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Note to the SFA – When you solve questions from Dr. Raju's threads, please mention the month in which the questions had appeared.
1) Given the equation of a parabola as y=x^2+10.If the line intersects the parabola at (1,9) and (3,y) then find the value of y?
Solution:
Simply substitute the (3, y) in y = x^2 + 10y = 9 + 10 = 19Hence y = 19
2) In a class of 10 students,6 are boys and 4 are girls. Find the probability of selecting 6 students for a game, such that 2 particular girls are always selected?
Solution:We need to always select two girls.So remaining students will be 8.We need to select 4 from these 8 students.So probability will be 8C4/10C6
2. Find the total number of 4-digit odd integers greater than 1000 which have 6 in their hundredthplace?Answerunit digits place = 1,3,5,7,9 = 5 valuesTen's digit place = 0.1,2,3,4,5,6,7,8,9 = 10 valuesHundred's digit 's value = 6 only = i valueThousand's digit value = 2,3,4,5,6,7,8,9 = 8 valuesTherefore total no = 5x10x1x8 = 400This is correct , they have not mentioned about repetition so if you consider that the digitsare repeated then this answer is fine , otherwise it will have to be broken into cases. But according tothe language you have to consider the repetition,
7. Col A: (x^x)^xCol B: x^(x^x)Answer) D chck for x=2 , both will be equal and for x=3 column b will be greater , so nothing can be said.
11. Given that two points (0, 2) and (2, 0) lie on the circle.Col A: Radius of the circleCol B: 2Answer DThere are many circles possible. If u consider one of them where the third point at the origin.
Then in that case the radius is 2root2. For many other points you will get diff results.
13. Given a set of three numbers {x, x^2, x^3}; -1 < x < 0. What is the ascending order of the set?Answer) x<x^3<x^2take x = -1/2 .. Now X^2 is + value i.e. 1/4 , so is highest , X^3 is -1/8 which is greater than xi.e.- 1/2so the order is x<x^3<X^2if you take x= -1/2 then x^2=-0.25 and x^3= -0.125.So clearly x^3 is the greatest among them and then x^2 and then x.
1. A rectangular solid is given which consists of 10 cubes in 1 row and 3 cubes in 1 column. In that manner there are 10 rows and 3 columns. If the length of edge of the cube is 1, then what is the surface area of the rectangular solid?
Just imagine it a bit. You can think of a matchbox. When you imagine.Combining all these small cubes will give you a cuboid something of the form of a match box.This cuboid will have new dimensions, just think of the dimensions.The length will be 10 as there are 10 rows the vertical height will be 3 because there are three cubes in a column.The breadth will be 1 because all cubes are of dimension 1.So this reduces to a cuboid of length , breadth and height = 10 by 3 by 1.You just need to find the surface area of this cuboid.
7. Col A: Quadratic square of -12, 3 & 10Col B: Arithematic mean of -12, 3 & 10Col A : means that you need to calculate the root mean squra = sqrt
( (144+9+100)/3)=9.1A.M = 12+3+10/3 =8.33So column A is greater.
11. Given a series of numbers 1, -1, 2, -2, 3, -3.......Col A: The sum of the first 67 termsCol B: 34See if you do the sum , upto the 66 th term the series will be of the form1,-1,2,-2,3,-3...................32,-32,33,-33 [So if you add upto here all theterms will cancel out each other. So the 67th term will be 34.So in this caseboth the columns are equal.
8. How many cubes of edge length 1 and 2 can be fitted into the rectangular solid, if the volume of the rectangular solid is 35*10*15?[there are only 2 dimensions for the cube given , can you check once again because it is impossible to calculate without the last dimension given
3. Three people are to be seated on a bench. How many different sitting arrangementsare possible if Erik must sit next to Joe?
a) 2.b) 4.c) 6.d) 8.e) 10.
Answer is given 4 . how it should be 2 acc. To me?????
The answer should be 4. It is simple. Suppose that Erik and Joe have to sit together.So the following favorable cases is possible. Suppose the third guy is T
1. T,Erik,Joe2. T,Joe,Erik3. Erik,JoeT4. Joe,Erik,T
6. A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card numbers exist?a) 27.b) 36.c) 72.d) 112.e) 422.
Answer) is given 27 . why not 81 as 3x3x3x3 pls explain???
