldquocommonrdquo or shared

happiness

Choices A C and D are incorrect because in this context ldquocommonrdquo does

not mean average coarse or similar

QUESTION 32

Choice C is the best answer In lines 25-30 the authors o Passage 1 state

that women should seek ldquogentle occupations and the cares o the homerdquo

so they can avoid perorming difficult or ldquostrenuousrdquo and unpleasant or

ldquoonerousrdquo tasks

Choices A B and D are incorrect because the authors o Passage 1 do notsuggest that running a household and raising children are rewarding or

both sexes yield less value or society or require proessional or political

skills

QUESTION 33

Choice C is the best answer In lines 25-30 the authors o Passage 1 provide

evidence that women should run households and raise children because

these roles do not require ldquostrenuous habits and onerous dutiesrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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9

Choices A B and D do not provide the best evidence that running a house-

hold and raising children entail very ew activities that are difficult or

unpleasant rather these lines offer general inormation about the differ-

ences between the sexes

QUESTION 34

Choice D is the best answer In lines 41-46 Wollstonecraf argues that i

women do not receive an education ldquoto become the companion o manrdquo or

one that is comparable to menrsquos education then society will not progress in

ldquoknowledge and virtuerdquo

Choices A B and C are incorrect because Wollstonecraf does not suggest

that society can progress only i women have happiness and financial secu-

rity ollow societal rules or replace men as figures o power

QUESTION 35

Choice C is the best answer Wollstonecraf argues that women should be

granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo

(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-

enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context

Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or

intellect and allow women to consider their role in society

Choices A B and D are incorrect because in this context ldquoreasonrdquo does not

mean motive sanity or explanation

QUESTION 36

Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws

passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to

ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf

is arguing that societyrsquos leaders grant men reedoms that are denied to women

Choices B C and D are incorrect because Wollstonecraf does not claim

that societyrsquos leaders have granted reedoms that created a general reduction

in individual virtue caused arguments about happiness or ensured equality

or all people

QUESTION 37

Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-

dence that societyrsquos leaders grant reedoms that privilege men She argues

that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-

lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to

ldquocontend or their reedomrdquo

Choices A B and C do not provide the best evidence that societyrsquos leaders

grant reedoms that privilege men over women

7262019 PrepScholar Sat Practice Test 3 Answers

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10

QUESTION 38

Choice C is the best answer Wollstonecraf cites the statement made by

the authors o Passage 1 that excluding women rom political participation

is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)

Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe

abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument

by highlighting a flaw in the reasoning presented by the authors o Passage 1

Choices A B and D are incorrect because Wollstonecraf does not reer to

the statement made in Passage 1 to call into question the authorsrsquo qualifica-

tions dispute the assertion that women are excluded by their own govern-

ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on

gender roles

QUESTION 39

Choice A is the best answer Te authors o Passage 1 argue that while

restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)

this restriction is necessary or societyrsquos overall happiness (lines 13-17)

Wollstonecraf however strongly challenges this argument asking the

authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-

doms are granted to women and likening societyrsquos male leaders to tyrants as

they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in

the darkrdquo (lines 78-88)

Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2

QUESTION 40

Choice D is the best answer Te authors o Passage 1 admit that women are

ldquoexcluded by the other hal [men] rom any participation in governmentrdquo

(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws

that deny women ldquocivil and political rightsrdquo (line 86)

Choices A B and C are incorrect because the authors o both passages

would not agree that women had the same preerences as men required agood education or were as happy as men

QUESTION 41

Choice A is the best answer Wollstonecraf argues in the final paragraph

o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women

ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would

most likely argue that allowing women these rights would be ldquoa reversal o

[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos

interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1240

11

mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created

two sexes or a particular reason so while men can exercise civil and politi-

cal rights women are not naturally suited to these activities (lines 30-36)

Choices B and C are incorrect because they are not supported by inorma-

tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do

not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo

QUESTION 42

Choice C is the best answer When discussing problems with bee colo-

nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo

(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-

tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a

tentative tone and provides urther evidence that the authors believe but are

not certain that their hypothesis is correct

Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone

QUESTION 43

Choice C is the best answer In lines 24-28 the authors hypothesize that bee

colonies will be susceptible to mite inestations i they do not occasionally

eed on pyrethrum producing plants In lines 42-46 they suggest creating a

trial where a ldquosmall number o commercial honey bee colonies are offered a

number o pyrethrum producing plantsrdquo to test their hypothesis

Choices A B and D are incorrect because the authors do not hypothesize that

honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees

to develop secondary inections that beekeepers should increase their use o

insecticides or that humans are more susceptible to varroa mites

QUESTION 44

Choice D is the best answer In lines 24-28 the authors provide evidence

that a bee colony may be more resistant to mite inections i the bees eat

pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-

nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees

Choices A B and C do not describe any o the authorsrsquo hypotheses

QUESTION 45

Choice D is the best answer Te authors explain that when beekeepers

use commercially produced insecticides to fight mite inections they may

ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-

cientrdquo (lines 31-35)

7262019 PrepScholar Sat Practice Test 3 Answers

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12

Choices A B and C are incorrect because the authors do not suggest that

beekeepersrsquo use o commercially produced insecticides increases mite popu-

lations kills bacteria or destroys beesrsquo primary ood source

QUESTION 46

Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-

ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo

Choices A B and D are incorrect because they do not provide the best evi-

dence that beekeepersrsquo use o commercially produced insecticides may be

harmul to bees choices A B and D ocus on mite inestationsrsquo impact on

honeybees

QUESTION 47

Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some

bees Te authors then state ldquoWe urther postulate that the proper dosage

necessary to prevent mite inestation may be better lef to the beesrdquo (lines

35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the

bees may naturally control mite inestations better than insecticides

Choices A C and D are incorrect because in this context ldquopostulaterdquo does

not mean to make an unounded assumption question a belie or theory or

conclude based on firm evidence

QUESTION 48

Choice B is the best answer In the ourth paragraph the authors propose

a trial to study i honeybeesrsquo consumption o pyrethrum producing plants

helps the honeybees deend against mite inestations In the experiment the

authors plan to offer honey bee colonies both pyrethrum producing plants

and ldquoa typical bee ood source such as cloverrdquo to determine i these different

diets affect the beesrsquo susceptibility to mite inestations

Choices A C and D are incorrect because the main purpose o the ourth

paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished

experiment

QUESTION 49

Choice A is the best answer In lines 43-45 the authors propose a scien-

tific trial in which honeybees are ldquooffered a number o pyrethrum producing

plants as well as a typical bee ood source such as cloverrdquo Since the authors

contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood

sourcerdquo it can be assumed that clover does not produce pyrethrums

7262019 PrepScholar Sat Practice Test 3 Answers

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13

Choice B is incorrect because it is stated in the passage Choices C and D are

incorrect because they are not assumptions made by the authors

QUESTION 50

Choice B is the best answer Te table shows that 77 percent o the honeybee

colonies with colony collapse disorder were inected by all our pathogens

Choices A C and D are incorrect because they do not identiy the percent

o honeybee colonies with colony collapse disorder that were inected by all

our pathogens as based on data in the table

QUESTION 51

Choice D is the best answer Te table shows that 81 percent o colo-

nies without colony collapse disorder were affected by the pathogen

Nosema ceranae

Choices A B and C are incorrect because they do not identiy the pathogen

that inected the highest percentage o honeybee colonies without colony

collapse disorder as based on data in the table

QUESTION 52

Choice D is the best answer Te table discusses pathogen occurrence in

honeybee colonies but it includes no inormation as to whether these hon-

eybees were inected with mites Because the table does not suggest mites

inested the honeybee colonies no conclusions can be made as to whether

mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)

Choices A B and C are incorrect because the table provides no inormation

about whether these honeybees were inected with mites

Section 2 Writing and Language Test

QUESTION 1

Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-

ates a parallel structure within the list that begins with ldquohappierrdquo

Choices B C and D are incorrect because none creates a parallel structure

within the list o qualities

QUESTION 2

Choice B is the best answer Te ways in which exposure to natural light

affects employees is the main subject o the passage

7262019 PrepScholar Sat Practice Test 3 Answers

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14

Choices A C and D are incorrect because none introduces the topic dis-

cussed in the remainder o the passage

QUESTION 3

Choice C is the best answer It accurately notes that the proposed sentence

would be placed directly between the first mention o circadian rhythms andthe explanation o the term

Choices A B and D are incorrect because each misinterprets the relation-

ship between the proposed additional text and the ideas in the paragraph

QUESTION 4

Choice C is the best answer It provides the correct possessive construction

or ldquobodyrdquo which must be a singular noun when discussed in general terms

as in this sentence Choice C also provides the correct plural construction

or ldquoclocksrdquo

Choices A B and D are incorrect because each applies either a possessive or

a plural construction in a place where it doesnrsquot belong

QUESTION 5

Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular

noun ldquoabsenteeismrdquo

Choices B C and D are incorrect because each provides a verb that

either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy

QUESTION 6

Choice B is the best answer It contains a direct reerence to productivity

the topic introduced in the previous sentence

Choices A C and D are incorrect because none directly addresses employee

productivity the primary subject o the previous sentence

QUESTION 7

Choice A is the best answer It opens with a reerence to lowered worker

productivity creating a transition rom the previous paragraph and clearly

positions the high energy costs o artificial light sources as an additional

disadvantage

Choices B C and D are incorrect because none o the choices offer an ade-

quate transition rom the previous paragraph Each awkwardly inserts the

issue o lower worker productivity into a statement about the high energy

costs o artificial light sources

7262019 PrepScholar Sat Practice Test 3 Answers

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15

QUESTION 8

Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-

cate that the savings occurred every year

Choices A B and C are incorrect because each proposes an option that

would result in a redundancy with ldquoannualrdquo

QUESTION 9

Choice C is the best answer It provides a transitional adverb that accurately

communicates that this sentence describes an option that companies could

choose (ldquolight tubesrdquo) instead o the option described in the previous sen-

tence (ldquoull-pane windowsrdquo)

Choices A B and D are incorrect because each proposes a transitional

adverb that does not accurately reflect the relationship between this sen-

tence and the one preceding it

QUESTION 10

Choice C is the best answer It provides the correct relative pronoun to cor-

respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-

duce the definition that ollows

Choices A B and D are incorrect because each offers a pronoun inappropri-

ate or opening a dependent clause defining ldquolight tubesrdquo

QUESTION 11

Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the

noun ldquomeansrdquo particularly as a way to connect it to another noun or verb

Choices A C and D are incorrect because each results in nonstandard

phrasing with ldquomeansrdquo

QUESTION 12

Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-

responds with the plural noun ldquosettlersrdquo

Choices B C and D are incorrect because each provides either a nonstan-

dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo

QUESTION 13

Choice C is the best answer It creates a transition rom the poor ood qual-

ity mentioned in the previous sentence to the inormation about Harvey in

the remainder o the sentence

7262019 PrepScholar Sat Practice Test 3 Answers

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16

Choices A B and D are incorrect because none offers a transition rom the

previous sentence or a detail that corresponds precisely with the inorma-

tion in the remainder o the sentence

QUESTION 14

Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens

with a comma

Choices A B and C are incorrect because each proposes punctuation that

creates an inappropriately strong separation between the subject ldquoFred

Harveyrdquo and the verb ldquodecidedrdquo

QUESTION 15

Choice B is the best answer It provides the plural verb and plural posses-

sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo

Choices A C and D are incorrect because each either ails to provide a verb

that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide

the appropriate possessive pronoun

QUESTION 16

Choice C is the best answer It accurately echoes an earlier characterization

o the ood as being o ldquoterrible qualityrdquo while maintaining the established

tone o the passage

Choices A B and D are incorrect either because the word is less ormal than

the established tone o the passage (ldquoickyrdquo) or because it illogically attributes

agency to ood (ldquosinisterrdquo ldquosurlyrdquo)

QUESTION 17

Choice C is the best answer It accurately interprets ldquonot content to ollow

conventional business practicesrdquo as logically introducing the new practice o

ldquoemploying womenrdquo described in the ollowing sentences

Choices A B and D are incorrect because none recognizes why the sentence

is relevant to this particular location in the passage

QUESTION 18

Choice B is the best answer It is concise and ree o redundancies

Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and

ldquotremendousrdquo adjectives so close in meaning that together they present a

redundancy

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17

QUESTION 19

Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary

reerence to ldquosuch regulationsrdquo in the previous clause

Choices A B and C are incorrect because each lacks a necessary subject

such as a pronoun or noun

QUESTION 20

Choice C is the best answer It reers directly to benefits or the restaurantsrsquo

emale employees the subject o the previous sentence

Choices A B and D are incorrect because none logically builds upon the

sentence that precedes it

QUESTION 21

Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo

Choices A B and C are incorrect because each uses the punctuation or

a dependent clause (ldquoLiving independently and demonstrating an intense

work ethicrdquo) as i it were an independent clause

QUESTION 22

Choice A is the best answer It recognizes that the new inormation sup-

ports the previous sentencersquos claim that ldquothe Harvey Girls became known as

a transormative orcerdquo

Choices B C and D are incorrect because each misinterprets the relation-

ship between the proposed text and the passage

QUESTION 23

Choice A is the best answer It opens with a clause that identifies how

1-MCP affects apples which ocuses the sentence on 1-MCP as the subject

and allows the ideas in the sentence to progress logically

Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy

QUESTION 24

Choice D is the best answer Only the comma is necessary to separate

ldquoethylenerdquo rom the appositive noun phrase that defines it

Choices A B and C are incorrect because each creates a comma splice and

or adds unnecessary words

7262019 PrepScholar Sat Practice Test 3 Answers

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18

QUESTION 25

Choice B is the best answer It offers an adjective that accurately describes

resh apples

Choices A C and D are incorrect because each proposes an adjective that

does not describe a plausible ruit texture

QUESTION 26

Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-

sponds with the plural reerent ldquoapplesrdquo

Choices B C and D are incorrect because none provides a pronoun that is

both possessive and plural

QUESTION 27

Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins

the relative clause

Choices A B and C are incorrect because each contains a pronoun that

either does not correspond with the human reerent ldquoconsumersrdquo or does

not correctly begin the relative clause

QUESTION 28

Choice B is the best answer It provides the present tense verb ldquodordquo which

corresponds to the present tense established earlier in the sentence

Choices A C and D are incorrect because each contains a verb that deviates

rom the simple present tense established in the sentence

QUESTION 29

Choice B is the best answer It provides a colon to appropriately introduce the

clause that ollows an elaboration on the preceding claim that Bartlett pears

are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo

Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically

QUESTION 30

Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-

trast with a previous idea and goes on to mention that 1-MCP can have

negative effects Sentence 1 continues the discussion o benefits o 1-MCP

and sentence 2 names the adverse effect o limiting scent production so the

most logical spot or sentence 4 is between these sentences

7262019 PrepScholar Sat Practice Test 3 Answers

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19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240

21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340

22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540

24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

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25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

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26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

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27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3740

36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3840

37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3940

38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040

QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 8: PrepScholar Sat Practice Test 3 Answers

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httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 840

7

QUESTION 25

Choice C is the best answer When a rancher observed Dialrsquos laboratory

setup he was ldquoincredulousrdquo that the Chukars were living on the ground and

he advised Dial to give the birds ldquosomething to climb onrdquo (lines 16-23) Tis

ldquokey piece o advicerdquo (line 14) led Dial to add hay bales to his laboratory

Dial later noticed that the Chukars were using their legs and wings to scalethe hay bales and this observation became the ocal point o his research

Choices A B and D are incorrect because the incident with the local rancher

did not serve to reveal Dialrsquos motivation or creating the project emphasize

differences in laboratory and field research or introduce a contributor to a

scientific theory

QUESTION 26

Choice C is the best answer Te author explains that Dialrsquos ldquoaha momentrdquo

came when he determined the Chukars used ldquotheir legs and wings coop-erativelyrdquo to scale the hay bales (lines 40-42) Dial then created additional

experiments to study how the birds dealt with gradually steeper inclines

ldquo[he filmed] the birds as they raced up textured ramps tilted at increasing

anglesrdquo (lines 46-48)

Choices A B and D are incorrect because Dialrsquos ldquoaha momentrdquo was not ol-

lowed by Dial teaching the birds to fly studying videos to find out why the

birds no longer hopped or consulting with other researchers

QUESTION 27

Choice B is the best answer Dial observed that as the Chukars raced up

steep ramps they ldquobegan to flaprdquo and ldquoaimed their flapping down and back-

ward using the orce to keep their eet firmly pressed against the ramprdquo

(lines 49-53) Dial determined that the position o their flapping wings acil-

itated the baby Chukarsrsquo traction on the steep ramps

Choices A C and D are incorrect because the passage does not indicate that

the Chukarsrsquo speed alternation o wing and oot movement or continual

hopping motions acilitated their traction on steep ramps

QUESTION 28

Choice B is the best answer In lines 61-63 the author explains that Dial

named his scientific finding ldquoWAIR or wing-assisted incline running and

went on to document it in a wide range o speciesrdquo In this context Dial

ldquodocumentedrdquo or recorded the existence o WAIR in numerous bird species

Choices A C and D are incorrect because in this context ldquodocumentrdquo does

not mean to portray publish or process

7262019 PrepScholar Sat Practice Test 3 Answers

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8

QUESTION 29

Choice D is the best answer In lines 70-74 the author explains that glid-

ing animals do not use a ldquoflapping flight strokerdquo or WAIR wing-assisted

incline running Since Chukars a ground bird use WAIR to help scale steep

inclines it can be reasonably inerred that gliding animals do not use WAIR

to aid in climbing slopes

Choices A B and C are incorrect because the passage does not include

inormation on gliding animalsrsquo offspring their method o locomotion or

their eeding habits

QUESTION 30

Choice D is the best answer In lines 73-75 the author provides evidence

that ldquothe flapping flight strokerdquo is ldquosomething gliding animals donrsquot dordquo

Choices A B and C do not provide the best evidence that gliding animalsdo not use a flapping stroke to aid in climbing slopes Tese choices do not

contain inormation about gliding animals

QUESTION 31

Choice B is the best answer In lines 21-24 the authors o Passage 1 state

societyrsquos ldquocommon happinessrdquo is dependent on women never becoming

involved in politics In this context the authors o Passage 1 are sug-

gesting that all members o society can have a ldquocommonrdquo or shared

happiness

Choices A C and D are incorrect because in this context ldquocommonrdquo does

not mean average coarse or similar

QUESTION 32

Choice C is the best answer In lines 25-30 the authors o Passage 1 state

that women should seek ldquogentle occupations and the cares o the homerdquo

so they can avoid perorming difficult or ldquostrenuousrdquo and unpleasant or

ldquoonerousrdquo tasks

Choices A B and D are incorrect because the authors o Passage 1 do notsuggest that running a household and raising children are rewarding or

both sexes yield less value or society or require proessional or political

skills

QUESTION 33

Choice C is the best answer In lines 25-30 the authors o Passage 1 provide

evidence that women should run households and raise children because

these roles do not require ldquostrenuous habits and onerous dutiesrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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9

Choices A B and D do not provide the best evidence that running a house-

hold and raising children entail very ew activities that are difficult or

unpleasant rather these lines offer general inormation about the differ-

ences between the sexes

QUESTION 34

Choice D is the best answer In lines 41-46 Wollstonecraf argues that i

women do not receive an education ldquoto become the companion o manrdquo or

one that is comparable to menrsquos education then society will not progress in

ldquoknowledge and virtuerdquo

Choices A B and C are incorrect because Wollstonecraf does not suggest

that society can progress only i women have happiness and financial secu-

rity ollow societal rules or replace men as figures o power

QUESTION 35

Choice C is the best answer Wollstonecraf argues that women should be

granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo

(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-

enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context

Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or

intellect and allow women to consider their role in society

Choices A B and D are incorrect because in this context ldquoreasonrdquo does not

mean motive sanity or explanation

QUESTION 36

Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws

passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to

ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf

is arguing that societyrsquos leaders grant men reedoms that are denied to women

Choices B C and D are incorrect because Wollstonecraf does not claim

that societyrsquos leaders have granted reedoms that created a general reduction

in individual virtue caused arguments about happiness or ensured equality

or all people

QUESTION 37

Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-

dence that societyrsquos leaders grant reedoms that privilege men She argues

that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-

lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to

ldquocontend or their reedomrdquo

Choices A B and C do not provide the best evidence that societyrsquos leaders

grant reedoms that privilege men over women

7262019 PrepScholar Sat Practice Test 3 Answers

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10

QUESTION 38

Choice C is the best answer Wollstonecraf cites the statement made by

the authors o Passage 1 that excluding women rom political participation

is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)

Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe

abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument

by highlighting a flaw in the reasoning presented by the authors o Passage 1

Choices A B and D are incorrect because Wollstonecraf does not reer to

the statement made in Passage 1 to call into question the authorsrsquo qualifica-

tions dispute the assertion that women are excluded by their own govern-

ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on

gender roles

QUESTION 39

Choice A is the best answer Te authors o Passage 1 argue that while

restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)

this restriction is necessary or societyrsquos overall happiness (lines 13-17)

Wollstonecraf however strongly challenges this argument asking the

authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-

doms are granted to women and likening societyrsquos male leaders to tyrants as

they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in

the darkrdquo (lines 78-88)

Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2

QUESTION 40

Choice D is the best answer Te authors o Passage 1 admit that women are

ldquoexcluded by the other hal [men] rom any participation in governmentrdquo

(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws

that deny women ldquocivil and political rightsrdquo (line 86)

Choices A B and C are incorrect because the authors o both passages

would not agree that women had the same preerences as men required agood education or were as happy as men

QUESTION 41

Choice A is the best answer Wollstonecraf argues in the final paragraph

o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women

ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would

most likely argue that allowing women these rights would be ldquoa reversal o

[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos

interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as

7262019 PrepScholar Sat Practice Test 3 Answers

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11

mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created

two sexes or a particular reason so while men can exercise civil and politi-

cal rights women are not naturally suited to these activities (lines 30-36)

Choices B and C are incorrect because they are not supported by inorma-

tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do

not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo

QUESTION 42

Choice C is the best answer When discussing problems with bee colo-

nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo

(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-

tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a

tentative tone and provides urther evidence that the authors believe but are

not certain that their hypothesis is correct

Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone

QUESTION 43

Choice C is the best answer In lines 24-28 the authors hypothesize that bee

colonies will be susceptible to mite inestations i they do not occasionally

eed on pyrethrum producing plants In lines 42-46 they suggest creating a

trial where a ldquosmall number o commercial honey bee colonies are offered a

number o pyrethrum producing plantsrdquo to test their hypothesis

Choices A B and D are incorrect because the authors do not hypothesize that

honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees

to develop secondary inections that beekeepers should increase their use o

insecticides or that humans are more susceptible to varroa mites

QUESTION 44

Choice D is the best answer In lines 24-28 the authors provide evidence

that a bee colony may be more resistant to mite inections i the bees eat

pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-

nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees

Choices A B and C do not describe any o the authorsrsquo hypotheses

QUESTION 45

Choice D is the best answer Te authors explain that when beekeepers

use commercially produced insecticides to fight mite inections they may

ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-

cientrdquo (lines 31-35)

7262019 PrepScholar Sat Practice Test 3 Answers

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12

Choices A B and C are incorrect because the authors do not suggest that

beekeepersrsquo use o commercially produced insecticides increases mite popu-

lations kills bacteria or destroys beesrsquo primary ood source

QUESTION 46

Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-

ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo

Choices A B and D are incorrect because they do not provide the best evi-

dence that beekeepersrsquo use o commercially produced insecticides may be

harmul to bees choices A B and D ocus on mite inestationsrsquo impact on

honeybees

QUESTION 47

Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some

bees Te authors then state ldquoWe urther postulate that the proper dosage

necessary to prevent mite inestation may be better lef to the beesrdquo (lines

35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the

bees may naturally control mite inestations better than insecticides

Choices A C and D are incorrect because in this context ldquopostulaterdquo does

not mean to make an unounded assumption question a belie or theory or

conclude based on firm evidence

QUESTION 48

Choice B is the best answer In the ourth paragraph the authors propose

a trial to study i honeybeesrsquo consumption o pyrethrum producing plants

helps the honeybees deend against mite inestations In the experiment the

authors plan to offer honey bee colonies both pyrethrum producing plants

and ldquoa typical bee ood source such as cloverrdquo to determine i these different

diets affect the beesrsquo susceptibility to mite inestations

Choices A C and D are incorrect because the main purpose o the ourth

paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished

experiment

QUESTION 49

Choice A is the best answer In lines 43-45 the authors propose a scien-

tific trial in which honeybees are ldquooffered a number o pyrethrum producing

plants as well as a typical bee ood source such as cloverrdquo Since the authors

contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood

sourcerdquo it can be assumed that clover does not produce pyrethrums

7262019 PrepScholar Sat Practice Test 3 Answers

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13

Choice B is incorrect because it is stated in the passage Choices C and D are

incorrect because they are not assumptions made by the authors

QUESTION 50

Choice B is the best answer Te table shows that 77 percent o the honeybee

colonies with colony collapse disorder were inected by all our pathogens

Choices A C and D are incorrect because they do not identiy the percent

o honeybee colonies with colony collapse disorder that were inected by all

our pathogens as based on data in the table

QUESTION 51

Choice D is the best answer Te table shows that 81 percent o colo-

nies without colony collapse disorder were affected by the pathogen

Nosema ceranae

Choices A B and C are incorrect because they do not identiy the pathogen

that inected the highest percentage o honeybee colonies without colony

collapse disorder as based on data in the table

QUESTION 52

Choice D is the best answer Te table discusses pathogen occurrence in

honeybee colonies but it includes no inormation as to whether these hon-

eybees were inected with mites Because the table does not suggest mites

inested the honeybee colonies no conclusions can be made as to whether

mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)

Choices A B and C are incorrect because the table provides no inormation

about whether these honeybees were inected with mites

Section 2 Writing and Language Test

QUESTION 1

Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-

ates a parallel structure within the list that begins with ldquohappierrdquo

Choices B C and D are incorrect because none creates a parallel structure

within the list o qualities

QUESTION 2

Choice B is the best answer Te ways in which exposure to natural light

affects employees is the main subject o the passage

7262019 PrepScholar Sat Practice Test 3 Answers

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14

Choices A C and D are incorrect because none introduces the topic dis-

cussed in the remainder o the passage

QUESTION 3

Choice C is the best answer It accurately notes that the proposed sentence

would be placed directly between the first mention o circadian rhythms andthe explanation o the term

Choices A B and D are incorrect because each misinterprets the relation-

ship between the proposed additional text and the ideas in the paragraph

QUESTION 4

Choice C is the best answer It provides the correct possessive construction

or ldquobodyrdquo which must be a singular noun when discussed in general terms

as in this sentence Choice C also provides the correct plural construction

or ldquoclocksrdquo

Choices A B and D are incorrect because each applies either a possessive or

a plural construction in a place where it doesnrsquot belong

QUESTION 5

Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular

noun ldquoabsenteeismrdquo

Choices B C and D are incorrect because each provides a verb that

either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy

QUESTION 6

Choice B is the best answer It contains a direct reerence to productivity

the topic introduced in the previous sentence

Choices A C and D are incorrect because none directly addresses employee

productivity the primary subject o the previous sentence

QUESTION 7

Choice A is the best answer It opens with a reerence to lowered worker

productivity creating a transition rom the previous paragraph and clearly

positions the high energy costs o artificial light sources as an additional

disadvantage

Choices B C and D are incorrect because none o the choices offer an ade-

quate transition rom the previous paragraph Each awkwardly inserts the

issue o lower worker productivity into a statement about the high energy

costs o artificial light sources

7262019 PrepScholar Sat Practice Test 3 Answers

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15

QUESTION 8

Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-

cate that the savings occurred every year

Choices A B and C are incorrect because each proposes an option that

would result in a redundancy with ldquoannualrdquo

QUESTION 9

Choice C is the best answer It provides a transitional adverb that accurately

communicates that this sentence describes an option that companies could

choose (ldquolight tubesrdquo) instead o the option described in the previous sen-

tence (ldquoull-pane windowsrdquo)

Choices A B and D are incorrect because each proposes a transitional

adverb that does not accurately reflect the relationship between this sen-

tence and the one preceding it

QUESTION 10

Choice C is the best answer It provides the correct relative pronoun to cor-

respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-

duce the definition that ollows

Choices A B and D are incorrect because each offers a pronoun inappropri-

ate or opening a dependent clause defining ldquolight tubesrdquo

QUESTION 11

Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the

noun ldquomeansrdquo particularly as a way to connect it to another noun or verb

Choices A C and D are incorrect because each results in nonstandard

phrasing with ldquomeansrdquo

QUESTION 12

Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-

responds with the plural noun ldquosettlersrdquo

Choices B C and D are incorrect because each provides either a nonstan-

dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo

QUESTION 13

Choice C is the best answer It creates a transition rom the poor ood qual-

ity mentioned in the previous sentence to the inormation about Harvey in

the remainder o the sentence

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1740

16

Choices A B and D are incorrect because none offers a transition rom the

previous sentence or a detail that corresponds precisely with the inorma-

tion in the remainder o the sentence

QUESTION 14

Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens

with a comma

Choices A B and C are incorrect because each proposes punctuation that

creates an inappropriately strong separation between the subject ldquoFred

Harveyrdquo and the verb ldquodecidedrdquo

QUESTION 15

Choice B is the best answer It provides the plural verb and plural posses-

sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo

Choices A C and D are incorrect because each either ails to provide a verb

that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide

the appropriate possessive pronoun

QUESTION 16

Choice C is the best answer It accurately echoes an earlier characterization

o the ood as being o ldquoterrible qualityrdquo while maintaining the established

tone o the passage

Choices A B and D are incorrect either because the word is less ormal than

the established tone o the passage (ldquoickyrdquo) or because it illogically attributes

agency to ood (ldquosinisterrdquo ldquosurlyrdquo)

QUESTION 17

Choice C is the best answer It accurately interprets ldquonot content to ollow

conventional business practicesrdquo as logically introducing the new practice o

ldquoemploying womenrdquo described in the ollowing sentences

Choices A B and D are incorrect because none recognizes why the sentence

is relevant to this particular location in the passage

QUESTION 18

Choice B is the best answer It is concise and ree o redundancies

Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and

ldquotremendousrdquo adjectives so close in meaning that together they present a

redundancy

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1840

17

QUESTION 19

Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary

reerence to ldquosuch regulationsrdquo in the previous clause

Choices A B and C are incorrect because each lacks a necessary subject

such as a pronoun or noun

QUESTION 20

Choice C is the best answer It reers directly to benefits or the restaurantsrsquo

emale employees the subject o the previous sentence

Choices A B and D are incorrect because none logically builds upon the

sentence that precedes it

QUESTION 21

Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo

Choices A B and C are incorrect because each uses the punctuation or

a dependent clause (ldquoLiving independently and demonstrating an intense

work ethicrdquo) as i it were an independent clause

QUESTION 22

Choice A is the best answer It recognizes that the new inormation sup-

ports the previous sentencersquos claim that ldquothe Harvey Girls became known as

a transormative orcerdquo

Choices B C and D are incorrect because each misinterprets the relation-

ship between the proposed text and the passage

QUESTION 23

Choice A is the best answer It opens with a clause that identifies how

1-MCP affects apples which ocuses the sentence on 1-MCP as the subject

and allows the ideas in the sentence to progress logically

Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy

QUESTION 24

Choice D is the best answer Only the comma is necessary to separate

ldquoethylenerdquo rom the appositive noun phrase that defines it

Choices A B and C are incorrect because each creates a comma splice and

or adds unnecessary words

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1940

18

QUESTION 25

Choice B is the best answer It offers an adjective that accurately describes

resh apples

Choices A C and D are incorrect because each proposes an adjective that

does not describe a plausible ruit texture

QUESTION 26

Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-

sponds with the plural reerent ldquoapplesrdquo

Choices B C and D are incorrect because none provides a pronoun that is

both possessive and plural

QUESTION 27

Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins

the relative clause

Choices A B and C are incorrect because each contains a pronoun that

either does not correspond with the human reerent ldquoconsumersrdquo or does

not correctly begin the relative clause

QUESTION 28

Choice B is the best answer It provides the present tense verb ldquodordquo which

corresponds to the present tense established earlier in the sentence

Choices A C and D are incorrect because each contains a verb that deviates

rom the simple present tense established in the sentence

QUESTION 29

Choice B is the best answer It provides a colon to appropriately introduce the

clause that ollows an elaboration on the preceding claim that Bartlett pears

are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo

Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically

QUESTION 30

Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-

trast with a previous idea and goes on to mention that 1-MCP can have

negative effects Sentence 1 continues the discussion o benefits o 1-MCP

and sentence 2 names the adverse effect o limiting scent production so the

most logical spot or sentence 4 is between these sentences

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040

19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2140

20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240

21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340

22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440

23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540

24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640

25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740

26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840

27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940

28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 9: PrepScholar Sat Practice Test 3 Answers

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8

QUESTION 29

Choice D is the best answer In lines 70-74 the author explains that glid-

ing animals do not use a ldquoflapping flight strokerdquo or WAIR wing-assisted

incline running Since Chukars a ground bird use WAIR to help scale steep

inclines it can be reasonably inerred that gliding animals do not use WAIR

to aid in climbing slopes

Choices A B and C are incorrect because the passage does not include

inormation on gliding animalsrsquo offspring their method o locomotion or

their eeding habits

QUESTION 30

Choice D is the best answer In lines 73-75 the author provides evidence

that ldquothe flapping flight strokerdquo is ldquosomething gliding animals donrsquot dordquo

Choices A B and C do not provide the best evidence that gliding animalsdo not use a flapping stroke to aid in climbing slopes Tese choices do not

contain inormation about gliding animals

QUESTION 31

Choice B is the best answer In lines 21-24 the authors o Passage 1 state

societyrsquos ldquocommon happinessrdquo is dependent on women never becoming

involved in politics In this context the authors o Passage 1 are sug-

gesting that all members o society can have a ldquocommonrdquo or shared

happiness

Choices A C and D are incorrect because in this context ldquocommonrdquo does

not mean average coarse or similar

QUESTION 32

Choice C is the best answer In lines 25-30 the authors o Passage 1 state

that women should seek ldquogentle occupations and the cares o the homerdquo

so they can avoid perorming difficult or ldquostrenuousrdquo and unpleasant or

ldquoonerousrdquo tasks

Choices A B and D are incorrect because the authors o Passage 1 do notsuggest that running a household and raising children are rewarding or

both sexes yield less value or society or require proessional or political

skills

QUESTION 33

Choice C is the best answer In lines 25-30 the authors o Passage 1 provide

evidence that women should run households and raise children because

these roles do not require ldquostrenuous habits and onerous dutiesrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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9

Choices A B and D do not provide the best evidence that running a house-

hold and raising children entail very ew activities that are difficult or

unpleasant rather these lines offer general inormation about the differ-

ences between the sexes

QUESTION 34

Choice D is the best answer In lines 41-46 Wollstonecraf argues that i

women do not receive an education ldquoto become the companion o manrdquo or

one that is comparable to menrsquos education then society will not progress in

ldquoknowledge and virtuerdquo

Choices A B and C are incorrect because Wollstonecraf does not suggest

that society can progress only i women have happiness and financial secu-

rity ollow societal rules or replace men as figures o power

QUESTION 35

Choice C is the best answer Wollstonecraf argues that women should be

granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo

(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-

enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context

Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or

intellect and allow women to consider their role in society

Choices A B and D are incorrect because in this context ldquoreasonrdquo does not

mean motive sanity or explanation

QUESTION 36

Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws

passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to

ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf

is arguing that societyrsquos leaders grant men reedoms that are denied to women

Choices B C and D are incorrect because Wollstonecraf does not claim

that societyrsquos leaders have granted reedoms that created a general reduction

in individual virtue caused arguments about happiness or ensured equality

or all people

QUESTION 37

Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-

dence that societyrsquos leaders grant reedoms that privilege men She argues

that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-

lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to

ldquocontend or their reedomrdquo

Choices A B and C do not provide the best evidence that societyrsquos leaders

grant reedoms that privilege men over women

7262019 PrepScholar Sat Practice Test 3 Answers

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10

QUESTION 38

Choice C is the best answer Wollstonecraf cites the statement made by

the authors o Passage 1 that excluding women rom political participation

is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)

Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe

abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument

by highlighting a flaw in the reasoning presented by the authors o Passage 1

Choices A B and D are incorrect because Wollstonecraf does not reer to

the statement made in Passage 1 to call into question the authorsrsquo qualifica-

tions dispute the assertion that women are excluded by their own govern-

ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on

gender roles

QUESTION 39

Choice A is the best answer Te authors o Passage 1 argue that while

restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)

this restriction is necessary or societyrsquos overall happiness (lines 13-17)

Wollstonecraf however strongly challenges this argument asking the

authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-

doms are granted to women and likening societyrsquos male leaders to tyrants as

they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in

the darkrdquo (lines 78-88)

Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2

QUESTION 40

Choice D is the best answer Te authors o Passage 1 admit that women are

ldquoexcluded by the other hal [men] rom any participation in governmentrdquo

(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws

that deny women ldquocivil and political rightsrdquo (line 86)

Choices A B and C are incorrect because the authors o both passages

would not agree that women had the same preerences as men required agood education or were as happy as men

QUESTION 41

Choice A is the best answer Wollstonecraf argues in the final paragraph

o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women

ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would

most likely argue that allowing women these rights would be ldquoa reversal o

[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos

interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as

7262019 PrepScholar Sat Practice Test 3 Answers

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11

mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created

two sexes or a particular reason so while men can exercise civil and politi-

cal rights women are not naturally suited to these activities (lines 30-36)

Choices B and C are incorrect because they are not supported by inorma-

tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do

not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo

QUESTION 42

Choice C is the best answer When discussing problems with bee colo-

nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo

(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-

tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a

tentative tone and provides urther evidence that the authors believe but are

not certain that their hypothesis is correct

Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone

QUESTION 43

Choice C is the best answer In lines 24-28 the authors hypothesize that bee

colonies will be susceptible to mite inestations i they do not occasionally

eed on pyrethrum producing plants In lines 42-46 they suggest creating a

trial where a ldquosmall number o commercial honey bee colonies are offered a

number o pyrethrum producing plantsrdquo to test their hypothesis

Choices A B and D are incorrect because the authors do not hypothesize that

honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees

to develop secondary inections that beekeepers should increase their use o

insecticides or that humans are more susceptible to varroa mites

QUESTION 44

Choice D is the best answer In lines 24-28 the authors provide evidence

that a bee colony may be more resistant to mite inections i the bees eat

pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-

nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees

Choices A B and C do not describe any o the authorsrsquo hypotheses

QUESTION 45

Choice D is the best answer Te authors explain that when beekeepers

use commercially produced insecticides to fight mite inections they may

ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-

cientrdquo (lines 31-35)

