01. Workshop on Number & Reasoning

8/8/2019 01. Workshop on Number & Reasoning

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Workshop on Number & Reasoning


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QuestionQ uestion 1

Given a set of four consecutive integers, a possible value of their product is

(1) 144 (2) 1728

(3) 625 (4) None of the above


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Q uestion 2

T he number of positive integers n in the range 2 < n < 20, such that(n 1)! is not divisible by n is:

(1) 0 (2) 7 (3) 8 (4) 17


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S ome children stand in a queue and share a box of chocolates inthe following manner:

First, Child 1 takes 100 chocolates plus th of whatever remains

in the box. T hen Child 2 takes 200 chocolates plus th of

whatever remains, then Child 3 takes 300 chocolates plus

th of whatever remains, and so on for each child in the queue.

It turns out that each child gets the same number of chocolates.T hen

Q uestion 3

110

1

10

110


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(1) there must be exactly 7 children in the queue.

(2) each child must have received 900 chocolates.

(3) the total number of chocolates initially in the box must have been6300.

(4) none of the above is necessarily true.


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Q uestion 4

A n integer yields a perfect square if you add it to 100. T he same

integer also yields another perfect square if you add it to 168. T hesum of the digits of this integer is

(1) 9 (2) 10 (3) 11 (4) 12


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Q uestion 5

Four couples together drank 44 bottles of Coca Cola. T he ladies werenamed Blue, Red, Pink, and White. T he gentlemen were named A lpha, Beta, Gamma, and Delta. It was seen that Red had 2, Blue 3,Pink 4, and White 5 bottles to drink. Mr. Delta drank just as many ashis wife, but each of the other men drank more than his wife: Mr.Gamma twice, Mr. Beta three times, and Mr. A lpha four times as

many bottles. T hen

(1) Mr. A lpha is the husband of Red.

(2) Mr. Beta is not the husband of Blue.

(3) Mr. Gamma is the husband of White.(4) Mr. Delta is the husband of Pink.


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Q uestion 6

Multiplication of a four digit number by 9 produces a four digitnumber with the same digits in reverse order. T he sum of the digitsof the number must be

(1) 9 (2) 12 (3) 15 (4) 18


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If a, b, c, and d are integers in the range 10 to 15 (both inclusive), thegreatest value of (a + b) (c + d) is:

(1) 750 (2) 731

(3) 729 (4) 700

Q uestion 7


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Q uestion 8

H ow many numbers between 5 and 95 (both inclusive) have oddnumber of distinct factors?

(1) 7 (2) 9

(3) 16 (4) None of these


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Q uestion 9

When 55 55 is divided by 8, the remainder must be

(1) 1 (2) 3 (3) 5 (4) 7


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Q uestion 10

H ow many integers between 1 and 500 divisible by exactly two of the three numbers 3, 5 and 7?

(1) 64 (2) 66 (3) 70 (4) 58


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Q uestion 11

A teacher writes 101 numbers on the blackboard, of which 50 are

zeros, and 51 are ones. A student is asked to perform the followingoperation 100 times on the board: strike out any two numbers. If theyare equal, write another zero. If they are unequal, write a one. Whatare the numbers left on the board?

(1) S ingle One (2) S ingle Zero(3) Two Ones. (4) None of the above


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Q uestion 12

T he Institute of Perfect Management uses a unique scheme ingenerating roll numbers for its students. Each roll number has four distinct digits where the first digit is never a zero. T he maximumnumber of students who can be assigned roll numbers using thisscheme is

(1) 5040 (2) 4320

(3) 4536 (4) 4532


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Q uestion 13

T he Principal of a college issues an order that, for administrativereasons, every student of the college must take exactly four of theseven courses offered in a semester. In addition, he also wants toensure that each course has the same number of takers. If the actualnumber of students is 53, how many of the students would have toleave the college to make the Principal's plan feasible?

(1) 5 (2) 6

(3) 4 (4) 7


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Q uestion 14

A plane is uniformly covered by square cells of unit side. A cell isuniquely identified by a pair of integers (i, j). A cell (k, l) is at a distance

d from the cell (i, j), provided that . For example,

the cell (0, 0) has 4 cells (0, 1), (1, 0), (0, 1) and (1, 0) which are at

distance 1; and has 8 cells (1, 1), (1, 1), (1, 1), (1, 1), (0, 2), (2, 0),(0, 2) and (2,0) which are at distance 2. T he d-neighbourhood of acell C consists of all the cells which are at distance d or less (of courseexcluding the cell C itself). T hus, the 1neighbourhood of any cellcontains 4 cells; and the 2neighbourhood contains 12 cells.T herefore, the total number of cells in the d-neighbourhood of any cellis

(1) 2d (d + 1) (2) 2d (d 1)

(3) 2d 2 (4) d 2

k i l j d !