Solution: See we will go digit by digit.The first 2 digits are fixed= 1,2 third can be filled in 3 ways (7,8,9 as greater than 9)fourth in 3 ways (3,6,9 as should be a multiple of 3)fifth depends entirely on 6 th so whatever 6th digit we choose accordingly the 5th will be chosen.So the ways of choosing 6 th is 3 ways (1,2,3 so that the 5th digit number remains a single digit number)So the total number of ways= 3*3*3= 27
18. The probability of having a girl is identical to the probability of having a boy. In a family with three children, what is the probability that all the children are of the same gender?a) 1/8.b) 1/6.c) 1/3.d) 1/5.e) 1/4
Answer) is given 1/ 4 ;
shouldn't it be 1/ 8? Pls explain?
It is also very simple just go by the definition of probability.Consider it analogous to a 3 digit number such that each place can be filled in 2 ways.So the total number of ways is = 2*2*2=8Out of these only two cases are favorable = BBB or GGGSo by the basic definition probability= favorable(2)/not favorable(8)= ¼
1) In a room there are more than 12 members which are divided into a 5 member,8 member and a 12 member group. Find the least possible members in room such that finally non are left.Solution : See it is mentioned that we need the least number of people. It is also mentioned that we need to from at least one group of 5 member, 8 member and 12 member each. So if we need minimum of 25 people(5+8+12) so that at least one of each the groups is formed.
2) A group can charter a particular aircraft at a fixed total cost.If 36 people charter aircraft rather than 40,loss per person is 12$. What is cost per person if 40 people charter it?Solution: It is mentioned that there is a fixed cost to charter the aircraft. Let the fixed cost be x thenif there were 40 people then the price per person would be x/40.But now there are 36 people only so the cost per person increases and so there will be a loss. The new cost per person is =x/36So x/36 - x/40 = 12so x= 4320.So we now the total cost and so the cost if 40 people charter it will be = 4320/40= 108.
3) In how many ways can 21 books on english and 19 books on hindi be placed in a row on a shelf so that two books on hindi may not be together?
Solution :This is quite simple.First arrange the 21 english books among them selves in 21! ways. Now if we represent the English books as E so a distribution of the books will look like :E1 E2 E3 E4...................E21So there will be 22 spaces in between the english books, including the one before E1 and the one after E21.So if we place the hindi books at any of these places we will get a distribution such that no hindi books will be together.so choosing 19 places out of the 22 available can be done in 22C19 and then these books can be arranged among themselves in 19! ways.So the total number of ways : 21!* 22C19* 19!
1. If x<y<0 thenA: xy
B:Y – x,[ For such problems always check for all the cases, check out for the fractional case also and alsofor the integral case.I will show you how to do it:We will choose x and y satisfying the above given conditions:let x=-0.2 and y=-0.1 so xy= 0.02 and y-x = 0.1 , so in this case column B is greater.Now let us consider x=-5 and y=-4 then xy = 20 and y-x =1 . in this case column A is greater.As we see that for diff values of x we get diff answers so we will mark the answer as cannot bedetermined.
2. If N is an integer btw 200 and 300 with unit digit 5 and tens digit x,A: N/5B: 40+2xSince the number lies between 200 and 300 so the hundreds place will be 2 and let the tens place bex.So the number N= 2x5N= 200+10x+5N=205+10xSo N/5 = 41+2xColumn B= 40+2xClearly Column A is greater.
4. series given -8, -3, 5, 8, 3, -5.A: the number that would first time repeat 3rd time.B: 3the language is not very clear for this problem can you verify and send it to me again?
Q5) Find the total number of 4 digit odd integers greater than 1000 which have 6 in their hundreths place.?Solution : Just go by digit by digit and find otu in how many ways can you fill each of the digits.Units digit : 5 ways because the number is odd so it can be filled only by 1,3,5,7,9Tens digit: 10 ways : As there is no restrictionHundreds place : one way as it can only be filled in 1 way.Thousands place: 9 ways because the thousands place cannot be filled by 0 so the remainging 8 digits are possible.So the total required ways: 9*10*5=450
Q6) Given x((75+y)+(75-y))=900this gives the value of x as 6. But since this is independent of y so we cannot calculate xy and so the answer to this problem must be: Nothing can be said.