7262019 PrepScholar Sat Practice Test 3 Answers

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12

Choices A B and C are incorrect because the authors do not suggest that

beekeepersrsquo use o commercially produced insecticides increases mite popu-

lations kills bacteria or destroys beesrsquo primary ood source

QUESTION 46

Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-

ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo

Choices A B and D are incorrect because they do not provide the best evi-

dence that beekeepersrsquo use o commercially produced insecticides may be

harmul to bees choices A B and D ocus on mite inestationsrsquo impact on

honeybees

QUESTION 47

Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some

bees Te authors then state ldquoWe urther postulate that the proper dosage

necessary to prevent mite inestation may be better lef to the beesrdquo (lines

35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the

bees may naturally control mite inestations better than insecticides

Choices A C and D are incorrect because in this context ldquopostulaterdquo does

not mean to make an unounded assumption question a belie or theory or

conclude based on firm evidence

QUESTION 48

Choice B is the best answer In the ourth paragraph the authors propose

a trial to study i honeybeesrsquo consumption o pyrethrum producing plants

helps the honeybees deend against mite inestations In the experiment the

authors plan to offer honey bee colonies both pyrethrum producing plants

and ldquoa typical bee ood source such as cloverrdquo to determine i these different

diets affect the beesrsquo susceptibility to mite inestations

Choices A C and D are incorrect because the main purpose o the ourth

paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished

experiment

QUESTION 49

Choice A is the best answer In lines 43-45 the authors propose a scien-

tific trial in which honeybees are ldquooffered a number o pyrethrum producing

plants as well as a typical bee ood source such as cloverrdquo Since the authors

contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood

sourcerdquo it can be assumed that clover does not produce pyrethrums

7262019 PrepScholar Sat Practice Test 3 Answers

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13

Choice B is incorrect because it is stated in the passage Choices C and D are

incorrect because they are not assumptions made by the authors

QUESTION 50

Choice B is the best answer Te table shows that 77 percent o the honeybee

colonies with colony collapse disorder were inected by all our pathogens

Choices A C and D are incorrect because they do not identiy the percent

o honeybee colonies with colony collapse disorder that were inected by all

our pathogens as based on data in the table

QUESTION 51

Choice D is the best answer Te table shows that 81 percent o colo-

nies without colony collapse disorder were affected by the pathogen

Nosema ceranae

Choices A B and C are incorrect because they do not identiy the pathogen

that inected the highest percentage o honeybee colonies without colony

collapse disorder as based on data in the table

QUESTION 52

Choice D is the best answer Te table discusses pathogen occurrence in

honeybee colonies but it includes no inormation as to whether these hon-

eybees were inected with mites Because the table does not suggest mites

inested the honeybee colonies no conclusions can be made as to whether

mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)

Choices A B and C are incorrect because the table provides no inormation

about whether these honeybees were inected with mites

Section 2 Writing and Language Test

QUESTION 1

Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-

ates a parallel structure within the list that begins with ldquohappierrdquo

Choices B C and D are incorrect because none creates a parallel structure

within the list o qualities

QUESTION 2

Choice B is the best answer Te ways in which exposure to natural light

affects employees is the main subject o the passage

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14

Choices A C and D are incorrect because none introduces the topic dis-

cussed in the remainder o the passage

QUESTION 3

Choice C is the best answer It accurately notes that the proposed sentence

would be placed directly between the first mention o circadian rhythms andthe explanation o the term

Choices A B and D are incorrect because each misinterprets the relation-

ship between the proposed additional text and the ideas in the paragraph

QUESTION 4

Choice C is the best answer It provides the correct possessive construction

or ldquobodyrdquo which must be a singular noun when discussed in general terms

as in this sentence Choice C also provides the correct plural construction

or ldquoclocksrdquo

Choices A B and D are incorrect because each applies either a possessive or

a plural construction in a place where it doesnrsquot belong

QUESTION 5

Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular

noun ldquoabsenteeismrdquo

Choices B C and D are incorrect because each provides a verb that

either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy

QUESTION 6

Choice B is the best answer It contains a direct reerence to productivity

the topic introduced in the previous sentence

Choices A C and D are incorrect because none directly addresses employee

productivity the primary subject o the previous sentence

QUESTION 7

Choice A is the best answer It opens with a reerence to lowered worker

productivity creating a transition rom the previous paragraph and clearly

positions the high energy costs o artificial light sources as an additional

disadvantage

Choices B C and D are incorrect because none o the choices offer an ade-

quate transition rom the previous paragraph Each awkwardly inserts the

issue o lower worker productivity into a statement about the high energy

costs o artificial light sources

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15

QUESTION 8

Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-

cate that the savings occurred every year

Choices A B and C are incorrect because each proposes an option that

would result in a redundancy with ldquoannualrdquo

QUESTION 9

Choice C is the best answer It provides a transitional adverb that accurately

communicates that this sentence describes an option that companies could

choose (ldquolight tubesrdquo) instead o the option described in the previous sen-

tence (ldquoull-pane windowsrdquo)

Choices A B and D are incorrect because each proposes a transitional

adverb that does not accurately reflect the relationship between this sen-

tence and the one preceding it

QUESTION 10

Choice C is the best answer It provides the correct relative pronoun to cor-

respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-

duce the definition that ollows

Choices A B and D are incorrect because each offers a pronoun inappropri-

ate or opening a dependent clause defining ldquolight tubesrdquo

QUESTION 11

Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the

noun ldquomeansrdquo particularly as a way to connect it to another noun or verb

Choices A C and D are incorrect because each results in nonstandard

phrasing with ldquomeansrdquo

QUESTION 12

Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-

responds with the plural noun ldquosettlersrdquo

Choices B C and D are incorrect because each provides either a nonstan-

dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo

QUESTION 13

Choice C is the best answer It creates a transition rom the poor ood qual-

ity mentioned in the previous sentence to the inormation about Harvey in

the remainder o the sentence

7262019 PrepScholar Sat Practice Test 3 Answers

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16

Choices A B and D are incorrect because none offers a transition rom the

previous sentence or a detail that corresponds precisely with the inorma-

tion in the remainder o the sentence

QUESTION 14

Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens

with a comma

Choices A B and C are incorrect because each proposes punctuation that

creates an inappropriately strong separation between the subject ldquoFred

Harveyrdquo and the verb ldquodecidedrdquo

QUESTION 15

Choice B is the best answer It provides the plural verb and plural posses-

sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo

Choices A C and D are incorrect because each either ails to provide a verb

that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide

the appropriate possessive pronoun

QUESTION 16

Choice C is the best answer It accurately echoes an earlier characterization

o the ood as being o ldquoterrible qualityrdquo while maintaining the established

tone o the passage

Choices A B and D are incorrect either because the word is less ormal than

the established tone o the passage (ldquoickyrdquo) or because it illogically attributes

agency to ood (ldquosinisterrdquo ldquosurlyrdquo)

QUESTION 17

Choice C is the best answer It accurately interprets ldquonot content to ollow

conventional business practicesrdquo as logically introducing the new practice o

ldquoemploying womenrdquo described in the ollowing sentences

Choices A B and D are incorrect because none recognizes why the sentence

is relevant to this particular location in the passage

QUESTION 18

Choice B is the best answer It is concise and ree o redundancies

Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and

ldquotremendousrdquo adjectives so close in meaning that together they present a

redundancy

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17

QUESTION 19

Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary

reerence to ldquosuch regulationsrdquo in the previous clause

Choices A B and C are incorrect because each lacks a necessary subject

such as a pronoun or noun

QUESTION 20

Choice C is the best answer It reers directly to benefits or the restaurantsrsquo

emale employees the subject o the previous sentence

Choices A B and D are incorrect because none logically builds upon the

sentence that precedes it

QUESTION 21

Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo

Choices A B and C are incorrect because each uses the punctuation or

a dependent clause (ldquoLiving independently and demonstrating an intense

work ethicrdquo) as i it were an independent clause

QUESTION 22

Choice A is the best answer It recognizes that the new inormation sup-

ports the previous sentencersquos claim that ldquothe Harvey Girls became known as

a transormative orcerdquo

Choices B C and D are incorrect because each misinterprets the relation-

ship between the proposed text and the passage

QUESTION 23

Choice A is the best answer It opens with a clause that identifies how

1-MCP affects apples which ocuses the sentence on 1-MCP as the subject

and allows the ideas in the sentence to progress logically

Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy

QUESTION 24

Choice D is the best answer Only the comma is necessary to separate

ldquoethylenerdquo rom the appositive noun phrase that defines it

Choices A B and C are incorrect because each creates a comma splice and

or adds unnecessary words

7262019 PrepScholar Sat Practice Test 3 Answers

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18

QUESTION 25

Choice B is the best answer It offers an adjective that accurately describes

resh apples

Choices A C and D are incorrect because each proposes an adjective that

does not describe a plausible ruit texture

QUESTION 26

Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-

sponds with the plural reerent ldquoapplesrdquo

Choices B C and D are incorrect because none provides a pronoun that is

both possessive and plural

QUESTION 27

Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins

the relative clause

Choices A B and C are incorrect because each contains a pronoun that

either does not correspond with the human reerent ldquoconsumersrdquo or does

not correctly begin the relative clause

QUESTION 28

Choice B is the best answer It provides the present tense verb ldquodordquo which

corresponds to the present tense established earlier in the sentence

Choices A C and D are incorrect because each contains a verb that deviates

rom the simple present tense established in the sentence

QUESTION 29

Choice B is the best answer It provides a colon to appropriately introduce the

clause that ollows an elaboration on the preceding claim that Bartlett pears

are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo

Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically

QUESTION 30

Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-

trast with a previous idea and goes on to mention that 1-MCP can have

negative effects Sentence 1 continues the discussion o benefits o 1-MCP

and sentence 2 names the adverse effect o limiting scent production so the

most logical spot or sentence 4 is between these sentences

7262019 PrepScholar Sat Practice Test 3 Answers

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19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240

21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

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22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440

23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540

24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

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25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

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26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

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27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3540

34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640

35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3740

36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3940

38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 10: PrepScholar Sat Practice Test 3 Answers

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9

Choices A B and D do not provide the best evidence that running a house-

hold and raising children entail very ew activities that are difficult or

unpleasant rather these lines offer general inormation about the differ-

ences between the sexes

QUESTION 34

Choice D is the best answer In lines 41-46 Wollstonecraf argues that i

women do not receive an education ldquoto become the companion o manrdquo or

one that is comparable to menrsquos education then society will not progress in

ldquoknowledge and virtuerdquo

Choices A B and C are incorrect because Wollstonecraf does not suggest

that society can progress only i women have happiness and financial secu-

rity ollow societal rules or replace men as figures o power

QUESTION 35

Choice C is the best answer Wollstonecraf argues that women should be

granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo

(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-

enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context

Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or

intellect and allow women to consider their role in society

Choices A B and D are incorrect because in this context ldquoreasonrdquo does not

mean motive sanity or explanation

QUESTION 36

Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws

passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to

ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf

is arguing that societyrsquos leaders grant men reedoms that are denied to women

Choices B C and D are incorrect because Wollstonecraf does not claim

that societyrsquos leaders have granted reedoms that created a general reduction

in individual virtue caused arguments about happiness or ensured equality

or all people

QUESTION 37

Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-

dence that societyrsquos leaders grant reedoms that privilege men She argues

that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-

lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to

ldquocontend or their reedomrdquo

Choices A B and C do not provide the best evidence that societyrsquos leaders

grant reedoms that privilege men over women

7262019 PrepScholar Sat Practice Test 3 Answers

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10

QUESTION 38

Choice C is the best answer Wollstonecraf cites the statement made by

the authors o Passage 1 that excluding women rom political participation

is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)

Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe

abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument

by highlighting a flaw in the reasoning presented by the authors o Passage 1

Choices A B and D are incorrect because Wollstonecraf does not reer to

the statement made in Passage 1 to call into question the authorsrsquo qualifica-

tions dispute the assertion that women are excluded by their own govern-

ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on

gender roles

QUESTION 39

Choice A is the best answer Te authors o Passage 1 argue that while

restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)

this restriction is necessary or societyrsquos overall happiness (lines 13-17)

Wollstonecraf however strongly challenges this argument asking the

authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-

doms are granted to women and likening societyrsquos male leaders to tyrants as

they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in

the darkrdquo (lines 78-88)

Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2

QUESTION 40

Choice D is the best answer Te authors o Passage 1 admit that women are

ldquoexcluded by the other hal [men] rom any participation in governmentrdquo

(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws

that deny women ldquocivil and political rightsrdquo (line 86)

Choices A B and C are incorrect because the authors o both passages

would not agree that women had the same preerences as men required agood education or were as happy as men

QUESTION 41

Choice A is the best answer Wollstonecraf argues in the final paragraph

o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women

ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would

most likely argue that allowing women these rights would be ldquoa reversal o

[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos

interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as

7262019 PrepScholar Sat Practice Test 3 Answers

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11

mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created

two sexes or a particular reason so while men can exercise civil and politi-

cal rights women are not naturally suited to these activities (lines 30-36)

Choices B and C are incorrect because they are not supported by inorma-

tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do

not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo

QUESTION 42

Choice C is the best answer When discussing problems with bee colo-

nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo

(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-

tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a

tentative tone and provides urther evidence that the authors believe but are

not certain that their hypothesis is correct

Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone

QUESTION 43

Choice C is the best answer In lines 24-28 the authors hypothesize that bee

colonies will be susceptible to mite inestations i they do not occasionally

eed on pyrethrum producing plants In lines 42-46 they suggest creating a

trial where a ldquosmall number o commercial honey bee colonies are offered a

number o pyrethrum producing plantsrdquo to test their hypothesis

Choices A B and D are incorrect because the authors do not hypothesize that

honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees

to develop secondary inections that beekeepers should increase their use o

insecticides or that humans are more susceptible to varroa mites

QUESTION 44

Choice D is the best answer In lines 24-28 the authors provide evidence

that a bee colony may be more resistant to mite inections i the bees eat

pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-

nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees

Choices A B and C do not describe any o the authorsrsquo hypotheses

QUESTION 45

Choice D is the best answer Te authors explain that when beekeepers

use commercially produced insecticides to fight mite inections they may

ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-

cientrdquo (lines 31-35)

7262019 PrepScholar Sat Practice Test 3 Answers

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12

Choices A B and C are incorrect because the authors do not suggest that

beekeepersrsquo use o commercially produced insecticides increases mite popu-

lations kills bacteria or destroys beesrsquo primary ood source

QUESTION 46

Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-

ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo

Choices A B and D are incorrect because they do not provide the best evi-

dence that beekeepersrsquo use o commercially produced insecticides may be

harmul to bees choices A B and D ocus on mite inestationsrsquo impact on

honeybees

QUESTION 47

Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some

bees Te authors then state ldquoWe urther postulate that the proper dosage

necessary to prevent mite inestation may be better lef to the beesrdquo (lines

35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the

bees may naturally control mite inestations better than insecticides

Choices A C and D are incorrect because in this context ldquopostulaterdquo does

not mean to make an unounded assumption question a belie or theory or

conclude based on firm evidence

QUESTION 48

Choice B is the best answer In the ourth paragraph the authors propose

a trial to study i honeybeesrsquo consumption o pyrethrum producing plants

helps the honeybees deend against mite inestations In the experiment the

authors plan to offer honey bee colonies both pyrethrum producing plants

and ldquoa typical bee ood source such as cloverrdquo to determine i these different

diets affect the beesrsquo susceptibility to mite inestations

Choices A C and D are incorrect because the main purpose o the ourth

paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished

experiment

QUESTION 49

Choice A is the best answer In lines 43-45 the authors propose a scien-

tific trial in which honeybees are ldquooffered a number o pyrethrum producing

plants as well as a typical bee ood source such as cloverrdquo Since the authors

contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood

sourcerdquo it can be assumed that clover does not produce pyrethrums

7262019 PrepScholar Sat Practice Test 3 Answers

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13

Choice B is incorrect because it is stated in the passage Choices C and D are

incorrect because they are not assumptions made by the authors

QUESTION 50

Choice B is the best answer Te table shows that 77 percent o the honeybee

colonies with colony collapse disorder were inected by all our pathogens

Choices A C and D are incorrect because they do not identiy the percent

o honeybee colonies with colony collapse disorder that were inected by all

our pathogens as based on data in the table

QUESTION 51

Choice D is the best answer Te table shows that 81 percent o colo-

nies without colony collapse disorder were affected by the pathogen

Nosema ceranae

Choices A B and C are incorrect because they do not identiy the pathogen

that inected the highest percentage o honeybee colonies without colony

collapse disorder as based on data in the table

QUESTION 52

Choice D is the best answer Te table discusses pathogen occurrence in

honeybee colonies but it includes no inormation as to whether these hon-

eybees were inected with mites Because the table does not suggest mites

inested the honeybee colonies no conclusions can be made as to whether

mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)

Choices A B and C are incorrect because the table provides no inormation

about whether these honeybees were inected with mites

Section 2 Writing and Language Test

QUESTION 1

Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-

ates a parallel structure within the list that begins with ldquohappierrdquo

Choices B C and D are incorrect because none creates a parallel structure

within the list o qualities

QUESTION 2

Choice B is the best answer Te ways in which exposure to natural light

affects employees is the main subject o the passage

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1540

14

Choices A C and D are incorrect because none introduces the topic dis-

cussed in the remainder o the passage

QUESTION 3

Choice C is the best answer It accurately notes that the proposed sentence

would be placed directly between the first mention o circadian rhythms andthe explanation o the term

Choices A B and D are incorrect because each misinterprets the relation-

ship between the proposed additional text and the ideas in the paragraph

QUESTION 4

Choice C is the best answer It provides the correct possessive construction

or ldquobodyrdquo which must be a singular noun when discussed in general terms

as in this sentence Choice C also provides the correct plural construction

or ldquoclocksrdquo

Choices A B and D are incorrect because each applies either a possessive or

a plural construction in a place where it doesnrsquot belong

QUESTION 5

Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular

noun ldquoabsenteeismrdquo

Choices B C and D are incorrect because each provides a verb that

either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy

QUESTION 6

Choice B is the best answer It contains a direct reerence to productivity

the topic introduced in the previous sentence

Choices A C and D are incorrect because none directly addresses employee

productivity the primary subject o the previous sentence

QUESTION 7

Choice A is the best answer It opens with a reerence to lowered worker

productivity creating a transition rom the previous paragraph and clearly

positions the high energy costs o artificial light sources as an additional

disadvantage

Choices B C and D are incorrect because none o the choices offer an ade-

quate transition rom the previous paragraph Each awkwardly inserts the

issue o lower worker productivity into a statement about the high energy

costs o artificial light sources

7262019 PrepScholar Sat Practice Test 3 Answers

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15

QUESTION 8

Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-

cate that the savings occurred every year

Choices A B and C are incorrect because each proposes an option that

would result in a redundancy with ldquoannualrdquo

QUESTION 9

Choice C is the best answer It provides a transitional adverb that accurately

communicates that this sentence describes an option that companies could

choose (ldquolight tubesrdquo) instead o the option described in the previous sen-

tence (ldquoull-pane windowsrdquo)

Choices A B and D are incorrect because each proposes a transitional

adverb that does not accurately reflect the relationship between this sen-

tence and the one preceding it

QUESTION 10

Choice C is the best answer It provides the correct relative pronoun to cor-

respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-

duce the definition that ollows

Choices A B and D are incorrect because each offers a pronoun inappropri-

ate or opening a dependent clause defining ldquolight tubesrdquo

QUESTION 11

Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the

noun ldquomeansrdquo particularly as a way to connect it to another noun or verb

Choices A C and D are incorrect because each results in nonstandard

phrasing with ldquomeansrdquo

QUESTION 12

Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-

responds with the plural noun ldquosettlersrdquo

Choices B C and D are incorrect because each provides either a nonstan-

dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo

QUESTION 13

Choice C is the best answer It creates a transition rom the poor ood qual-

ity mentioned in the previous sentence to the inormation about Harvey in

the remainder o the sentence

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1740

16

Choices A B and D are incorrect because none offers a transition rom the

previous sentence or a detail that corresponds precisely with the inorma-

tion in the remainder o the sentence

QUESTION 14

Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens

with a comma

Choices A B and C are incorrect because each proposes punctuation that

creates an inappropriately strong separation between the subject ldquoFred

Harveyrdquo and the verb ldquodecidedrdquo

QUESTION 15

Choice B is the best answer It provides the plural verb and plural posses-

sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo

Choices A C and D are incorrect because each either ails to provide a verb

that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide

the appropriate possessive pronoun

QUESTION 16

Choice C is the best answer It accurately echoes an earlier characterization

o the ood as being o ldquoterrible qualityrdquo while maintaining the established

tone o the passage

Choices A B and D are incorrect either because the word is less ormal than

the established tone o the passage (ldquoickyrdquo) or because it illogically attributes

agency to ood (ldquosinisterrdquo ldquosurlyrdquo)