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Q uestion 15

T he first and the last digits of 2 43 respectively are

(1) 8 and 6 (2) 4 and 6

(3) 8 and 8 (4) None of these


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Q uestion 16

A BC is interested in determining the minimum cost schedule for picking up goods from a warehouse where all its suppliers send theshipments. Estimated arrivals of shipments in the next four periodsare 16, 5, 12, 9 hundred cubic feet respectively. A BC has to payRs.50/period/hundred cu.ft of space it utilises. A BC can hire a truck(capacity 50 hundred cu.ft) in any period for picking up the goods.

Cost of such truck service is Rs.1000. T he following pick-up isoptimal.

(1) Pick up on 2 nd and the 4 th day.

(2) Pick up all on the last day.

(3) Pick up on every day.

(4) None of these.


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Q uestion 17

In practical inventory problems, the total cost ( T C) of ordering and

carrying the inventory, is expressed as,

where C is the cost incurred for each order, D is the annual demandfor the item, k is the per unit inventory holding cost of the term, andQ is the number of items procured per order. A ssuming that C, Dand k are constant, the minimum value of T C is

(1) (2)

(3) (4)

C D Q KT C ,Q 2

v v ! -

C Kv vC

K2

v v

2 C Kv v v C Kv v


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Q uestion 18

If you have 3 tickets to a lottery for which 10 tickets were sold and 5prizes are to be given, the probability that you will win at least oneprize is:

(1) (2)

(3) (4)

12 12

112

1112


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Q uestion 19

Two circles C 1 and C 2 having the same radius of 2 cm and centres at Pand Q respectively intersect each other such that the line of centres PQintersects C 1 and C 2 at F and E respectively. EF = 1 cm. T he wholeassembly is enclosed in a rectangle of minimum area. T he perimeter of rectangle is:

(1) 20 units (2) 22 units

(3) 24 units (4) 26 units


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Q uestion 20

T he smallest positive value of x for which the fractions

are in their simplest form is

(1) 47 (2) 49

(3) 51 (4) 53

x 2 x 13 x 26 x 41, , , , ,10 11 12 13

x 1913 x 2002,

49 50


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T he age of Mr. Chetan in 2002 was of his birth year. What is hisage in 2006?

(1) 30 (2) 28

(3) 26 (4) 22

Q uestion 21

10


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Q uestion 22

In a family of husband, wife and a daughter, the sum of the husbandsage, twice the wifes age, and thrice the daughters age is 85; while thesum of twice the husbands age, four times the wifes age, and six timesthe daughters age is 170. It is also given that the sum of five times thehusbands age, ten times the wifes age and fifteen time the daughtersage equals 450. T he number of possible solutions, in terms of the agesof the husband, wife and the daughter, to this problem is

(1) 0 (2) 1

(3) 2 (4) infinitely many


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Q uestion 23

When 4 101 + 6 101 is divided by 25, the remainder is

(1) 20 (2) 10

(3) 5 (4) 0


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Q uestion 24

For non-zero real numbers a, b and c the set of possible values the

quantity can take is

(1) {0} (2) { 4, 0,4}

(3) { 4, 2, 2, 2, 4} (4) { 4, 2, 0, 2, 4}

a b c a b ca b c a b c


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Q uestion 25

T he number of distinct real number x for which is a positiveinteger is

(1) 3 (2) 4

(3) 5 (4) Infinite

2

8

4x x


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Q uestion 26

Company BELI A NCE hosted a party for 8 members of Company

AX I A L. In the party no member of AX I A L had interacted with more thanthree members of BELI A NCE. Out of all the members of BELI A NCE,three members each interacted with four members of AX I A L and theremaining members each interacted with two members of AX I A L. T hegreatest possible number of members of company BELI A NCE in theparty is:

(1) 9 (2) 10

(3) 11 (4) 12

(5) None of the above


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Q uestion 27

In an examination there are 30 questions. I mark is given for eachcorrect answer and 0.25 is deducted for every incorrect answer. A nkur attempted all the questions and scored 13.75. H ow many incorrectanswers did he have?

(1) 10 (2) 11(3) 12 (4) 15

(5) None of the above.


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Instructions: Consider the information given below for questions28 and 29.

In the diagram below, the seven letters correspond to seven uniquedigits chosen from 0 to 9. T he relationship among the digits is suchthat:

AXY

. . X.Y. .A.Y


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Q uestion 28

T he value of A is:

(1) 0 (2) 2 (3) 3

(4) 6 (5) None of the above.


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Q uestion 29

T he sum of digits which are not used is:

(1) 8 (2) 10 (3) 14



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Q uestion 30

Let X be a four-digit number with exactly three consecutive digits being

same and is a multiple of 9. H ow many such X s are possible?