Q7) Given that two points (0,2) and (2,0) lie on the circle.Col A: Radius of the circleCol B: 2
The distance between these two points is 2root2. But we dont know whether this is a chord or diameter. If it is chord such that it is root 2 distance from the center then in that case the radius will be 2. If a chord such that the distance is greater than root 2 then the radius will be greater than 2. But if it is such that distance between the center and the chord is less than root 2 then the radius will be less than 2. So nothing can be said about it.
Q 8) A : (x^x)^x B: x^(x^x)
This is a simple application of the formula (am)n= amn
A= (xx)x= xx^2
B= x^(xx)As you can both are not the same so the comparison can be made only if we know the value of x.So the correct option D.
GRE QUANT DATABASE updated by Abhinav
5. Compare A and B
Col A: Area of square ACol B: 4/3(81– x)
Answer: D..........................Correct(Here we don’t know the measurement of x hence we cannot determine.)
2. Given that a person invites 10 members to a party, of which 3 are his best friends and 7 are his casual friends. If 2 members are to be selected from 10, find the probability that selected 2 are his best friends?
Answer: 1/15( Number of ways two members out of 10 can be selected(a): 10C2
Number of ways two members can be selected from 3 best frns(b): 3C2
Probability: b/a= 1/15)............................Correct3.
Given area of the triangle as 12Col A: xCol B: 4
Answer: no coordinate system is given so how should we proceed?[Since we know that the base line is the x axis as you can see the y coordinates of both the base points is 0. So the height of the triangle should be 4 and the area is 0.5*base*heightwe know area as 12 and height as 4 so the base will be 6. That is possible only if x=3 so column B is greater.4. Col A: xCol B: 60°
Answer: D[ suppose that the angle is 60. then the triangle becomes and equlateral triangle.So the third common side is 10.Now 9+1=10 so the trianlge inequality is satisfied.But in all other cases the sum of two sides of a triangle should be greater than or equal to the thrid side. So certainly the third side should be greater than 10 and in that case x will be greater than 60. So since two cases one of equality and one greater than 60 is arising so it should be cannot be determined.]
5. 3. Col A: Number of odd numbers from 100 to 200Col B: Number of even numbers from 100 to 200
Answer: B......................correct( Here the question says from 100 to 200, so including both the values we get total odd number 50 and total even number 51)
6. 5. In triangle ABC, ‘D’ is the midpoint of AC and BD is the median. Which of the following angles could be 90°?A. <AB. <B
C. <CD. <D
E. None of the above
see only b can be the option in that case we can draw a circle with AC as the diameter such that the anlgle it subtends is 90
Answer: (unable to solve)
7. Given slope of the line k = -2/3Col A: x-interceptCol B: y-intercept[Correct]Answer: D( As x-intercept or y-intercept may be – ve)
8. Given six symbols @, $, $, $, @, &. Find the number of different possible arrangements?
Answer: 6^6[the arrangements is with or without repitition is not stated but if with repitition then ur answer is correct but if without repetition then think](As the question does not explicitly states that the symbols should not be repeated, hence number of possible combination: 6*6*6*6*6*6 )
9. What is the value of AD?
Answer: Here if BC is perpendicular to CD then AD= square root 85
BUT it is not given in the figure how to proceed then?[Ya not very clear]10. Given (x + 1/x)/(1/(1-x)) = 99, find the value of x? Answer: Unable to solve[see if you factorize it comes out to be (x^2+1)(1-x)/x =99Note that the value of this expression will positive only if x is between x and 1 so the answer should be a fraction but solving for x by normal methods should be difficult. If i come to a solution will mail you later ]
GRE QUANT DATABASE updated by Abhinav
4. Given that in a pack of plates, 1/3 plates are damaged, 2/3 plates are cracked and 1/3of them are damaged and cracked. If 80 are not hampered, then what is the number oftotal plates?