QUESTION 17

Choice C is the best answer It accurately interprets ldquonot content to ollow

conventional business practicesrdquo as logically introducing the new practice o

ldquoemploying womenrdquo described in the ollowing sentences

Choices A B and D are incorrect because none recognizes why the sentence

is relevant to this particular location in the passage

QUESTION 18

Choice B is the best answer It is concise and ree o redundancies

Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and

ldquotremendousrdquo adjectives so close in meaning that together they present a

redundancy

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1840

17

QUESTION 19

Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary

reerence to ldquosuch regulationsrdquo in the previous clause

Choices A B and C are incorrect because each lacks a necessary subject

such as a pronoun or noun

QUESTION 20

Choice C is the best answer It reers directly to benefits or the restaurantsrsquo

emale employees the subject o the previous sentence

Choices A B and D are incorrect because none logically builds upon the

sentence that precedes it

QUESTION 21

Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo

Choices A B and C are incorrect because each uses the punctuation or

a dependent clause (ldquoLiving independently and demonstrating an intense

work ethicrdquo) as i it were an independent clause

QUESTION 22

Choice A is the best answer It recognizes that the new inormation sup-

ports the previous sentencersquos claim that ldquothe Harvey Girls became known as

a transormative orcerdquo

Choices B C and D are incorrect because each misinterprets the relation-

ship between the proposed text and the passage

QUESTION 23

Choice A is the best answer It opens with a clause that identifies how

1-MCP affects apples which ocuses the sentence on 1-MCP as the subject

and allows the ideas in the sentence to progress logically

Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy

QUESTION 24

Choice D is the best answer Only the comma is necessary to separate

ldquoethylenerdquo rom the appositive noun phrase that defines it

Choices A B and C are incorrect because each creates a comma splice and

or adds unnecessary words

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1940

18

QUESTION 25

Choice B is the best answer It offers an adjective that accurately describes

resh apples

Choices A C and D are incorrect because each proposes an adjective that

does not describe a plausible ruit texture

QUESTION 26

Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-

sponds with the plural reerent ldquoapplesrdquo

Choices B C and D are incorrect because none provides a pronoun that is

both possessive and plural

QUESTION 27

Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins

the relative clause

Choices A B and C are incorrect because each contains a pronoun that

either does not correspond with the human reerent ldquoconsumersrdquo or does

not correctly begin the relative clause

QUESTION 28

Choice B is the best answer It provides the present tense verb ldquodordquo which

corresponds to the present tense established earlier in the sentence

Choices A C and D are incorrect because each contains a verb that deviates

rom the simple present tense established in the sentence

QUESTION 29

Choice B is the best answer It provides a colon to appropriately introduce the

clause that ollows an elaboration on the preceding claim that Bartlett pears

are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo

Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically

QUESTION 30

Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-

trast with a previous idea and goes on to mention that 1-MCP can have

negative effects Sentence 1 continues the discussion o benefits o 1-MCP

and sentence 2 names the adverse effect o limiting scent production so the

most logical spot or sentence 4 is between these sentences

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040

19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2140

20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240

21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340

22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440

23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540

24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640

25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740

26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840

27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940

28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 11: PrepScholar Sat Practice Test 3 Answers

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10

QUESTION 38

Choice C is the best answer Wollstonecraf cites the statement made by

the authors o Passage 1 that excluding women rom political participation

is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)

Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe

abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument

by highlighting a flaw in the reasoning presented by the authors o Passage 1

Choices A B and D are incorrect because Wollstonecraf does not reer to

the statement made in Passage 1 to call into question the authorsrsquo qualifica-

tions dispute the assertion that women are excluded by their own govern-

ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on

gender roles

QUESTION 39

Choice A is the best answer Te authors o Passage 1 argue that while

restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)

this restriction is necessary or societyrsquos overall happiness (lines 13-17)

Wollstonecraf however strongly challenges this argument asking the

authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-

doms are granted to women and likening societyrsquos male leaders to tyrants as

they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in

the darkrdquo (lines 78-88)

Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2

QUESTION 40

Choice D is the best answer Te authors o Passage 1 admit that women are

ldquoexcluded by the other hal [men] rom any participation in governmentrdquo

(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws

that deny women ldquocivil and political rightsrdquo (line 86)

Choices A B and C are incorrect because the authors o both passages

would not agree that women had the same preerences as men required agood education or were as happy as men

QUESTION 41

Choice A is the best answer Wollstonecraf argues in the final paragraph

o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women

ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would

most likely argue that allowing women these rights would be ldquoa reversal o

[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos

interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1240

11

mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created

two sexes or a particular reason so while men can exercise civil and politi-

cal rights women are not naturally suited to these activities (lines 30-36)

Choices B and C are incorrect because they are not supported by inorma-

tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do

not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo

QUESTION 42

Choice C is the best answer When discussing problems with bee colo-

nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo

(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-

tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a

tentative tone and provides urther evidence that the authors believe but are

not certain that their hypothesis is correct

Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone

QUESTION 43

Choice C is the best answer In lines 24-28 the authors hypothesize that bee

colonies will be susceptible to mite inestations i they do not occasionally

eed on pyrethrum producing plants In lines 42-46 they suggest creating a

trial where a ldquosmall number o commercial honey bee colonies are offered a

number o pyrethrum producing plantsrdquo to test their hypothesis

Choices A B and D are incorrect because the authors do not hypothesize that

honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees

to develop secondary inections that beekeepers should increase their use o

insecticides or that humans are more susceptible to varroa mites

QUESTION 44

Choice D is the best answer In lines 24-28 the authors provide evidence

that a bee colony may be more resistant to mite inections i the bees eat

pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-

nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees

Choices A B and C do not describe any o the authorsrsquo hypotheses

QUESTION 45

Choice D is the best answer Te authors explain that when beekeepers

use commercially produced insecticides to fight mite inections they may

ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-

cientrdquo (lines 31-35)

7262019 PrepScholar Sat Practice Test 3 Answers

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12

Choices A B and C are incorrect because the authors do not suggest that

beekeepersrsquo use o commercially produced insecticides increases mite popu-

lations kills bacteria or destroys beesrsquo primary ood source

QUESTION 46

Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-

ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo

Choices A B and D are incorrect because they do not provide the best evi-

dence that beekeepersrsquo use o commercially produced insecticides may be

harmul to bees choices A B and D ocus on mite inestationsrsquo impact on

honeybees

QUESTION 47

Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some

bees Te authors then state ldquoWe urther postulate that the proper dosage

necessary to prevent mite inestation may be better lef to the beesrdquo (lines

35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the

bees may naturally control mite inestations better than insecticides

Choices A C and D are incorrect because in this context ldquopostulaterdquo does

not mean to make an unounded assumption question a belie or theory or

conclude based on firm evidence

QUESTION 48

Choice B is the best answer In the ourth paragraph the authors propose

a trial to study i honeybeesrsquo consumption o pyrethrum producing plants

helps the honeybees deend against mite inestations In the experiment the

authors plan to offer honey bee colonies both pyrethrum producing plants

and ldquoa typical bee ood source such as cloverrdquo to determine i these different

diets affect the beesrsquo susceptibility to mite inestations

Choices A C and D are incorrect because the main purpose o the ourth

paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished

experiment

QUESTION 49

Choice A is the best answer In lines 43-45 the authors propose a scien-

tific trial in which honeybees are ldquooffered a number o pyrethrum producing

plants as well as a typical bee ood source such as cloverrdquo Since the authors

contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood

sourcerdquo it can be assumed that clover does not produce pyrethrums

7262019 PrepScholar Sat Practice Test 3 Answers

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13

Choice B is incorrect because it is stated in the passage Choices C and D are

incorrect because they are not assumptions made by the authors

QUESTION 50

Choice B is the best answer Te table shows that 77 percent o the honeybee

colonies with colony collapse disorder were inected by all our pathogens

Choices A C and D are incorrect because they do not identiy the percent

o honeybee colonies with colony collapse disorder that were inected by all

our pathogens as based on data in the table

QUESTION 51

Choice D is the best answer Te table shows that 81 percent o colo-

nies without colony collapse disorder were affected by the pathogen

Nosema ceranae

Choices A B and C are incorrect because they do not identiy the pathogen

that inected the highest percentage o honeybee colonies without colony

collapse disorder as based on data in the table

QUESTION 52

Choice D is the best answer Te table discusses pathogen occurrence in

honeybee colonies but it includes no inormation as to whether these hon-

eybees were inected with mites Because the table does not suggest mites

inested the honeybee colonies no conclusions can be made as to whether

mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)

Choices A B and C are incorrect because the table provides no inormation

about whether these honeybees were inected with mites

Section 2 Writing and Language Test

QUESTION 1

Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-

ates a parallel structure within the list that begins with ldquohappierrdquo

Choices B C and D are incorrect because none creates a parallel structure

within the list o qualities

QUESTION 2

Choice B is the best answer Te ways in which exposure to natural light

affects employees is the main subject o the passage

7262019 PrepScholar Sat Practice Test 3 Answers

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14

Choices A C and D are incorrect because none introduces the topic dis-

cussed in the remainder o the passage

QUESTION 3

Choice C is the best answer It accurately notes that the proposed sentence

would be placed directly between the first mention o circadian rhythms andthe explanation o the term

Choices A B and D are incorrect because each misinterprets the relation-

ship between the proposed additional text and the ideas in the paragraph

QUESTION 4

Choice C is the best answer It provides the correct possessive construction

or ldquobodyrdquo which must be a singular noun when discussed in general terms

as in this sentence Choice C also provides the correct plural construction

or ldquoclocksrdquo

Choices A B and D are incorrect because each applies either a possessive or

a plural construction in a place where it doesnrsquot belong

QUESTION 5

Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular

noun ldquoabsenteeismrdquo

Choices B C and D are incorrect because each provides a verb that

either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy

QUESTION 6

Choice B is the best answer It contains a direct reerence to productivity

the topic introduced in the previous sentence

Choices A C and D are incorrect because none directly addresses employee

productivity the primary subject o the previous sentence

QUESTION 7

Choice A is the best answer It opens with a reerence to lowered worker

productivity creating a transition rom the previous paragraph and clearly

positions the high energy costs o artificial light sources as an additional

disadvantage

Choices B C and D are incorrect because none o the choices offer an ade-

quate transition rom the previous paragraph Each awkwardly inserts the

issue o lower worker productivity into a statement about the high energy

costs o artificial light sources

7262019 PrepScholar Sat Practice Test 3 Answers

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15

QUESTION 8

Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-

cate that the savings occurred every year

Choices A B and C are incorrect because each proposes an option that

would result in a redundancy with ldquoannualrdquo

QUESTION 9

Choice C is the best answer It provides a transitional adverb that accurately

communicates that this sentence describes an option that companies could

choose (ldquolight tubesrdquo) instead o the option described in the previous sen-

tence (ldquoull-pane windowsrdquo)

Choices A B and D are incorrect because each proposes a transitional

adverb that does not accurately reflect the relationship between this sen-

tence and the one preceding it

QUESTION 10

Choice C is the best answer It provides the correct relative pronoun to cor-

respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-

duce the definition that ollows

Choices A B and D are incorrect because each offers a pronoun inappropri-

ate or opening a dependent clause defining ldquolight tubesrdquo

QUESTION 11

Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the

noun ldquomeansrdquo particularly as a way to connect it to another noun or verb

Choices A C and D are incorrect because each results in nonstandard

phrasing with ldquomeansrdquo

QUESTION 12

Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-

responds with the plural noun ldquosettlersrdquo

Choices B C and D are incorrect because each provides either a nonstan-

dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo

QUESTION 13

Choice C is the best answer It creates a transition rom the poor ood qual-

ity mentioned in the previous sentence to the inormation about Harvey in

the remainder o the sentence

7262019 PrepScholar Sat Practice Test 3 Answers

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16

Choices A B and D are incorrect because none offers a transition rom the

previous sentence or a detail that corresponds precisely with the inorma-

tion in the remainder o the sentence

QUESTION 14

Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens

with a comma

Choices A B and C are incorrect because each proposes punctuation that

creates an inappropriately strong separation between the subject ldquoFred

Harveyrdquo and the verb ldquodecidedrdquo

QUESTION 15

Choice B is the best answer It provides the plural verb and plural posses-

sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo

Choices A C and D are incorrect because each either ails to provide a verb

that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide

the appropriate possessive pronoun

QUESTION 16

Choice C is the best answer It accurately echoes an earlier characterization

o the ood as being o ldquoterrible qualityrdquo while maintaining the established

tone o the passage

Choices A B and D are incorrect either because the word is less ormal than

the established tone o the passage (ldquoickyrdquo) or because it illogically attributes

agency to ood (ldquosinisterrdquo ldquosurlyrdquo)

QUESTION 17

Choice C is the best answer It accurately interprets ldquonot content to ollow

conventional business practicesrdquo as logically introducing the new practice o

ldquoemploying womenrdquo described in the ollowing sentences

Choices A B and D are incorrect because none recognizes why the sentence

is relevant to this particular location in the passage

QUESTION 18

Choice B is the best answer It is concise and ree o redundancies

Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and

ldquotremendousrdquo adjectives so close in meaning that together they present a

redundancy

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17

QUESTION 19

Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary

reerence to ldquosuch regulationsrdquo in the previous clause

Choices A B and C are incorrect because each lacks a necessary subject

such as a pronoun or noun

QUESTION 20

Choice C is the best answer It reers directly to benefits or the restaurantsrsquo

emale employees the subject o the previous sentence

Choices A B and D are incorrect because none logically builds upon the

sentence that precedes it

QUESTION 21

Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo

Choices A B and C are incorrect because each uses the punctuation or

a dependent clause (ldquoLiving independently and demonstrating an intense

work ethicrdquo) as i it were an independent clause

QUESTION 22

Choice A is the best answer It recognizes that the new inormation sup-

ports the previous sentencersquos claim that ldquothe Harvey Girls became known as

a transormative orcerdquo

Choices B C and D are incorrect because each misinterprets the relation-

ship between the proposed text and the passage

QUESTION 23

Choice A is the best answer It opens with a clause that identifies how

1-MCP affects apples which ocuses the sentence on 1-MCP as the subject

and allows the ideas in the sentence to progress logically

Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy

QUESTION 24

Choice D is the best answer Only the comma is necessary to separate

ldquoethylenerdquo rom the appositive noun phrase that defines it

Choices A B and C are incorrect because each creates a comma splice and

or adds unnecessary words

7262019 PrepScholar Sat Practice Test 3 Answers

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18

QUESTION 25

Choice B is the best answer It offers an adjective that accurately describes

resh apples

Choices A C and D are incorrect because each proposes an adjective that

does not describe a plausible ruit texture

QUESTION 26

Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-

sponds with the plural reerent ldquoapplesrdquo

Choices B C and D are incorrect because none provides a pronoun that is

both possessive and plural

QUESTION 27

Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins

the relative clause

Choices A B and C are incorrect because each contains a pronoun that

either does not correspond with the human reerent ldquoconsumersrdquo or does

not correctly begin the relative clause

QUESTION 28

Choice B is the best answer It provides the present tense verb ldquodordquo which

corresponds to the present tense established earlier in the sentence

Choices A C and D are incorrect because each contains a verb that deviates

rom the simple present tense established in the sentence

QUESTION 29

Choice B is the best answer It provides a colon to appropriately introduce the

clause that ollows an elaboration on the preceding claim that Bartlett pears

are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo

Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically

QUESTION 30

Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-

trast with a previous idea and goes on to mention that 1-MCP can have

negative effects Sentence 1 continues the discussion o benefits o 1-MCP

and sentence 2 names the adverse effect o limiting scent production so the

most logical spot or sentence 4 is between these sentences

7262019 PrepScholar Sat Practice Test 3 Answers

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19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240

21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340

22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

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24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

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25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

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26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

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27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3740

36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040

QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 12: PrepScholar Sat Practice Test 3 Answers

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11

mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created

two sexes or a particular reason so while men can exercise civil and politi-

cal rights women are not naturally suited to these activities (lines 30-36)

Choices B and C are incorrect because they are not supported by inorma-

tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do

not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo

QUESTION 42

Choice C is the best answer When discussing problems with bee colo-

nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo

(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-

tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a

tentative tone and provides urther evidence that the authors believe but are

not certain that their hypothesis is correct

Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone

QUESTION 43

Choice C is the best answer In lines 24-28 the authors hypothesize that bee

colonies will be susceptible to mite inestations i they do not occasionally

eed on pyrethrum producing plants In lines 42-46 they suggest creating a

trial where a ldquosmall number o commercial honey bee colonies are offered a

number o pyrethrum producing plantsrdquo to test their hypothesis

Choices A B and D are incorrect because the authors do not hypothesize that

honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees

to develop secondary inections that beekeepers should increase their use o

insecticides or that humans are more susceptible to varroa mites

QUESTION 44

Choice D is the best answer In lines 24-28 the authors provide evidence

that a bee colony may be more resistant to mite inections i the bees eat

pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-

nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees

Choices A B and C do not describe any o the authorsrsquo hypotheses

QUESTION 45

Choice D is the best answer Te authors explain that when beekeepers

use commercially produced insecticides to fight mite inections they may

ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-

cientrdquo (lines 31-35)

7262019 PrepScholar Sat Practice Test 3 Answers

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12

Choices A B and C are incorrect because the authors do not suggest that

beekeepersrsquo use o commercially produced insecticides increases mite popu-

lations kills bacteria or destroys beesrsquo primary ood source

QUESTION 46

Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-

ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo

Choices A B and D are incorrect because they do not provide the best evi-

dence that beekeepersrsquo use o commercially produced insecticides may be

harmul to bees choices A B and D ocus on mite inestationsrsquo impact on

honeybees

QUESTION 47

Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some

bees Te authors then state ldquoWe urther postulate that the proper dosage

necessary to prevent mite inestation may be better lef to the beesrdquo (lines

35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the

bees may naturally control mite inestations better than insecticides

Choices A C and D are incorrect because in this context ldquopostulaterdquo does

not mean to make an unounded assumption question a belie or theory or

conclude based on firm evidence

QUESTION 48

Choice B is the best answer In the ourth paragraph the authors propose

a trial to study i honeybeesrsquo consumption o pyrethrum producing plants

helps the honeybees deend against mite inestations In the experiment the

authors plan to offer honey bee colonies both pyrethrum producing plants

and ldquoa typical bee ood source such as cloverrdquo to determine i these different

diets affect the beesrsquo susceptibility to mite inestations

Choices A C and D are incorrect because the main purpose o the ourth

paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished

experiment

QUESTION 49

Choice A is the best answer In lines 43-45 the authors propose a scien-

tific trial in which honeybees are ldquooffered a number o pyrethrum producing

plants as well as a typical bee ood source such as cloverrdquo Since the authors

contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood

sourcerdquo it can be assumed that clover does not produce pyrethrums

7262019 PrepScholar Sat Practice Test 3 Answers

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13

Choice B is incorrect because it is stated in the passage Choices C and D are

incorrect because they are not assumptions made by the authors

QUESTION 50

Choice B is the best answer Te table shows that 77 percent o the honeybee

colonies with colony collapse disorder were inected by all our pathogens

Choices A C and D are incorrect because they do not identiy the percent

o honeybee colonies with colony collapse disorder that were inected by all

our pathogens as based on data in the table

QUESTION 51

Choice D is the best answer Te table shows that 81 percent o colo-

nies without colony collapse disorder were affected by the pathogen

Nosema ceranae

Choices A B and C are incorrect because they do not identiy the pathogen

that inected the highest percentage o honeybee colonies without colony

collapse disorder as based on data in the table

QUESTION 52

Choice D is the best answer Te table discusses pathogen occurrence in

honeybee colonies but it includes no inormation as to whether these hon-

eybees were inected with mites Because the table does not suggest mites

inested the honeybee colonies no conclusions can be made as to whether

mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)

Choices A B and C are incorrect because the table provides no inormation

about whether these honeybees were inected with mites

Section 2 Writing and Language Test

QUESTION 1

Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-

ates a parallel structure within the list that begins with ldquohappierrdquo

Choices B C and D are incorrect because none creates a parallel structure

within the list o qualities

QUESTION 2

Choice B is the best answer Te ways in which exposure to natural light

affects employees is the main subject o the passage

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14

Choices A C and D are incorrect because none introduces the topic dis-

cussed in the remainder o the passage

QUESTION 3

Choice C is the best answer It accurately notes that the proposed sentence

would be placed directly between the first mention o circadian rhythms andthe explanation o the term