(1) 12 (2) 16 (3) 19



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Q uestion 31

A rural child specialist has to determine the weight of five children of

different ages. H e knows from his past experience that each of thechildren would weigh less than 30 g and each of them would havedifferent weights. Unfortunately, the scale available in the village canmeasure weight only over 30 g. T he doctor decides to weigh thechildren in pairs. H owever, his new assistant weighed the childrenwithout noting down the names. T he weights were: 35, 36, 37, 39, 40,41, 42, 45, 46 and 47 g. T he weight of the lightest child is:

(1) 15 g. (2) 16 g. (3) 17 g.

(4) 18 g. (5) 20 g.


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Q uestion 32

S angeeta and S wati bought two wristwatches from Jamshedpur Electronics at 11.40 A .M. IST . A fter purchasing they found that when60 minutes elapses on a correct clock (I ST ), S angeetas wristwatchregisters 62 minutes whereas S watis wristwatch registers 56minutes. Later in the day S angeetas wristwatch reads 10 P.M., thenthe time on S watis wristwatch is:

(1) 8:40 PM (2) 9:00 PM

(3) 9:20 (4) 9:40 PM

(5) Cannot be calculated.


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Q uestion 33

A manufacturer produces two types of products- A and B, which are

subjected to two types of operations, viz. grinding and polishing.Each unit of product A takes 2 hours of grinding and 3 hours of polishing whereas product B takes 3 hours of grinding and 2 hours of polishing. T he manufacturer has 10 grinders and 15 polishers. Eachgrinder operates for 12 hours/day and each polisher 10 hours/day.T he profit margin per unit of A and B are Rs. 5/- and Rs. 7/-

respectively. If the manufacturer utilises all his resources for producing these two types of items, what is the maximum profit thatthe manufacturer can earn?

(1) Rs. 280/- (2) Rs. 294/-

(3) Rs. 515/- (4) Rs. 550/-

(5) None of the above


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Q uestion 34

a, b, c d and e are integers such that If a, b, c,

d and e are in geometric progression and lcm (m , n ) is the leastcommon multiple of m and n , then the maximum value of

(1) 1 (2) (3)

(4) (5) None of the above

1 a b c d e.e

1 1 1 1is

lcm(a,b) lcm(b,c) lcm(c,d) lcm(d,e)

1516

7981

7

8


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Q uestion 35

Let X be a four-digit positive integer such that the unit digit of X is prime

and the product of all digits of X

is also prime.H

ow many such integersare possible?

(1) 4 (2) 8 (3) 12

(4) 24 (5) None of the above


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Q uestion 36

Given x 1 = 5; x 2 = 25 & x n+2 = gcd (x n+1 , x n) + x n; gcd = greater commondivisor. T hen the least common multiple of x 19 and x 20 is:-

(1) 2560 (2) 1280



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D irection for questions 37 and 38: A nswer the questions based onthe following information.

A salesman enters the quantity sold and the price into the computer.

Both the numbers are two-digit numbers. But, by mistake, both thenumbers were entered with their digits interchanged. T he total salesvalue remained the same, i.e. Rs. 1,148, but the inventory reduced by54.


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Q uestion 37

What is the actual price per piece?

(1) Rs. 82 (2) Rs. 41

(3) Rs. 6 (4) Rs. 28


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Q uestion 38

What is the actual quantity sold?

(1) 28 (2) 14

(3) 82 (4) 14


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D irection for questions 39 and 40: A nswer the questions based onthe following information.

Production pattern for number of units (in cubic feet) per day.

For a truck that can carry 2,000 cubic ft, hiring cost per day is Rs.1,000. S toring cost per cubic feet is Rs. 5 per day.

Day 1 2 3 4 5 6 7Number of units 150 180 120 250 160 120 15


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Q uestion 39

If all the units should be sent to the market, then on which daysshould the trucks be hired to minimize the cost?

(1) 2nd, 4th, 6th, 7th (2) 7th

(3) 2nd, 4th, 5th, 7th (4) None of these


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Q uestion 40

If the storage cost is reduced to Re 0.80 per cubic feet per day, then

on which day(s), should the truck be hired?

(1) 4th (2) 7th

(3) 4th and 7th (4) None of these


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Q uestion 41

S hyam visited Ram during his brief vacation. In the mornings they both

would go for yoga. In the evenings they would play tennis. To havemore fun, they indulge only in one activity per day, i.e. either they wentfor yoga or played tennis each day. T here were days when they werelazy and stayed home all day long. T here were 24 mornings when theydid nothing, 14 evenings when they stayed at home, and a total of 22days when they did yoga or played tennis. For how many days S hyamstayed with Ram?

(1) 32 (2) 24



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T hank You

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01. Workshop on Number & Reasoning