This is quite simple. Assume the total number of plates to be = xNow the no of plates that are damaged is x/3 no of plates cracked is 2x/3 and the number ofplates that are damaged and cracked is x/3.So using the concept of sets the number of plates that are damaged or cracked = onlydamaged+only cracked +bothHere only damaged= 0????????????? given here 1/3 are damaged so how come 0?only cracked= 2x/3-x/3=x/3Both= x/3So the number of plates that are damaged or cracked = 2x/3So the number of plates that are not dameged = x-2x/3 = x/3So x/3= 80 , so x= 240So the required total number of plates is 240.
pls explain this in detail . i still didn't get it?
hampered means either damaged or cracked . In both of the cases the plate is hampered. So for finding the total number of plates that are there. We need to add the hampered and the non hampered. We know that the non hampered ones are 80.We need to find the hampered ones.Suppose that the total no of plates are x. x/3 are damaged , 2x/3 are cracked and x/3 are damaged and cracked. So using the set notations :nAUB= nA+nB-nA(intersection) BnAUB: x/3+2x/3- x/3 = 2x/3So 2x/3 +80=xso x/3= 80 and x= 240
GRE QUANT DATABASE updated by Abhinav
1.A certain population of bacteria doubles every 10 minutes. If the number of bacteria in the population initially was 104, what was the number in the population 1 hour later?
2(104)6(10)4 (26)(26)(104)(106)(104)(104)6
Given answer: CMy answer: A [It should only be 26 * 104
[See suppose that at time zero there were x, so after 10 minutes it will be 2x , again at 20 minutes it will double of 2x that is 4x ....So at the end of 60 minutes will be 26x. Same is the case here.]
2.A string of length 12 inches is bent first into a square PQRS and then into a right-angled triangle PQT by keeping the side PQ of the square fixed. Then the area of PQRS equals
area of PQT2(area of PQT)3(area of PQT)3(area of PQT)/2none of these
Given answer is 3(area of PQT)[See it is correct. If the right angled triangle given has one side PQ=3 which is fixed. So this side cannot be the hypotenuse for the right angled triangle. So let the hypotenuse be y and the other side be x. Since we know that sum of all the sides ahoud be 12 so from there we get a relation that x+y=9 . Similarly since it is a right angled triangle so 9+x^2=y^2.This gives another equation y-x=1. From this you can find x and y and then answer the problem.My answer: D
3.A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim make in terms of x?
48/x75x48x24xnone of these
Given answer: 48 xMy answer: E[It is correct . See the first statement means that if we consider one second the circumference distance moved by both the rim is the same.
So if the smaller rim covers x revolutions per sec so the distance per second moved by the smaller in one sec will be 2pi*14*x and this should be equal to the distance moved by the bigger rime.
If the bigger rim makes y revolutions per sec then 2pi*y*35/2= 2pi*14*x. From here we get y=4x/5. So this is the number of revolutions per second. So the number of revolutions in one minute will be multiply by 60 so we get it as 48x.
4.A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?
w²+pw+k=0
w²-pw+2k=0
2w²-pw+2k=0
2w²-pw-2k=0
none of these
Given answer: 2w²-pw-2k=0, My answer: C[Your answer is correct]
GRE QUANT DATABASE updated by Abhinav
1. Jack and Jill, who both work in the evening wish to arrange for an evening off together.Each evening that Jack is off is followed by 3 evenings that he is a work, and each eveningthat Jill is off is followed by 5 evenings that she is at work. If Jack will be off thisevening, and Jill will be off tomorrow evening, how many evenings must pass before theyhave an evening off together?(A) 10(B) 12(C) 24(D) 28(E) So long as they continue this working pattern, they will never have the same evening off.
Solution:
If we denote the evening off as o and working evenings as w then we can form the following description for the two people:For Jack: o w w w o w w w o w w w o w w w o w w w o w w w o w
For Jill: w o w w w w w o w w w w w o w w w w w o w w w w w oSo if we form the series for off evenings for the two people and check whether the two A.P. series formed have any terms in common, then our problem will be solved:For Jack: 1 5 9 13 17 21 25 29For Jill: 2 8 14 20 26 32 38 44 Clearly the two series has no common terms so among the options the choice E seems to be correct.
2. A certain car dealership sells only full-size and mid-size cars. One of its sales representativesreceives an annual salary of $15,000. He also receives a commission of $800 for each full-sizecar he sells and $500 for each midsize car he sells. What is the least number of cars he mustsell in a year to receive total annual earnings of exactly $25,000?(A) 7(B) 12(C) 13(D) 14(E) 17
Solution: Since the representative gets a fixed salary of $15000 so if his earnings in a month were $25000 then it implies that $10000 must come from the commision from cars.It is important to note that though it may seem that the information gives only one equation and solving is not possible but since it asks for a minimum number of cars so this information leads us to an unique solution.Let the number full size cars be x and the number of midsize cars be y.Now we can write the equation as 10000=800x+500ySimplify this equation, you get the equation as 100=8x+5y.Now in order that the number of cars be minimum the criteria here will be that we must have many x cars and fewer y cars.Now see each option one by one:7-Not possible because if all are x cars 8*7=56 , but the total should be exactly 100.12-Not possible be cause even if it is all x cars the total is 96 and the total is 100 , same with 13.Only possible is 14: 10x types and 4 y types such that the total is exactly 100 and so option D is the correct choice.