Choices A B and D are incorrect because each misinterprets the relation-

ship between the proposed additional text and the ideas in the paragraph

QUESTION 4

Choice C is the best answer It provides the correct possessive construction

or ldquobodyrdquo which must be a singular noun when discussed in general terms

as in this sentence Choice C also provides the correct plural construction

or ldquoclocksrdquo

Choices A B and D are incorrect because each applies either a possessive or

a plural construction in a place where it doesnrsquot belong

QUESTION 5

Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular

noun ldquoabsenteeismrdquo

Choices B C and D are incorrect because each provides a verb that

either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy

QUESTION 6

Choice B is the best answer It contains a direct reerence to productivity

the topic introduced in the previous sentence

Choices A C and D are incorrect because none directly addresses employee

productivity the primary subject o the previous sentence

QUESTION 7

Choice A is the best answer It opens with a reerence to lowered worker

productivity creating a transition rom the previous paragraph and clearly

positions the high energy costs o artificial light sources as an additional

disadvantage

Choices B C and D are incorrect because none o the choices offer an ade-

quate transition rom the previous paragraph Each awkwardly inserts the

issue o lower worker productivity into a statement about the high energy

costs o artificial light sources

7262019 PrepScholar Sat Practice Test 3 Answers

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15

QUESTION 8

Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-

cate that the savings occurred every year

Choices A B and C are incorrect because each proposes an option that

would result in a redundancy with ldquoannualrdquo

QUESTION 9

Choice C is the best answer It provides a transitional adverb that accurately

communicates that this sentence describes an option that companies could

choose (ldquolight tubesrdquo) instead o the option described in the previous sen-

tence (ldquoull-pane windowsrdquo)

Choices A B and D are incorrect because each proposes a transitional

adverb that does not accurately reflect the relationship between this sen-

tence and the one preceding it

QUESTION 10

Choice C is the best answer It provides the correct relative pronoun to cor-

respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-

duce the definition that ollows

Choices A B and D are incorrect because each offers a pronoun inappropri-

ate or opening a dependent clause defining ldquolight tubesrdquo

QUESTION 11

Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the

noun ldquomeansrdquo particularly as a way to connect it to another noun or verb

Choices A C and D are incorrect because each results in nonstandard

phrasing with ldquomeansrdquo

QUESTION 12

Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-

responds with the plural noun ldquosettlersrdquo

Choices B C and D are incorrect because each provides either a nonstan-

dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo

QUESTION 13

Choice C is the best answer It creates a transition rom the poor ood qual-

ity mentioned in the previous sentence to the inormation about Harvey in

the remainder o the sentence

7262019 PrepScholar Sat Practice Test 3 Answers

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16

Choices A B and D are incorrect because none offers a transition rom the

previous sentence or a detail that corresponds precisely with the inorma-

tion in the remainder o the sentence

QUESTION 14

Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens

with a comma

Choices A B and C are incorrect because each proposes punctuation that

creates an inappropriately strong separation between the subject ldquoFred

Harveyrdquo and the verb ldquodecidedrdquo

QUESTION 15

Choice B is the best answer It provides the plural verb and plural posses-

sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo

Choices A C and D are incorrect because each either ails to provide a verb

that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide

the appropriate possessive pronoun

QUESTION 16

Choice C is the best answer It accurately echoes an earlier characterization

o the ood as being o ldquoterrible qualityrdquo while maintaining the established

tone o the passage

Choices A B and D are incorrect either because the word is less ormal than

the established tone o the passage (ldquoickyrdquo) or because it illogically attributes

agency to ood (ldquosinisterrdquo ldquosurlyrdquo)

QUESTION 17

Choice C is the best answer It accurately interprets ldquonot content to ollow

conventional business practicesrdquo as logically introducing the new practice o

ldquoemploying womenrdquo described in the ollowing sentences

Choices A B and D are incorrect because none recognizes why the sentence

is relevant to this particular location in the passage

QUESTION 18

Choice B is the best answer It is concise and ree o redundancies

Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and

ldquotremendousrdquo adjectives so close in meaning that together they present a

redundancy

7262019 PrepScholar Sat Practice Test 3 Answers

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17

QUESTION 19

Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary

reerence to ldquosuch regulationsrdquo in the previous clause

Choices A B and C are incorrect because each lacks a necessary subject

such as a pronoun or noun

QUESTION 20

Choice C is the best answer It reers directly to benefits or the restaurantsrsquo

emale employees the subject o the previous sentence

Choices A B and D are incorrect because none logically builds upon the

sentence that precedes it

QUESTION 21

Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo

Choices A B and C are incorrect because each uses the punctuation or

a dependent clause (ldquoLiving independently and demonstrating an intense

work ethicrdquo) as i it were an independent clause

QUESTION 22

Choice A is the best answer It recognizes that the new inormation sup-

ports the previous sentencersquos claim that ldquothe Harvey Girls became known as

a transormative orcerdquo

Choices B C and D are incorrect because each misinterprets the relation-

ship between the proposed text and the passage

QUESTION 23

Choice A is the best answer It opens with a clause that identifies how

1-MCP affects apples which ocuses the sentence on 1-MCP as the subject

and allows the ideas in the sentence to progress logically

Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy

QUESTION 24

Choice D is the best answer Only the comma is necessary to separate

ldquoethylenerdquo rom the appositive noun phrase that defines it

Choices A B and C are incorrect because each creates a comma splice and

or adds unnecessary words

7262019 PrepScholar Sat Practice Test 3 Answers

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18

QUESTION 25

Choice B is the best answer It offers an adjective that accurately describes

resh apples

Choices A C and D are incorrect because each proposes an adjective that

does not describe a plausible ruit texture

QUESTION 26

Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-

sponds with the plural reerent ldquoapplesrdquo

Choices B C and D are incorrect because none provides a pronoun that is

both possessive and plural

QUESTION 27

Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins

the relative clause

Choices A B and C are incorrect because each contains a pronoun that

either does not correspond with the human reerent ldquoconsumersrdquo or does

not correctly begin the relative clause

QUESTION 28

Choice B is the best answer It provides the present tense verb ldquodordquo which

corresponds to the present tense established earlier in the sentence

Choices A C and D are incorrect because each contains a verb that deviates

rom the simple present tense established in the sentence

QUESTION 29

Choice B is the best answer It provides a colon to appropriately introduce the

clause that ollows an elaboration on the preceding claim that Bartlett pears

are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo

Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically

QUESTION 30

Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-

trast with a previous idea and goes on to mention that 1-MCP can have

negative effects Sentence 1 continues the discussion o benefits o 1-MCP

and sentence 2 names the adverse effect o limiting scent production so the

most logical spot or sentence 4 is between these sentences

7262019 PrepScholar Sat Practice Test 3 Answers

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19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240

21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340

22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440

23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540

24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

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25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

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26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840

27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940

28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040

29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3140

30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3240

31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3440

33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640

35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3740

36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 13: PrepScholar Sat Practice Test 3 Answers

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12

Choices A B and C are incorrect because the authors do not suggest that

beekeepersrsquo use o commercially produced insecticides increases mite popu-

lations kills bacteria or destroys beesrsquo primary ood source

QUESTION 46

Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-

ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo

Choices A B and D are incorrect because they do not provide the best evi-

dence that beekeepersrsquo use o commercially produced insecticides may be

harmul to bees choices A B and D ocus on mite inestationsrsquo impact on

honeybees

QUESTION 47

Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some

bees Te authors then state ldquoWe urther postulate that the proper dosage

necessary to prevent mite inestation may be better lef to the beesrdquo (lines

35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the

bees may naturally control mite inestations better than insecticides

Choices A C and D are incorrect because in this context ldquopostulaterdquo does

not mean to make an unounded assumption question a belie or theory or

conclude based on firm evidence

QUESTION 48

Choice B is the best answer In the ourth paragraph the authors propose

a trial to study i honeybeesrsquo consumption o pyrethrum producing plants

helps the honeybees deend against mite inestations In the experiment the

authors plan to offer honey bee colonies both pyrethrum producing plants

and ldquoa typical bee ood source such as cloverrdquo to determine i these different

diets affect the beesrsquo susceptibility to mite inestations

Choices A C and D are incorrect because the main purpose o the ourth

paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished

experiment

QUESTION 49

Choice A is the best answer In lines 43-45 the authors propose a scien-

tific trial in which honeybees are ldquooffered a number o pyrethrum producing

plants as well as a typical bee ood source such as cloverrdquo Since the authors

contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood

sourcerdquo it can be assumed that clover does not produce pyrethrums

7262019 PrepScholar Sat Practice Test 3 Answers

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13

Choice B is incorrect because it is stated in the passage Choices C and D are

incorrect because they are not assumptions made by the authors

QUESTION 50

Choice B is the best answer Te table shows that 77 percent o the honeybee

colonies with colony collapse disorder were inected by all our pathogens

Choices A C and D are incorrect because they do not identiy the percent

o honeybee colonies with colony collapse disorder that were inected by all

our pathogens as based on data in the table

QUESTION 51

Choice D is the best answer Te table shows that 81 percent o colo-

nies without colony collapse disorder were affected by the pathogen

Nosema ceranae

Choices A B and C are incorrect because they do not identiy the pathogen

that inected the highest percentage o honeybee colonies without colony

collapse disorder as based on data in the table

QUESTION 52

Choice D is the best answer Te table discusses pathogen occurrence in

honeybee colonies but it includes no inormation as to whether these hon-

eybees were inected with mites Because the table does not suggest mites

inested the honeybee colonies no conclusions can be made as to whether

mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)

Choices A B and C are incorrect because the table provides no inormation

about whether these honeybees were inected with mites

Section 2 Writing and Language Test

QUESTION 1

Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-

ates a parallel structure within the list that begins with ldquohappierrdquo

Choices B C and D are incorrect because none creates a parallel structure

within the list o qualities

QUESTION 2

Choice B is the best answer Te ways in which exposure to natural light

affects employees is the main subject o the passage

7262019 PrepScholar Sat Practice Test 3 Answers

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14

Choices A C and D are incorrect because none introduces the topic dis-

cussed in the remainder o the passage

QUESTION 3

Choice C is the best answer It accurately notes that the proposed sentence

would be placed directly between the first mention o circadian rhythms andthe explanation o the term

Choices A B and D are incorrect because each misinterprets the relation-

ship between the proposed additional text and the ideas in the paragraph

QUESTION 4

Choice C is the best answer It provides the correct possessive construction

or ldquobodyrdquo which must be a singular noun when discussed in general terms

as in this sentence Choice C also provides the correct plural construction

or ldquoclocksrdquo

Choices A B and D are incorrect because each applies either a possessive or

a plural construction in a place where it doesnrsquot belong

QUESTION 5

Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular

noun ldquoabsenteeismrdquo

Choices B C and D are incorrect because each provides a verb that

either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy

QUESTION 6

Choice B is the best answer It contains a direct reerence to productivity

the topic introduced in the previous sentence

Choices A C and D are incorrect because none directly addresses employee

productivity the primary subject o the previous sentence

QUESTION 7

Choice A is the best answer It opens with a reerence to lowered worker

productivity creating a transition rom the previous paragraph and clearly

positions the high energy costs o artificial light sources as an additional

disadvantage

Choices B C and D are incorrect because none o the choices offer an ade-

quate transition rom the previous paragraph Each awkwardly inserts the

issue o lower worker productivity into a statement about the high energy

costs o artificial light sources

7262019 PrepScholar Sat Practice Test 3 Answers

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15

QUESTION 8

Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-

cate that the savings occurred every year

Choices A B and C are incorrect because each proposes an option that

would result in a redundancy with ldquoannualrdquo

QUESTION 9

Choice C is the best answer It provides a transitional adverb that accurately

communicates that this sentence describes an option that companies could

choose (ldquolight tubesrdquo) instead o the option described in the previous sen-

tence (ldquoull-pane windowsrdquo)

Choices A B and D are incorrect because each proposes a transitional

adverb that does not accurately reflect the relationship between this sen-

tence and the one preceding it

QUESTION 10

Choice C is the best answer It provides the correct relative pronoun to cor-

respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-

duce the definition that ollows

Choices A B and D are incorrect because each offers a pronoun inappropri-

ate or opening a dependent clause defining ldquolight tubesrdquo

QUESTION 11

Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the

noun ldquomeansrdquo particularly as a way to connect it to another noun or verb

Choices A C and D are incorrect because each results in nonstandard

phrasing with ldquomeansrdquo

QUESTION 12

Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-

responds with the plural noun ldquosettlersrdquo

Choices B C and D are incorrect because each provides either a nonstan-

dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo

QUESTION 13

Choice C is the best answer It creates a transition rom the poor ood qual-

ity mentioned in the previous sentence to the inormation about Harvey in

the remainder o the sentence

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1740

16

Choices A B and D are incorrect because none offers a transition rom the

previous sentence or a detail that corresponds precisely with the inorma-

tion in the remainder o the sentence

QUESTION 14

Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens

with a comma

Choices A B and C are incorrect because each proposes punctuation that

creates an inappropriately strong separation between the subject ldquoFred

Harveyrdquo and the verb ldquodecidedrdquo

QUESTION 15

Choice B is the best answer It provides the plural verb and plural posses-

sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo

Choices A C and D are incorrect because each either ails to provide a verb

that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide

the appropriate possessive pronoun

QUESTION 16

Choice C is the best answer It accurately echoes an earlier characterization

o the ood as being o ldquoterrible qualityrdquo while maintaining the established

tone o the passage

Choices A B and D are incorrect either because the word is less ormal than

the established tone o the passage (ldquoickyrdquo) or because it illogically attributes

agency to ood (ldquosinisterrdquo ldquosurlyrdquo)

QUESTION 17

Choice C is the best answer It accurately interprets ldquonot content to ollow

conventional business practicesrdquo as logically introducing the new practice o

ldquoemploying womenrdquo described in the ollowing sentences

Choices A B and D are incorrect because none recognizes why the sentence

is relevant to this particular location in the passage

QUESTION 18

Choice B is the best answer It is concise and ree o redundancies

Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and

ldquotremendousrdquo adjectives so close in meaning that together they present a

redundancy

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1840

17

QUESTION 19

Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary

reerence to ldquosuch regulationsrdquo in the previous clause

Choices A B and C are incorrect because each lacks a necessary subject

such as a pronoun or noun

QUESTION 20

Choice C is the best answer It reers directly to benefits or the restaurantsrsquo

emale employees the subject o the previous sentence

Choices A B and D are incorrect because none logically builds upon the

sentence that precedes it

QUESTION 21

Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo

Choices A B and C are incorrect because each uses the punctuation or

a dependent clause (ldquoLiving independently and demonstrating an intense

work ethicrdquo) as i it were an independent clause

QUESTION 22

Choice A is the best answer It recognizes that the new inormation sup-

ports the previous sentencersquos claim that ldquothe Harvey Girls became known as

a transormative orcerdquo

Choices B C and D are incorrect because each misinterprets the relation-

ship between the proposed text and the passage

QUESTION 23

Choice A is the best answer It opens with a clause that identifies how

1-MCP affects apples which ocuses the sentence on 1-MCP as the subject

and allows the ideas in the sentence to progress logically

Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy

QUESTION 24

Choice D is the best answer Only the comma is necessary to separate

ldquoethylenerdquo rom the appositive noun phrase that defines it

Choices A B and C are incorrect because each creates a comma splice and

or adds unnecessary words

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1940

18

QUESTION 25

Choice B is the best answer It offers an adjective that accurately describes

resh apples

Choices A C and D are incorrect because each proposes an adjective that

does not describe a plausible ruit texture

QUESTION 26

Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-

sponds with the plural reerent ldquoapplesrdquo

Choices B C and D are incorrect because none provides a pronoun that is

both possessive and plural

QUESTION 27

Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins

the relative clause

Choices A B and C are incorrect because each contains a pronoun that

either does not correspond with the human reerent ldquoconsumersrdquo or does

not correctly begin the relative clause

QUESTION 28

Choice B is the best answer It provides the present tense verb ldquodordquo which

corresponds to the present tense established earlier in the sentence

Choices A C and D are incorrect because each contains a verb that deviates

rom the simple present tense established in the sentence

QUESTION 29

Choice B is the best answer It provides a colon to appropriately introduce the

clause that ollows an elaboration on the preceding claim that Bartlett pears

are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo

Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically

QUESTION 30

Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-

trast with a previous idea and goes on to mention that 1-MCP can have

negative effects Sentence 1 continues the discussion o benefits o 1-MCP

and sentence 2 names the adverse effect o limiting scent production so the

most logical spot or sentence 4 is between these sentences

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040

19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2140

20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240

21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340

22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440

23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540

24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640

25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740

26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840

27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940

28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040

29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 14: PrepScholar Sat Practice Test 3 Answers

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13

Choice B is incorrect because it is stated in the passage Choices C and D are

incorrect because they are not assumptions made by the authors

QUESTION 50

Choice B is the best answer Te table shows that 77 percent o the honeybee

colonies with colony collapse disorder were inected by all our pathogens

Choices A C and D are incorrect because they do not identiy the percent

o honeybee colonies with colony collapse disorder that were inected by all

our pathogens as based on data in the table

QUESTION 51

Choice D is the best answer Te table shows that 81 percent o colo-

nies without colony collapse disorder were affected by the pathogen

Nosema ceranae

Choices A B and C are incorrect because they do not identiy the pathogen

that inected the highest percentage o honeybee colonies without colony

collapse disorder as based on data in the table

QUESTION 52

Choice D is the best answer Te table discusses pathogen occurrence in

honeybee colonies but it includes no inormation as to whether these hon-

eybees were inected with mites Because the table does not suggest mites

inested the honeybee colonies no conclusions can be made as to whether

mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)

Choices A B and C are incorrect because the table provides no inormation

about whether these honeybees were inected with mites

Section 2 Writing and Language Test

QUESTION 1

Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-

ates a parallel structure within the list that begins with ldquohappierrdquo

Choices B C and D are incorrect because none creates a parallel structure

within the list o qualities

QUESTION 2

Choice B is the best answer Te ways in which exposure to natural light

affects employees is the main subject o the passage

7262019 PrepScholar Sat Practice Test 3 Answers

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14

Choices A C and D are incorrect because none introduces the topic dis-

cussed in the remainder o the passage

QUESTION 3

Choice C is the best answer It accurately notes that the proposed sentence

would be placed directly between the first mention o circadian rhythms andthe explanation o the term

Choices A B and D are incorrect because each misinterprets the relation-

ship between the proposed additional text and the ideas in the paragraph

QUESTION 4

Choice C is the best answer It provides the correct possessive construction

or ldquobodyrdquo which must be a singular noun when discussed in general terms

as in this sentence Choice C also provides the correct plural construction

or ldquoclocksrdquo

Choices A B and D are incorrect because each applies either a possessive or

a plural construction in a place where it doesnrsquot belong

QUESTION 5

Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular

noun ldquoabsenteeismrdquo

Choices B C and D are incorrect because each provides a verb that

either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy

QUESTION 6

Choice B is the best answer It contains a direct reerence to productivity

the topic introduced in the previous sentence

Choices A C and D are incorrect because none directly addresses employee

productivity the primary subject o the previous sentence

QUESTION 7

Choice A is the best answer It opens with a reerence to lowered worker

productivity creating a transition rom the previous paragraph and clearly

positions the high energy costs o artificial light sources as an additional

disadvantage

Choices B C and D are incorrect because none o the choices offer an ade-

quate transition rom the previous paragraph Each awkwardly inserts the

issue o lower worker productivity into a statement about the high energy

costs o artificial light sources

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1640

15

QUESTION 8

Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-

cate that the savings occurred every year

Choices A B and C are incorrect because each proposes an option that

would result in a redundancy with ldquoannualrdquo

QUESTION 9

Choice C is the best answer It provides a transitional adverb that accurately

communicates that this sentence describes an option that companies could

choose (ldquolight tubesrdquo) instead o the option described in the previous sen-

tence (ldquoull-pane windowsrdquo)

Choices A B and D are incorrect because each proposes a transitional

adverb that does not accurately reflect the relationship between this sen-

tence and the one preceding it

QUESTION 10

Choice C is the best answer It provides the correct relative pronoun to cor-

respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-

duce the definition that ollows

Choices A B and D are incorrect because each offers a pronoun inappropri-

ate or opening a dependent clause defining ldquolight tubesrdquo

QUESTION 11

Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the

noun ldquomeansrdquo particularly as a way to connect it to another noun or verb

Choices A C and D are incorrect because each results in nonstandard

phrasing with ldquomeansrdquo

QUESTION 12

Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-

responds with the plural noun ldquosettlersrdquo

Choices B C and D are incorrect because each provides either a nonstan-

dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo

QUESTION 13

Choice C is the best answer It creates a transition rom the poor ood qual-

ity mentioned in the previous sentence to the inormation about Harvey in

the remainder o the sentence

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1740

16

Choices A B and D are incorrect because none offers a transition rom the

previous sentence or a detail that corresponds precisely with the inorma-

tion in the remainder o the sentence

QUESTION 14

Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens

with a comma

Choices A B and C are incorrect because each proposes punctuation that

creates an inappropriately strong separation between the subject ldquoFred

Harveyrdquo and the verb ldquodecidedrdquo

QUESTION 15

Choice B is the best answer It provides the plural verb and plural posses-

sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo

Choices A C and D are incorrect because each either ails to provide a verb

that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide

the appropriate possessive pronoun

QUESTION 16

Choice C is the best answer It accurately echoes an earlier characterization

o the ood as being o ldquoterrible qualityrdquo while maintaining the established

tone o the passage

Choices A B and D are incorrect either because the word is less ormal than

the established tone o the passage (ldquoickyrdquo) or because it illogically attributes

agency to ood (ldquosinisterrdquo ldquosurlyrdquo)

QUESTION 17

Choice C is the best answer It accurately interprets ldquonot content to ollow

conventional business practicesrdquo as logically introducing the new practice o

ldquoemploying womenrdquo described in the ollowing sentences

Choices A B and D are incorrect because none recognizes why the sentence

is relevant to this particular location in the passage

QUESTION 18

Choice B is the best answer It is concise and ree o redundancies

Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and

ldquotremendousrdquo adjectives so close in meaning that together they present a

redundancy

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1840

17

QUESTION 19

Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary

reerence to ldquosuch regulationsrdquo in the previous clause

Choices A B and C are incorrect because each lacks a necessary subject

such as a pronoun or noun

QUESTION 20

Choice C is the best answer It reers directly to benefits or the restaurantsrsquo

emale employees the subject o the previous sentence

Choices A B and D are incorrect because none logically builds upon the

sentence that precedes it

QUESTION 21

Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo

Choices A B and C are incorrect because each uses the punctuation or

a dependent clause (ldquoLiving independently and demonstrating an intense

work ethicrdquo) as i it were an independent clause

QUESTION 22

Choice A is the best answer It recognizes that the new inormation sup-

ports the previous sentencersquos claim that ldquothe Harvey Girls became known as

a transormative orcerdquo

Choices B C and D are incorrect because each misinterprets the relation-

ship between the proposed text and the passage

QUESTION 23

Choice A is the best answer It opens with a clause that identifies how

1-MCP affects apples which ocuses the sentence on 1-MCP as the subject

and allows the ideas in the sentence to progress logically

Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy

QUESTION 24

Choice D is the best answer Only the comma is necessary to separate

ldquoethylenerdquo rom the appositive noun phrase that defines it

Choices A B and C are incorrect because each creates a comma splice and

or adds unnecessary words

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1940

18

QUESTION 25

Choice B is the best answer It offers an adjective that accurately describes

resh apples

Choices A C and D are incorrect because each proposes an adjective that

does not describe a plausible ruit texture

QUESTION 26

Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-

sponds with the plural reerent ldquoapplesrdquo

Choices B C and D are incorrect because none provides a pronoun that is

both possessive and plural

QUESTION 27

Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins

the relative clause

Choices A B and C are incorrect because each contains a pronoun that

either does not correspond with the human reerent ldquoconsumersrdquo or does

not correctly begin the relative clause

QUESTION 28

Choice B is the best answer It provides the present tense verb ldquodordquo which

corresponds to the present tense established earlier in the sentence

Choices A C and D are incorrect because each contains a verb that deviates

rom the simple present tense established in the sentence

QUESTION 29

Choice B is the best answer It provides a colon to appropriately introduce the

clause that ollows an elaboration on the preceding claim that Bartlett pears

are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo

Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically

QUESTION 30

Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-

trast with a previous idea and goes on to mention that 1-MCP can have

negative effects Sentence 1 continues the discussion o benefits o 1-MCP

and sentence 2 names the adverse effect o limiting scent production so the

most logical spot or sentence 4 is between these sentences

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040

19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2140

20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240

21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340

22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440

23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540

24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640

25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740

26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840

27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 15: PrepScholar Sat Practice Test 3 Answers

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1540

14

Choices A C and D are incorrect because none introduces the topic dis-

cussed in the remainder o the passage

QUESTION 3

Choice C is the best answer It accurately notes that the proposed sentence

would be placed directly between the first mention o circadian rhythms andthe explanation o the term

Choices A B and D are incorrect because each misinterprets the relation-

ship between the proposed additional text and the ideas in the paragraph

QUESTION 4

Choice C is the best answer It provides the correct possessive construction

or ldquobodyrdquo which must be a singular noun when discussed in general terms

as in this sentence Choice C also provides the correct plural construction

or ldquoclocksrdquo

Choices A B and D are incorrect because each applies either a possessive or

a plural construction in a place where it doesnrsquot belong

QUESTION 5

Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular

noun ldquoabsenteeismrdquo

Choices B C and D are incorrect because each provides a verb that

either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy

QUESTION 6

Choice B is the best answer It contains a direct reerence to productivity

the topic introduced in the previous sentence

Choices A C and D are incorrect because none directly addresses employee

productivity the primary subject o the previous sentence

QUESTION 7

Choice A is the best answer It opens with a reerence to lowered worker

productivity creating a transition rom the previous paragraph and clearly

positions the high energy costs o artificial light sources as an additional

disadvantage

Choices B C and D are incorrect because none o the choices offer an ade-

quate transition rom the previous paragraph Each awkwardly inserts the

issue o lower worker productivity into a statement about the high energy

costs o artificial light sources

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1640

15

QUESTION 8

Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-

cate that the savings occurred every year

Choices A B and C are incorrect because each proposes an option that

would result in a redundancy with ldquoannualrdquo

QUESTION 9

Choice C is the best answer It provides a transitional adverb that accurately

communicates that this sentence describes an option that companies could

choose (ldquolight tubesrdquo) instead o the option described in the previous sen-

tence (ldquoull-pane windowsrdquo)

Choices A B and D are incorrect because each proposes a transitional

adverb that does not accurately reflect the relationship between this sen-

tence and the one preceding it

QUESTION 10

Choice C is the best answer It provides the correct relative pronoun to cor-

respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-

duce the definition that ollows

Choices A B and D are incorrect because each offers a pronoun inappropri-

ate or opening a dependent clause defining ldquolight tubesrdquo

QUESTION 11

Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the

noun ldquomeansrdquo particularly as a way to connect it to another noun or verb

Choices A C and D are incorrect because each results in nonstandard

phrasing with ldquomeansrdquo

QUESTION 12

Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-

responds with the plural noun ldquosettlersrdquo

Choices B C and D are incorrect because each provides either a nonstan-

dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo

QUESTION 13

Choice C is the best answer It creates a transition rom the poor ood qual-

ity mentioned in the previous sentence to the inormation about Harvey in

the remainder o the sentence

7262019 PrepScholar Sat Practice Test 3 Answers

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16

Choices A B and D are incorrect because none offers a transition rom the

previous sentence or a detail that corresponds precisely with the inorma-

tion in the remainder o the sentence

QUESTION 14

Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens

with a comma

Choices A B and C are incorrect because each proposes punctuation that

creates an inappropriately strong separation between the subject ldquoFred

Harveyrdquo and the verb ldquodecidedrdquo

QUESTION 15

Choice B is the best answer It provides the plural verb and plural posses-

sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo

Choices A C and D are incorrect because each either ails to provide a verb

that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide

the appropriate possessive pronoun

QUESTION 16

Choice C is the best answer It accurately echoes an earlier characterization

o the ood as being o ldquoterrible qualityrdquo while maintaining the established

tone o the passage

Choices A B and D are incorrect either because the word is less ormal than

the established tone o the passage (ldquoickyrdquo) or because it illogically attributes

agency to ood (ldquosinisterrdquo ldquosurlyrdquo)

QUESTION 17

Choice C is the best answer It accurately interprets ldquonot content to ollow

conventional business practicesrdquo as logically introducing the new practice o

ldquoemploying womenrdquo described in the ollowing sentences

Choices A B and D are incorrect because none recognizes why the sentence

is relevant to this particular location in the passage

QUESTION 18

Choice B is the best answer It is concise and ree o redundancies

Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and

ldquotremendousrdquo adjectives so close in meaning that together they present a

redundancy

7262019 PrepScholar Sat Practice Test 3 Answers

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17

QUESTION 19

Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary

reerence to ldquosuch regulationsrdquo in the previous clause

Choices A B and C are incorrect because each lacks a necessary subject

such as a pronoun or noun

QUESTION 20

Choice C is the best answer It reers directly to benefits or the restaurantsrsquo

emale employees the subject o the previous sentence

Choices A B and D are incorrect because none logically builds upon the

sentence that precedes it

QUESTION 21

Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo

Choices A B and C are incorrect because each uses the punctuation or

a dependent clause (ldquoLiving independently and demonstrating an intense

work ethicrdquo) as i it were an independent clause

QUESTION 22

Choice A is the best answer It recognizes that the new inormation sup-

ports the previous sentencersquos claim that ldquothe Harvey Girls became known as

a transormative orcerdquo

Choices B C and D are incorrect because each misinterprets the relation-

ship between the proposed text and the passage

QUESTION 23

Choice A is the best answer It opens with a clause that identifies how

1-MCP affects apples which ocuses the sentence on 1-MCP as the subject

and allows the ideas in the sentence to progress logically

Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy

QUESTION 24

Choice D is the best answer Only the comma is necessary to separate

ldquoethylenerdquo rom the appositive noun phrase that defines it

Choices A B and C are incorrect because each creates a comma splice and

or adds unnecessary words

7262019 PrepScholar Sat Practice Test 3 Answers

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18

QUESTION 25

Choice B is the best answer It offers an adjective that accurately describes

resh apples

Choices A C and D are incorrect because each proposes an adjective that

does not describe a plausible ruit texture

QUESTION 26

Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-

sponds with the plural reerent ldquoapplesrdquo

Choices B C and D are incorrect because none provides a pronoun that is

both possessive and plural

QUESTION 27

Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins

the relative clause

Choices A B and C are incorrect because each contains a pronoun that

either does not correspond with the human reerent ldquoconsumersrdquo or does

not correctly begin the relative clause

QUESTION 28

Choice B is the best answer It provides the present tense verb ldquodordquo which

corresponds to the present tense established earlier in the sentence

Choices A C and D are incorrect because each contains a verb that deviates

rom the simple present tense established in the sentence

QUESTION 29

Choice B is the best answer It provides a colon to appropriately introduce the

clause that ollows an elaboration on the preceding claim that Bartlett pears

are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo

Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically

QUESTION 30

Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-

trast with a previous idea and goes on to mention that 1-MCP can have

negative effects Sentence 1 continues the discussion o benefits o 1-MCP

and sentence 2 names the adverse effect o limiting scent production so the

most logical spot or sentence 4 is between these sentences

7262019 PrepScholar Sat Practice Test 3 Answers

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19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340

22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440

23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540

24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640

25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740

26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

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27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040

29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040

QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 16: PrepScholar Sat Practice Test 3 Answers

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1640

15

QUESTION 8

Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-

cate that the savings occurred every year

Choices A B and C are incorrect because each proposes an option that

would result in a redundancy with ldquoannualrdquo

QUESTION 9

Choice C is the best answer It provides a transitional adverb that accurately

communicates that this sentence describes an option that companies could

choose (ldquolight tubesrdquo) instead o the option described in the previous sen-

tence (ldquoull-pane windowsrdquo)

Choices A B and D are incorrect because each proposes a transitional

adverb that does not accurately reflect the relationship between this sen-

tence and the one preceding it

QUESTION 10

Choice C is the best answer It provides the correct relative pronoun to cor-

respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-

duce the definition that ollows

Choices A B and D are incorrect because each offers a pronoun inappropri-

ate or opening a dependent clause defining ldquolight tubesrdquo

QUESTION 11

Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the

noun ldquomeansrdquo particularly as a way to connect it to another noun or verb

Choices A C and D are incorrect because each results in nonstandard

phrasing with ldquomeansrdquo

QUESTION 12

Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-

responds with the plural noun ldquosettlersrdquo

Choices B C and D are incorrect because each provides either a nonstan-

dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo

QUESTION 13

Choice C is the best answer It creates a transition rom the poor ood qual-

ity mentioned in the previous sentence to the inormation about Harvey in

the remainder o the sentence

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1740

16

Choices A B and D are incorrect because none offers a transition rom the

previous sentence or a detail that corresponds precisely with the inorma-

tion in the remainder o the sentence

QUESTION 14

Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens

with a comma

Choices A B and C are incorrect because each proposes punctuation that

creates an inappropriately strong separation between the subject ldquoFred

Harveyrdquo and the verb ldquodecidedrdquo

QUESTION 15

Choice B is the best answer It provides the plural verb and plural posses-

sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo

Choices A C and D are incorrect because each either ails to provide a verb

that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide

the appropriate possessive pronoun

QUESTION 16

Choice C is the best answer It accurately echoes an earlier characterization

o the ood as being o ldquoterrible qualityrdquo while maintaining the established

tone o the passage

Choices A B and D are incorrect either because the word is less ormal than

the established tone o the passage (ldquoickyrdquo) or because it illogically attributes

agency to ood (ldquosinisterrdquo ldquosurlyrdquo)

QUESTION 17

Choice C is the best answer It accurately interprets ldquonot content to ollow

conventional business practicesrdquo as logically introducing the new practice o

ldquoemploying womenrdquo described in the ollowing sentences

Choices A B and D are incorrect because none recognizes why the sentence

is relevant to this particular location in the passage

QUESTION 18

Choice B is the best answer It is concise and ree o redundancies

Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and

ldquotremendousrdquo adjectives so close in meaning that together they present a

redundancy

7262019 PrepScholar Sat Practice Test 3 Answers

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17

QUESTION 19

Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary

reerence to ldquosuch regulationsrdquo in the previous clause

Choices A B and C are incorrect because each lacks a necessary subject

such as a pronoun or noun

QUESTION 20

Choice C is the best answer It reers directly to benefits or the restaurantsrsquo

emale employees the subject o the previous sentence

Choices A B and D are incorrect because none logically builds upon the

sentence that precedes it

QUESTION 21

Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo

Choices A B and C are incorrect because each uses the punctuation or

a dependent clause (ldquoLiving independently and demonstrating an intense

work ethicrdquo) as i it were an independent clause

QUESTION 22

Choice A is the best answer It recognizes that the new inormation sup-

ports the previous sentencersquos claim that ldquothe Harvey Girls became known as

a transormative orcerdquo

Choices B C and D are incorrect because each misinterprets the relation-

ship between the proposed text and the passage

QUESTION 23

Choice A is the best answer It opens with a clause that identifies how

1-MCP affects apples which ocuses the sentence on 1-MCP as the subject

and allows the ideas in the sentence to progress logically

Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy

QUESTION 24

Choice D is the best answer Only the comma is necessary to separate

ldquoethylenerdquo rom the appositive noun phrase that defines it

Choices A B and C are incorrect because each creates a comma splice and

or adds unnecessary words

7262019 PrepScholar Sat Practice Test 3 Answers

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18

QUESTION 25

Choice B is the best answer It offers an adjective that accurately describes

resh apples

Choices A C and D are incorrect because each proposes an adjective that

does not describe a plausible ruit texture

QUESTION 26

Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-

sponds with the plural reerent ldquoapplesrdquo

Choices B C and D are incorrect because none provides a pronoun that is

both possessive and plural

QUESTION 27

Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins

the relative clause

Choices A B and C are incorrect because each contains a pronoun that

either does not correspond with the human reerent ldquoconsumersrdquo or does

not correctly begin the relative clause

QUESTION 28

Choice B is the best answer It provides the present tense verb ldquodordquo which

corresponds to the present tense established earlier in the sentence

Choices A C and D are incorrect because each contains a verb that deviates

rom the simple present tense established in the sentence

QUESTION 29

Choice B is the best answer It provides a colon to appropriately introduce the

clause that ollows an elaboration on the preceding claim that Bartlett pears

are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo

Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically

QUESTION 30

Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-

trast with a previous idea and goes on to mention that 1-MCP can have

negative effects Sentence 1 continues the discussion o benefits o 1-MCP

and sentence 2 names the adverse effect o limiting scent production so the

most logical spot or sentence 4 is between these sentences

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040

19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340

22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440

23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540

24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640

25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740

26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

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27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040

QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 17: PrepScholar Sat Practice Test 3 Answers

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1740

16

Choices A B and D are incorrect because none offers a transition rom the

previous sentence or a detail that corresponds precisely with the inorma-

tion in the remainder o the sentence

QUESTION 14

Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens

with a comma

Choices A B and C are incorrect because each proposes punctuation that

creates an inappropriately strong separation between the subject ldquoFred

Harveyrdquo and the verb ldquodecidedrdquo

QUESTION 15

Choice B is the best answer It provides the plural verb and plural posses-

sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo

Choices A C and D are incorrect because each either ails to provide a verb

that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide

the appropriate possessive pronoun

QUESTION 16

Choice C is the best answer It accurately echoes an earlier characterization

o the ood as being o ldquoterrible qualityrdquo while maintaining the established

tone o the passage

Choices A B and D are incorrect either because the word is less ormal than

the established tone o the passage (ldquoickyrdquo) or because it illogically attributes

agency to ood (ldquosinisterrdquo ldquosurlyrdquo)

QUESTION 17

Choice C is the best answer It accurately interprets ldquonot content to ollow

conventional business practicesrdquo as logically introducing the new practice o

ldquoemploying womenrdquo described in the ollowing sentences

Choices A B and D are incorrect because none recognizes why the sentence

is relevant to this particular location in the passage

QUESTION 18

Choice B is the best answer It is concise and ree o redundancies

Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and

ldquotremendousrdquo adjectives so close in meaning that together they present a

redundancy

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1840

17

QUESTION 19

Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary

reerence to ldquosuch regulationsrdquo in the previous clause

Choices A B and C are incorrect because each lacks a necessary subject

such as a pronoun or noun

QUESTION 20

Choice C is the best answer It reers directly to benefits or the restaurantsrsquo

emale employees the subject o the previous sentence

Choices A B and D are incorrect because none logically builds upon the

sentence that precedes it

QUESTION 21

Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo

Choices A B and C are incorrect because each uses the punctuation or

a dependent clause (ldquoLiving independently and demonstrating an intense

work ethicrdquo) as i it were an independent clause

QUESTION 22

Choice A is the best answer It recognizes that the new inormation sup-

ports the previous sentencersquos claim that ldquothe Harvey Girls became known as

a transormative orcerdquo

Choices B C and D are incorrect because each misinterprets the relation-

ship between the proposed text and the passage

QUESTION 23

Choice A is the best answer It opens with a clause that identifies how

1-MCP affects apples which ocuses the sentence on 1-MCP as the subject

and allows the ideas in the sentence to progress logically

Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy

QUESTION 24

Choice D is the best answer Only the comma is necessary to separate

ldquoethylenerdquo rom the appositive noun phrase that defines it

Choices A B and C are incorrect because each creates a comma splice and

or adds unnecessary words

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1940

18

QUESTION 25

Choice B is the best answer It offers an adjective that accurately describes

resh apples

Choices A C and D are incorrect because each proposes an adjective that

does not describe a plausible ruit texture

QUESTION 26

Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-

sponds with the plural reerent ldquoapplesrdquo

Choices B C and D are incorrect because none provides a pronoun that is

both possessive and plural

QUESTION 27

Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins

the relative clause

Choices A B and C are incorrect because each contains a pronoun that

either does not correspond with the human reerent ldquoconsumersrdquo or does

not correctly begin the relative clause

QUESTION 28

Choice B is the best answer It provides the present tense verb ldquodordquo which

corresponds to the present tense established earlier in the sentence

Choices A C and D are incorrect because each contains a verb that deviates

rom the simple present tense established in the sentence

QUESTION 29

Choice B is the best answer It provides a colon to appropriately introduce the

clause that ollows an elaboration on the preceding claim that Bartlett pears

are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo

Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically

QUESTION 30

Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-

trast with a previous idea and goes on to mention that 1-MCP can have

negative effects Sentence 1 continues the discussion o benefits o 1-MCP

and sentence 2 names the adverse effect o limiting scent production so the

most logical spot or sentence 4 is between these sentences

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040

19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2140

20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240

21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340

22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440

23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540

24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640

25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740

26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840

27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040

QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 18: PrepScholar Sat Practice Test 3 Answers

7262019 PrepScholar Sat Practice Test 3 Answers

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17

QUESTION 19

Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary

reerence to ldquosuch regulationsrdquo in the previous clause

Choices A B and C are incorrect because each lacks a necessary subject

such as a pronoun or noun

QUESTION 20

Choice C is the best answer It reers directly to benefits or the restaurantsrsquo

emale employees the subject o the previous sentence

Choices A B and D are incorrect because none logically builds upon the

sentence that precedes it

QUESTION 21

Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo

Choices A B and C are incorrect because each uses the punctuation or

a dependent clause (ldquoLiving independently and demonstrating an intense

work ethicrdquo) as i it were an independent clause

QUESTION 22

Choice A is the best answer It recognizes that the new inormation sup-

ports the previous sentencersquos claim that ldquothe Harvey Girls became known as

a transormative orcerdquo

Choices B C and D are incorrect because each misinterprets the relation-

ship between the proposed text and the passage

QUESTION 23

Choice A is the best answer It opens with a clause that identifies how

1-MCP affects apples which ocuses the sentence on 1-MCP as the subject

and allows the ideas in the sentence to progress logically

Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy

QUESTION 24

Choice D is the best answer Only the comma is necessary to separate

ldquoethylenerdquo rom the appositive noun phrase that defines it

Choices A B and C are incorrect because each creates a comma splice and

or adds unnecessary words

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1940

18

QUESTION 25

Choice B is the best answer It offers an adjective that accurately describes

resh apples

Choices A C and D are incorrect because each proposes an adjective that

does not describe a plausible ruit texture

QUESTION 26

Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-

sponds with the plural reerent ldquoapplesrdquo

Choices B C and D are incorrect because none provides a pronoun that is

both possessive and plural

QUESTION 27

Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins

the relative clause

Choices A B and C are incorrect because each contains a pronoun that

either does not correspond with the human reerent ldquoconsumersrdquo or does

not correctly begin the relative clause

QUESTION 28

Choice B is the best answer It provides the present tense verb ldquodordquo which

corresponds to the present tense established earlier in the sentence

Choices A C and D are incorrect because each contains a verb that deviates

rom the simple present tense established in the sentence

QUESTION 29

Choice B is the best answer It provides a colon to appropriately introduce the

clause that ollows an elaboration on the preceding claim that Bartlett pears

are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo

Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically

QUESTION 30

Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-

trast with a previous idea and goes on to mention that 1-MCP can have

negative effects Sentence 1 continues the discussion o benefits o 1-MCP

and sentence 2 names the adverse effect o limiting scent production so the

most logical spot or sentence 4 is between these sentences

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040

19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2140

20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240

21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340

22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540

24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640

25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740

26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840

27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940

28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 19: PrepScholar Sat Practice Test 3 Answers

7262019 PrepScholar Sat Practice Test 3 Answers

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18

QUESTION 25

Choice B is the best answer It offers an adjective that accurately describes

resh apples

Choices A C and D are incorrect because each proposes an adjective that

does not describe a plausible ruit texture

QUESTION 26

Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-

sponds with the plural reerent ldquoapplesrdquo

Choices B C and D are incorrect because none provides a pronoun that is

both possessive and plural

QUESTION 27

Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins

the relative clause

Choices A B and C are incorrect because each contains a pronoun that

either does not correspond with the human reerent ldquoconsumersrdquo or does

not correctly begin the relative clause

QUESTION 28

Choice B is the best answer It provides the present tense verb ldquodordquo which

corresponds to the present tense established earlier in the sentence

Choices A C and D are incorrect because each contains a verb that deviates

rom the simple present tense established in the sentence

QUESTION 29

Choice B is the best answer It provides a colon to appropriately introduce the

clause that ollows an elaboration on the preceding claim that Bartlett pears

are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo

Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically

QUESTION 30

Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-

trast with a previous idea and goes on to mention that 1-MCP can have

negative effects Sentence 1 continues the discussion o benefits o 1-MCP

and sentence 2 names the adverse effect o limiting scent production so the

most logical spot or sentence 4 is between these sentences

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040

19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2140

20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240

21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340

22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440

23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540

24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640

25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740

26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840

27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940

28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040

29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3140

30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3440

33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640

35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 20: PrepScholar Sat Practice Test 3 Answers

7262019 PrepScholar Sat Practice Test 3 Answers

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19

Choices A C and D are incorrect because each proposes placing the sen-

tence at a point where it would compromise the logical development o ideas

in the paragraph

QUESTION 31

Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when

untreated apples are lef in the open air or three weeks rather than placed

immediately into a controlled atmosphere

Choices A B and C are incorrect because each presents an inaccurate inter-

pretation o the data in the graph

QUESTION 32

Choice B is the best answer It accurately interprets the data as indicating

that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line

Choices A C and D are incorrect because each proposes an inaccurate

interpretation o the data

QUESTION 33

Choice C is the best answer It describes an action weighing the relative

values that ruit sellers must take as a result o 1-MCPrsquos limitations

Choices A B and D are incorrect because none specifically connects the

shortcomings o 1-MCP with any action on the part o ruit sellers

QUESTION 34

Choice D is the best answer It clearly communicates that the preceding

dependent clause modifies ldquoworks by human artistsrdquo

Choices A B and C are incorrect because each ails to link the preced-

ing dependent clause to an independent clause resulting in an incomplete

sentence

QUESTION 35

Choice B is the best answer It provides the necessary em dash to close the

aside about artist CM Coolidge which opens with an em dash

Choices A C and D are incorrect because each provides closing punctua-

tion or the aside that does not correspond with the opening punctuation

QUESTION 36

Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the

plural noun ldquoworks o artrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340

22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

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24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

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25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

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26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

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27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3540

34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640

35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 21: PrepScholar Sat Practice Test 3 Answers

7262019 PrepScholar Sat Practice Test 3 Answers

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20

Choices A B and D are incorrect because none provides the plural verb in

the present tense that the sentence requires

QUESTION 37

Choice D is the best answer It names a ldquomuseum in Russiardquo which is the

subject o the next paragraph

Choices A B and C are incorrect because each provides an overly general

phrase that does not specifically link to the paragraph that ollows

QUESTION 38

Choice C is the best answer It creates parallelism with the verb ldquocould

damagerdquo that appears earlier in the clause (ldquorodents that could damage

[and could] scare off visitorsrdquo)

Choices A B and D are incorrect because each presents a verb tense that is

inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)

that shares ldquomice rats and other rodentsrdquo as its subject

QUESTION 39

Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos

daughter continuing his tradition most logically ollows the sentence about

Peter the Great

Choices A B and D are incorrect because each presents a placement that

would compromise the logical development o the paragraph

QUESTION 40

Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an

artist to create a specific work

Choices A C and D are incorrect because each provides a word that does

not correspond logically with the context

QUESTION 41

Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-

son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo

Choices A B and C are incorrect because each ails to open and close the unin-

terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas

QUESTION 42

Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds

with the subsequent examples o portraits where the cats are depicted as

ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo

7262019 PrepScholar Sat Practice Test 3 Answers

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21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340

22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540

24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

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25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

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26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

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27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3840

37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3940

38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 22: PrepScholar Sat Practice Test 3 Answers

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21

Choices B C and D are incorrect because each provides a statement that

does not logically connect to the examples that ollow

QUESTION 43

Choice D is the best answer It accurately states that the inormation in the

proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph

Choices A B and C are incorrect because each ails to recognize that the

proposed sentence interrupts the logical development o the paragraph

QUESTION 44

Choice D is the best answer Te tone corresponds with that established in

the passage and the phrasing appropriately ocuses on the catsrsquo contribution

to protecting artwork rather than on simply killing rodents

Choices A B and C are incorrect because none makes explicit the link

between the catsrsquo hunting activities and the service to the museum

Section 3 Math Test mdash No Calculator

QUESTION 1

Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number

o walls K is a constant with units o dollars per square oot ℓ is the length

o each wall in eet and h is the height o each wall in eet Examining this

equation shows that ℓ and h will be used to determine the area o each wall

Te variable n is the number o walls so n times the area o the walls will

give the amount o area that will need to be painted Te only remaining

variable is K which represents the cost per square oot and is determined by

the painterrsquos time and the price o paint Tereore K is the only actor that

will change i the customer asks or a more expensive brand o paint

Choice A is incorrect because a more expensive brand o paint would not

cause the height o each wall to change Choice B is incorrect because a more

expensive brand o paint would not cause the length o each wall to change

Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change

QUESTION 2

Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives

r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39

Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting

18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39

7262019 PrepScholar Sat Practice Test 3 Answers

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22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

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24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

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25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

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26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

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27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940

28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040

29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 23: PrepScholar Sat Practice Test 3 Answers

7262019 PrepScholar Sat Practice Test 3 Answers

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22

Choice A is incorrect because 6 is the value o r however the question asks

or the value o the expression 6r + 3 Choices B and C are incorrect because

i 6r + 3 were equal to either o these values then it would not be possible or

3r to be equal to 18 as stated in the question

QUESTION 3

Choice D is correct By definition a m

_ n = n radic _ am or any positive integers m

and n It ollows thereore that a2

_ 3

=

3 radic _

a2

Choice A is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to the

expression radic_

a 1

_ 3 yields radic

_

a1

_ 3

= ( a 1

_ 3

) 1

_ 2

= a

1 _

6 Because a

1 _

6 ne a

2 _

3 radic_

a 1

_ 3

is not the correct

answer Choice B is incorrect By definition a 1

_ n =n radic _

a or any positive integer n

Applying this definition as well as the power property o exponents to

the expression radic _

a 3 yields radic _

a 3 = (

a 3 ) 1 _ 2

= a

3 _ 2

Because a 3

_ 2

ne a 2

_ 3

radic _

a 3 is not the

correct answer Choice C is incorrect By definition a 1 _ n = n radic _

a or any positive

integer n Applying this definition as well as the power property o expo-

nents to the expression3

radic _

a 1 _ 2

yields

3

radic _

a 1 _ 2

= ( a 1 _ 2

) 1

_ 3

= a

1 _ 6

Because a

1 _ 6

ne a 2 _ 3

3

radic _

a 1 _ 2

is

not the correct answer

QUESTION 4

Choice B is correct o fit the scenario described 30 must be twice as large

as x Tis can be written as 2x = 30

Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-

sion in choice C states that 30 is hal as large as x not twice as large as x

QUESTION 5

Choice C is correct Multiplying each side o5

_ x

=15

_

x + 20 by x (x + 20) gives

15x = 5(x + 20) Distributing the 5 over the values within the parenthe-

ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives

10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o

x _

5 is

10 _

5 = 2

Choice A is incorrect because it is the value o x notx

_ 5

Choices B and D

are incorrect and may be the result o errors in arithmetic operations on the

given equation

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23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

7262019 PrepScholar Sat Practice Test 3 Answers

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24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

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25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

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26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

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27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 24: PrepScholar Sat Practice Test 3 Answers

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23

QUESTION 6

Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by

3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by

2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the

corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side

o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is

2 minus 6 = minus4

Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and

3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4

Choices A B and D are incorrect and may be the result o an arithmetic

error when solving the system o equations

QUESTION 7

Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based

on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )

Choice A is incorrect because f (2) ne 0 choice B is incorrect because no

inormation is given about the value o f (3) so x minus 3 may or may not be a

actor o f (x ) and choice D is incorrect because f (5) ne 0

QUESTION 8

Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm

and so the slope o the line is k Since the line contains the point (c d ) the

coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving

this equation or the slope k gives k =d minus 4_

c

Choices B C and D are incorrect and may be the result o errors in substi-

tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in

the resulting equation

QUESTION 9

Choice A is correct I a system o two linear equations has no solution then

the lines represented by the equations in the coordinate plane are parallel

Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3

x minus 4 _ 3

where k _ 3

is the slope

o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4

_ 5

x minus7

_ 5

where4

_ 5

is the slope o the line I two lines are parallel then the slopes o

the line are equal Tereore4

_ 5

=k

_ 3

or k =12 _

5 (Since the y -intercepts o the

lines represented by the equations are minus4

_ 3

and minus7

_ 5

the lines are parallel not

identical)

Choices B C and D are incorrect and may be the result o a computational

error when rewriting the equations or solving the equation representing the

equality o the slopes or k

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24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

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25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

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26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

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27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 25: PrepScholar Sat Practice Test 3 Answers

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24

QUESTION 10

Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives

25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates

o the two points o intersection are x = 16 and x = 6 respectively Since

both points o intersection have a y -coordinate o 25 it ollows that the two

points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the

x -coordinates 16 minus 6 = 10

Choices B C and D are incorrect and may be the result o an error in solv-

ing the quadratic equation that results when substituting 25 or y in the

given quadratic equation

QUESTION 11

Choice B is correct Since the angles marked y deg and udeg are vertical angles

y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles

w = z Tereore x = z and so I must be true

Te equation in II need not be true For example i x = w = z = t = 70 and

y = u = 40 then all three pairs o vertical angles in the figure have equal

measure and the given condition x + y = u + w holds But it is not true in this

case that y is equal to w Tereore II need not be true

Since the top three angles in the figure orm a straight angle it ollows that

x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t

Subtracting the sides o the given equation x + y = u + w rom the corre-

sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true

Since only I and III must be true the correct answer is choice B

Choices A C and D are incorrect because each o these choices includes II

which need not be true

QUESTION 12

Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses

the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex

o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)

Tus the x -coordinate o the vertex isminus4 + 2

_

2 = minus1 Tis is the value o c o

find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)

y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a

Tereore the value o d is minus9a

7262019 PrepScholar Sat Practice Test 3 Answers

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25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

7262019 PrepScholar Sat Practice Test 3 Answers

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26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

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27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 26: PrepScholar Sat Practice Test 3 Answers

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25

Choice B is incorrect because the value o the constant term in the equa-

tion is not the y -coordinate o the vertex unless there were no linear terms

in the quadratic Choice C is incorrect and may be the result o a sign error

in finding the x -coordinate o the vertex Choice D is incorrect because

the negative o the coefficient o the linear term in the quadratic is not the

y -coordinate o the vertex

QUESTION 13

Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to

minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +

25x minus47 (Tis can be seen by multiplying each side o the given equation by

ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since

the coefficients o the x 2-term have to be equal on both sides o the equation

minus8a = 24 or a = minus3

Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the

value o a

QUESTION 14

Choice A is correct Dividing each side o the given equation by 3 gives

the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula

minusb plusmn radic _

b 2 minus 4ac__

2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic

_ 2

Choices B C and D are incorrect and may be the result o errors when

applying the quadratic ormula

QUESTION 15

Choice D is correct I C is graphed against F the slope o the graph is equal

to5

_ 9

degrees Celsiusdegrees Fahrenheit which means that or an increase o

1 degree Fahrenheit the increase is5

_ 9

o 1 degree Celsius Tus statement I

is true Tis is the equivalent to saying that an increase o 1 degree Celsius

is equal to an increase o9

_ 5

degrees Fahrenheit Since9

_ 5

= 18 statement II

is true On the other hand statement III is not true since a temperature

increase o9

_ 5

degrees Fahrenheit not5

_ 9

degree Fahrenheit is equal to a tem-

perature increase o 1 degree Celsius

Choices A B and C are incorrect because each o these choices omits a true

statement or includes a alse statement

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26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

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27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640

35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 27: PrepScholar Sat Practice Test 3 Answers

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26

QUESTION 16

The correct answer is either 1 or 2 Te given equation can be rewritten as

x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant

term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is

a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0

Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the

possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the

correct answer

QUESTION 17

The correct answer is 2 First clear the ractions rom the given equation by

multiplying each side o the equation by 36 (the least common multiple o 4

9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms

on each side o the equation yields 12x = 24 Finally dividing both sides o

the equation by 12 yields x = 2

Alternatively since7

_ 9

x minus4

_ 9

x =3

_ 9

x =1

_ 3

x and1

_ 4

+5

_

12 =

3 _

12 +

5 _

12 =

8 _

12 =

2 _

3 the

given equation simplifies to1

_ 3

x =2

_ 3

Multiplying each side o1

_ 3

x =2

_ 3

by 3

yields x = 2

QUESTION 18

The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that

180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles

triangle on the right has measure180deg minus 30deg

_

2 = 75deg Tereore the measure o

the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105

QUESTION 19

The correct answer is 370 A system o equations can be used where h rep-

resents the number o calories in a hamburger and f represents the number

o calories in an order o ries Te equation 2h + 3 f = 1700 represents the

act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories

and the equation h = f + 50 represents the act that one hamburger contains

50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =

1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows

2 f + 100 + 3 f = 1700

5 f + 100 = 1700

5 f = 1600

f = 320

Te number o calories in an order o ries is 320 so the number o calories

in a hamburger is 50 more than 320 or 370

7262019 PrepScholar Sat Practice Test 3 Answers

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27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 28: PrepScholar Sat Practice Test 3 Answers

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27

QUESTION 20

The correct answer is3

_ 5

or 6 riangle ABC is a right triangle with its right

angle at B Tus_

AC is the hypotenuse o right triangle ABC and_

AB and_

BC are the legs o right triangle ABC By the Pythagorean theorem AB =

radic

_

202

minus 162

= radic

_

400 minus 256 = radic

_

144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle

F equals the measure o angle C Tus sinF = sinC From the side lengths

o triangle ABC sinC =opposite side

_

hypotenuse =

AB

_

AC =

12 _

20 =

3 _

5 Tereore sinF =

3 _

5

Either3

_ 5

or its decimal equivalent 6 may be gridded as the correct answer

Section 4 Math Test ndash Calculator

QUESTION 1

Choice C is correct Marilynrsquos distance rom her campsite remained the same

during the time she ate lunch Tis is represented by a horizontal segment in

the graph Te only horizontal segment in the graph starts at a time o about

110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch

and continued her hike at about 140 983152983149

Choices A B and D are incorrect and may be the result o a misinterpre-

tation o the graph For example choice B is the time Marilyn started her

lunch and choice D is the time Marilyn was at the maximum distance rom

her campsite

QUESTION 2

Choice B is correct O the 25 people who entered the contest there are

8 emales under age 40 and 2 males age 40 or older Tereore the probabil-

ity that the contest winner will be either a emale under age 40 or a male age

40 or older is8

_

25 +

2 _

25 =

10 _

25

Choice A is incorrect and may be the result o dividing 8 by 2 instead o

adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-

ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8

and 2 instead o adding 8 and 2 to find the probability

QUESTION 3

Choice C is correct Based on the graph sales increased in the first 3 years

since 1997 which is until year 2000 and then generally decreased thereafer

Choices A B and D are incorrect each o these choices contains inaccura-

cies in describing the general trend o music album sales rom 1997 to 2000

7262019 PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 29: PrepScholar Sat Practice Test 3 Answers

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28

QUESTION 4

Choice C is correct Te graph o y = f (n) in the coordinate plane is a line

that passes through each o the points given in the table From the table one

can see that an increase o 1 unit in n results in an increase o 3 units in f (n)

or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the

coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in

n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since

f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the

graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5

Choices A B and D are incorrect because each equation has the incorrect

slope o the line (the y -intercept in each equation is also incorrect)

QUESTION 5

Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-

uated to determine the total number o juniors and seniors inducted into the

honor society O the given choices 69 is closest to the value o the expression

Choice A is incorrect and may be the result o adding the number o juniors

and seniors and the percentages given and then using the expression

(007 + 005)(562 + 602) Choices C and D are incorrect and may be the

result o finding either only the number o juniors inducted or only the

number o seniors inducted

QUESTION 6

Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +

( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms

(

3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (

3x 2 + 5x 2 ) + (

minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4

Choice B is incorrect and may be the result o a sign error when combining

the coefficients o the x-term Choice C is incorrect and may be the result o

adding the exponents as well as the coefficients o like terms Choice D is

incorrect and may be the result o a combination o the errors described in

B and C

QUESTION 7

Choice D is correct o solve the equation or w multiply both sides o the

equation by the reciprocal o3

_ 5

which is5

_ 3

Tis gives ( 5 _ 3

) middot3

_ 5

w =4

_ 5

middot ( 5

_ 3

) which simplifies to w =

20 _

9

Choices A B and C are incorrect and may be the result o errors in arithme-

tic when simpliying the given equation

7262019 PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 30: PrepScholar Sat Practice Test 3 Answers

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29

QUESTION 8

Choice C is correct In the equation y = 056x + 272 the value o x increases

by 1 or each year that passes Each time x increases by 1 y increases by

056 since 056 is the slope o the graph o this equation Since y represents

the average number o students per classroom in the year represented by

x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School

is 056

Choice A is incorrect because the total number o students in the school in

2000 is the product o the average number o students per classroom and

the total number o classrooms which would appropriately be approximated

by the y -intercept (272) times the total number o classrooms which is not

given Choice B is incorrect because the average number o students per

classroom in 2000 is given by the y -intercept o the graph o the equation

but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly

change in the average number o students per classroom Te estimated di-

erence between the average number o students per classroom in 2010 and

2000 is 056 times the number o years that have passed between 2000 and

2010 that is 056 times 10 = 56

QUESTION 9

Choice B is correct Because Nate walks 25 meters in 137 seconds and

4 minutes is equal to 240 seconds the proportion

25 meters

_

137 sec =

x meters_

240 sec can be used to find out how many meters x Nate walks in 4 minutes Te

proportion can be simplified to25

_

137 =

x

_

240 because the units o meters per

second cancel and then each side o the equation can be multiplied by 240

giving(240)(25)

_

137 = x asymp 438 Tereore o the given options 450 meters is

closest to the distance Nate will walk in 4 minutes

Choice A is incorrect and may be the result o setting up the proportion

as137 sec

_

25 meters

=x meters

_

240 sec

and finding that x asymp 132 which is close to 150

Choices C and D are incorrect and may be the result o errors in calculation

QUESTION 10

Choice D is correct On Mercury the acceleration due to gravity is

36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives

W = 90(36) = 324 newtons

7262019 PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 31: PrepScholar Sat Practice Test 3 Answers

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30

Choice A is incorrect and may be the result o dividing 90 by 36 Choice B

is incorrect and may be the result o subtracting 36 rom 90 and rounding

to the nearest whole number Choice C is incorrect because an object with

a weight o 101 newtons on Mercury would have a mass o about 28 kilo-

grams not 90 kilograms

QUESTION 11

Choice B is correct On Earth the acceleration due to gravity is 98 msec 2

Tus or an object with a weight o 150 newtons the ormula W = mg

becomes 150 = m(98) which shows that the mass o an object with a weight

o 150 newtons on Earth is about 153 kilograms Substituting this mass

into the ormula W = mg and now using the weight o 170 newtons gives

170 = 153 g which shows that the second planetrsquos acceleration due to gravity

is about 111 msec2 According to the table this value or the acceleration

due to gravity holds on Saturn

Choices A C and D are incorrect Using the ormula W = mg and the values

or g in the table shows that an object with a weight o 170 newtons on these

planets would not have the same mass as an object with a weight o 150 new-

tons on Earth

QUESTION 12

Choice D is correct A zero o a unction corresponds to an x -intercept o

the graph o the unction in the xy -plane Tereore the complete graph

o the unction f which has five distinct zeros must have five x -intercepts

Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the

xy -plane

Choices A B and C are incorrect Te number o x -intercepts o each o

these graphs is not equal to five thereore none o these graphs could be the

complete graph o f which has five distinct zeros

QUESTION 13

Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k

in order to get v in terms o the other variables minus16t 2 and k need to be

subtracted rom each side Tis yields vt = h + 16t 2 minus k which when

divided by t will give v in terms o the other variables However the equa-

tion v =h + 16t2 minus k

_

t is not one o the options so the right side needs to

be urther simplified Another way to write the previous equation is

v =h minus k

_

t +

16t 2 _

t which can be simplified to v =

h minus k

_

t + 16t

Choices A B and C are incorrect and may be the result o arithmetic errors

when rewriting the original equation to express v in terms o h t and k

7262019 PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3440

33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3540

34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640

35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3740

36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 32: PrepScholar Sat Practice Test 3 Answers

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31

QUESTION 14

Choice A is correct Te hotel charges $020 per minute to use the meeting-

room phone Tis per-minute rate can be converted to the hourly rate using

the conversion 1 hour = 60 minutes as shown below

$020

_

minute times

60 minutes

_

1 hour=

$(020 times 60)_

hour

Tus the hotel charges $(020 times 60) per hour to use the meeting-room

phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h

which is equivalent to c = 020(60h)

Choice B is incorrect because in this expression the per-minute rate is mul-

tiplied by h the number o hours o phone use Furthermore the equation

indicates that there is a flat ee o $60 in addition to the per-minute or per-

hour rate Tis is not the case Choice C is incorrect because the expression

indicates that the hotel charges $( 60

_

020 ) per hour or use o the meeting-

room phone not $020(60) per hour Choice D is incorrect because the

expression indicates that the hourly rate is1

_

60 times the per-minute rate not

60 times the per-minute rate

QUESTION 15

Choice A is the correct answer Experimental research is a method used

to study a small group o people and generalize the results to a larger

population However in order to make a generalization involving cause

and eect

Te population must be well defined

Te participants must be selected at random

Te participants must be randomly assigned to treatment groups

When these conditions are met the results o the study can be generalized

to the population with a conclusion about cause and effect In this study

all conditions are met and the population rom which the participants were

selected are people with poor eyesight Tereore a general conclusion can

be drawn about the effect o reatment X on the population o people with

poor eyesight

Choice B is incorrect Te study did not include all available treatments

so no conclusion can be made about the relative effectiveness o all avail-

able treatments Choice C is incorrect Te participants were selected at

random rom a large population o people with poor eyesight Tereore

the results can be generalized only to that population and not to anyone in

general Also the conclusion is too strong an experimental study might

show that people are likely to be helped by a treatment but it cannot show

that anyone who takes the treatment will be helped Choice D is incorrect

7262019 PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

7262019 PrepScholar Sat Practice Test 3 Answers

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640

35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 33: PrepScholar Sat Practice Test 3 Answers

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32

Tis conclusion is too strong Te study shows that reatment X is likely to

improve the eyesight o people with poor eyesight but it cannot show that

the treatment definitely will cause improvement in eyesight or every per-

son Furthermore since the people undergoing the treatment in the study

were selected rom people with poor eyesight the results can be generalized

only to this population not to all people

QUESTION 16

Choice B is correct For any value o x say x = x 0 the point (x

0 f (x

0)) lies

on the graph of f and the point (x 0 g (x

0)) lies on the graph of g hus or

any value o x say x = x 0 the value of f (x

0) + g (x

0) is equal to the sum of the

y -coordinates o the points on the graphs o f and g with x -coordinate equal

to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur

when the y -coordinates o the points representing f (x ) and g (x ) at the same

value o x are equidistant rom the x -axis and are on opposite sides o the

x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o

g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0

Choices A C and D are incorrect because none o these x -values satisy the

given equation f (x ) + g (x ) = 0

QUESTION 17

Choice B is correct Te quantity o the product supplied to the market is

given by the unction S(P ) =1

_

2

P + 40 I the price P o the product increases

by $10 the effect on the quantity o the product supplied can be determined

by substituting P + 10 or P as the argument in the unction his gives

S(P + 10) =1

_ 2

(P + 10) + 40 =1

_ 2

P + 45 which shows that S(P + 10) = S(P ) + 5

hereore the quantity supplied to the market will increase by 5 units when

the price o the product is increased by $10

Alternatively look at the coefficient o P in the linear unction S his is the

slope o the graph o the unction where P is on the horizontal axis and S(P )

is on the vertical axis Since the slope is1

_ 2

or every increase o 1 in P there

will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will

yield an increase o 5 in S(P )

Choice A is incorrect I the quantity supplied decreases as the price o the

product increases the unction S(P ) would be decreasing but S(P ) =1

_ 2

P + 40 is

an increasing unction Choice C is incorrect and may be the result o assum-

ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may

be the result o conusing the y -intercept o the graph o S(P ) with the slope

and then adding 10 to the y -intercept

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33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 34: PrepScholar Sat Practice Test 3 Answers

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3440

33

QUESTION 18

Choice B is correct he quantity o the product supplied to the market will

equal the quantity o the product demanded by the market i S(P ) is equal to

D(P ) that is i1

_ 2

P + 40 = 220 minus P Solving this equation gives P = 120 and

so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded

Choices A C and D are incorrect At these dollar amounts the quantities

given by S(P ) and D(P ) are not equal

QUESTION 19

Choice C is correct It is given that 1 ounce o graphene covers 7 ootball

fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each

ootball field has an area o 11

_

3

acres than 336 ootball fields have a total area

o 336 times 11 _ 3

= 448 acres Tereore o the choices given 450 acres is closest

to the number o acres 48 ounces o graphene could cover

Choice A is incorrect and may be the result o dividing instead o multiply-

ing the number o ootball fields by 11

_ 3

Choice B is incorrect and may be

the result o finding the number o ootball fields not the number o acres

that can be covered by 48 ounces o graphene Choice D is incorrect and

may be the result o setting up the expression7 times 48 times 4

_

3 and then finding

only the numerator o the raction

QUESTION 20

Choice B is correct o answer this question find the point in the graph

that represents Michaelrsquos 34-minute swim and then compare the actual

heart rate or that swim with the expected heart rate as defined by the line

o best fit o find the point that represents Michaelrsquos swim that took 34

minutes look along the vertical line o the graph that is marked ldquo34rdquo on

the horizontal axis hat vertical line intersects only one point in the scat-

terplot at 148 beats per minute On the other hand the line o best fit

intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart

rate was 150 minus 148 = 2 beats per minute less than predicted by the line o

best fit

Choices A C and D are incorrect and may be the result o misreading the

scale o the graph

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640

35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3740

36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3840

37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3940

38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 35: PrepScholar Sat Practice Test 3 Answers

7262019 PrepScholar Sat Practice Test 3 Answers

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34

QUESTION 21

Choice C is correct Let I be the initial savings I each successive year 1 o the

current value is added to the value o the account then afer 1 year the amount

in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the

account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2

and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account

Choice A is incorrect I each successive year 2 o the initial savings I

is added to the value o the account then afer t years the amount in the

account will be I + 002It which is linear growth Choice B is incorrect

I each successive year 15 o the initial savings I and $100 is added to

the value o the the account then afer t years the amount in the account

will be I + (0015I + 100)t which is linear growth Choice D is incorrect

I each successive year $100 is added to the value o the account then

afer t years the amount in the account will be I + 100t which is lineargrowth

QUESTION 22

Choice B is correct One o the three numbers is x let the other two numbers

be y and z Since the sum o three numbers is 855 the equation x + y + z = 855

is true Te statement that x is 50 more than the sum o the other two

numbers can be represented as x = 15( y + z ) orx

_

15 = y + z Substituting

x

_

15

or y + z in x + y + z = 855 gives x +x

_

15 = 855 his last equation can be

rewritten as x + 2x

_

3

= 855 or 5x

_

3

= 855 Tereore x equals 3 _ 5

times 855 = 513

Choices A C and D are incorrect and may be the result o calculation errors

QUESTION 23

Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows

rom the complementary angle property o sines and cosines that a + b = 90

Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90

which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125

Choice A is incorrect and may be the result o mistakenly assuming that

a + b and making a sign error Choices B and D are incorrect because they

result in values or a and b such that sin(adeg) ne cos(bdeg)

QUESTION 24

Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te

conditions described in the question can be represented by the equations

n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation

gives 3c + 5 + 21 = 4c which can be solved to find c = 26

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640

35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3740

36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3840

37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

7262019 PrepScholar Sat Practice Test 3 Answers

httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3940

38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 36: PrepScholar Sat Practice Test 3 Answers

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35

Choices A B and C are incorrect because the values given for the number of

students in the class cannot fulfill both conditions given in the question For

example if there were 16 students in the class then the first condition would

imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but

the second condition would imply that there are 4(16) minus 21 = 43 milliliters of

solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class

QUESTION 25

Choice A is incorrect because this is the volume of only the two cones

Choice B is incorrect because this is the volume of only the cylinder Choice

C is incorrect because this is the volume of only one of the cones plus the

cylinder

QUESTION 26

Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the

line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0

_

2 minus 0 =

k _

2

Similarly since the line passes through (0 0) and (k 32) the slope of the line

is equal to32 minus 0

_

k minus 0 =

32

_

k Since each expression gives the slope of the same line

it must be true thatk _

2 =

32

_

k Multiplying each side of

k _

2 =

32

_

k by 2k gives k2 = 64

from which it follows that k = 8 or k = minus8 Terefore of the given choices only

8 could be the value of k

Choices A B and D are incorrect and may be the result of calculation errors

QUESTION 27

Choice C is correct Let and w be the length and width respectively of the

original rectangle Te area of the original rectangle is A =w Te rectangle

is altered by increasing its length by 10 percent and decreasing its width by

p percent thus the length of the altered rectangle is 11 and the width of

the altered rectangle is ( 1 minus p

_

100 ) w Te alterations decrease the area by

12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A

Choice D is correct The volume of the grain silo can be found by adding

the volumes of all the solids of which it is composed The silo is made up

of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones

each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and

V cone =1

3 r 2h can be used to determine the total volume of the silo Since

the two cones have identical dimensions the total volume in cubic feet of

the silo is given by V silo = (5)2(10) + (2) 13

(5)2(5) =43 (250) which is

approximately equal to 10472 cubic feet

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 37: PrepScholar Sat Practice Test 3 Answers

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36

Te altered rectangle is the product o its length and width so 088 A =

(11)( 1 minus p _

100 ) w Since A = w this last equation can be rewritten as

088 A = (11)( 1 minusP _

100 ) w = (11)( 1 minus

P

_

100 ) A rom which it ollows that

088 = (11)

( 1 minus

P

_

100

) or 08 =

( 1 minus P

_

100

) Tereore

P

_

100 = 02 and so the

value o p is 20

Choice A is incorrect and may be the result o conusing the 12 percent

decrease in area with the percent decrease in width Choice B is incorrect

because decreasing the width by 15 percent results in a 65 percent decrease

in area not a 12 percent decrease Choice D is incorrect and may be the

result o adding the percents given in the question (10 + 12)

QUESTION 28

Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the

population will decrease by 10 percent every 20 years the present popula-

tion 50000 must be multiplied by (09)n where n is the number o 20-year

periods that will have elapsed t years rom now Afer t years the number o

20-year periods that have elapsed ist _

20 Tereore 50000(09)

t _

20 represents

the engineerrsquos estimate o the population o the city t years rom now

Choices A B and C are incorrect because each o these choices either con-

uses the percent decrease with the multiplicative actor that represents the

percent decrease or mistakenly multiplies t by 20 to find the number o

20-year periods that will have elapsed in t years

QUESTION 29

Choice A is correct Let x be the number o lef-handed emale students and

let y be the number o lef-handed male students Ten the number o right-

handed emale students will be 5x and the number o right-handed male

students will be 9 y Since the total number o lef-handed students is 18 and

the total number o right-handed students is 122 the system o equations

below must be satisfied

983093 x + y = 18

5x + 9 y = 122

Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed

students are emale Tereore the probability that a right-handed student

selected at random is emale is50

_

122 which to the nearest thousandth is 0410

Choices B C and D are incorrect and may be the result o incorrect calcula-

tion o the missing values in the table

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 38: PrepScholar Sat Practice Test 3 Answers

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37

QUESTION 30

Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-

sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since

b = c minus1

_ 2

or b minus c = minus1

_ 2

it ollows that (3x minus 3 y ) + ( minus1 _

2 ) = (5x minus 5 y ) Solving

this equation or x in terms o y gives x = y minus

1

_ 4 Tereore x is y minus

1

_ 4

Choices B C and D are incorrect and may be the result o making a compu-

tational error when solving the equations or x in terms o y

QUESTION 31

The correct answer is either 4 or 5 Because each student ticket costs $2 and

each adult ticket costs $3 the total amount in dollars that Chris spends on

x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at

least $11 but no more than $14 on the tickets one can write the compound

inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4

and x le 55 Tus the value o x must be an integer that is both greater than

or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4

or 5 may be gridded as the correct answer

QUESTION 32

The correct answer is 586 Te mean o a data set is determined by calculating

the sum o the values and dividing by the number o values in the data set Te

sum o the ages in years in the data set is 703 and the number o values in the

data set is 12 Tus the mean o the ages in years o the first 12 United States

presidents at the beginning o their terms is703

_

12 Te raction

703

_

12 cannot be

entered into the grid so the decimal equivalent rounded to the nearest tenth

is the correct answer Tis rounded decimal equivalent is 586

QUESTION 33

The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)

in the orm ax2 +bx +c the expression can be simplified by using the distributive

property and combining like terms as ollows

(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)

(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))

minus5x2 + 9x + 0

Te coefficient o x is the value o b which is 9

Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus

2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term

is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

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38

QUESTION 34

The correct answer is5

_ 8

or 625 A complete rotation around a point is 360deg

or 2π radians Since the central angle AOB has measure5π

_ 4

radians it rep-

resents

_ 4

_

=5

_

8

o a complete rotation around point O Tereore the sector

ormed by central angle AOB has area equal to 5 _ 8

the area o the entire circle

Either the raction5

_ 8

or its decimal equivalent 625 may be gridded as the

correct answer

QUESTION 35

The correct answer is 50 Te mean o a data set is the sum o the values

in the data set divided by the number o values in the data set Te mean o

75 is obtained by finding the sum o the first 10 ratings and dividing by 10

Tus the sum o the first 10 ratings was 750 In order or the mean o the

first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least

(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least

1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible

value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore

or the store to be able to have an average o at least 85 or the first 20 ratings

the least possible value or the 11th rating is 950 minus 900 = 50

QUESTION 36

The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x

can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-

tively Te solution set o the system o inequalities will be the intersection

o these hal-planes including the boundary lines and the solution (a b)

with the greatest possible value o b will be the point o intersection o the

boundary lines Te intersection o boundary lines o these inequalities can

be ound by setting them equal to each other 5x = minus15x + 3000 which has

solution x = 150 Tus the x-coordinate o the point o intersection is 150

Tereore the y -coordinate o the point o intersection o the boundary lines

is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b

or a point (a b) that is in the solution set o the system o inequalities

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time

Page 40: PrepScholar Sat Practice Test 3 Answers

7262019 PrepScholar Sat Practice Test 3 Answers

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QUESTION 37

The correct answer is 7 Te average number o shoppers N in the check-

out line at any time is N = rt where r is the number o shoppers entering

the checkout line per minute and T is the average number o minutes each

shopper spends in the checkout line Since 84 shoppers per hour make a

purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes

in one hour the rate is84 shoppers

_

60 minutes = 14 shoppers per minute Using the

given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore

the average number o shoppers N in the checkout line at any time during

business hours is 7

QUESTION 38

The correct answer is 60 Te estimated average number o shoppers in the

original store at any time is 45 In the new store the manager estimates that

an average o 90 shoppers per hour enter the store which is equivalent to

15 shoppers per minute Te manager also estimates that each shopper stays

in the store or an average o 12 minutes Tus by Littlersquos law there are on

average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis

is45 minus 18

_

45 times 100 = 60 percent less than the average number o shoppers in

the original store at any time