3. A school supply store sells only one kind of desk and one kind of chair, at a uniform cost perdesk or per chair. If the total cost of 3 desks and 1 chair is twice that of 1 desk and 3 chairsthen the total cost of 4 desks and 1 chair is how many times that of 1 desk and 4 chairs?
Solution:
Let the uniform cost of desk and the chair be x and y respectively.From the first condition the equation that can be formed is:3x+y=2(x+3y)From here we get the info that x=5y
Now we need to find k in :(4x+y)=k(x+4y)Substitute x=5y in this so that both the sides are in terms of y and so that y can be striked off from both the sides.From here we the value of k=7/3.
GRE QUANT DATABASE updated by Abhinav on February 3rd
1. Given xyz = odd integer, then which of the following is even? I. x(y + z) II. xy + z III. yz +x A. Only I B. Only II C. Only I and II D. Only III & so on.........
ANS: are the three are even.......................Correct
2. Col A: -2.4 + 4.8 │ │ │ │Col B: 2 Ans. A...........................Correct
Quant:
1. Given xyz = odd integer, then which of the following is even? I. x(y + z) II. xy + z III. yz +x A. Only I B. Only II C. Only I and II D. Only III & so on.........
ANS: are the three are even.......................Correct
2. Col A: │-2.4│+ │4.8│ Col B: 2 Ans. A...........................Correct
3.
As shown, if ‘d’ is the diagonal of the square ABCD, then find the area of the square? Ans. D^2/ 2..........................Correct
4.
Col A: y + z Col B: w Ans. W= 180-z and x+y+z=180 I think it cant b determined...............Correct
5. The discount on a certain product is x% in June and it is followed by another discount of x% in July. If the resulting price is 81% of the original price, then Col A: x Col B: 10% (Similar to this) Ans. Explain this to me. [Answer will be both are equal:
Let the intial price be M.So the selling price after a discount of 10% will be = M(1-x/100)Again a dicount of 10% is given on this so the new selling price will be = M(1-x/100)2
Now the problem says that this is 81% of the initial,So M(1-x/100)2= 0.81Mor 1-x/100=0.9 [Taking square root on both the sidesSolving you get the value of x as 10%.]
6. Given the standard deviation of set of three numbers w + 6, s + 6 and p + 6 as ‘k’, then what will be the standard deviation of set w, s and p? (Similar to this)
ANS in my opinion it would b same but still explain.
[The standard deviation will be the same in both the cases because for calculating the standard deviation you subtract the number from the mean term by term. As the number is increased by some amount,the mean will increase by the same amount. So when you take the difference this increase gets cancelled and the calculation is the same for either of the case.]
GRE QUANT DATABASE updated by Mohan on January 11th
JAN 7TH thread:
1. Given that there are three couples, who are to be arranged in 6 seats. Find how many ways they can be arranged, such that husband and wife sit together?
Solution: We can club each couple in to 1 single thing.Then there are 3 things which need to be arranged in 3 seats and that can be done in 3! ways.Each couple among themselves can be arranged in 2 ways.So, the total no.of arrangements with the given condition = 3!*2*2*2 = 6*8 = 48Hence total there are 48 ways we arrange them with the given condition
2. Given a figure of semicircle like above with the radius of circle given and the angle of the sector is also given. Find the area of the shaded region?
60/360*pir^2 - sqrt(3)/4r^2 if it is a equilateral triangle Correct
3. A person ‘X’ sells his TV set to another person ‘Y’ at a loss of 15%, but ‘Y’ sells it to another person ‘Z’ at a profit of 10%. If ‘Z’ pays $9350 to ‘Y’, thenCol A: The amount ‘Y’ pays to ‘X’Col B: 8500
Solution:Let the cost price of the TV set be CGiven that person X sells his TV set to another person Y at a loss of 15%So he must have sold at a selling price of 0.85C to YNow this 0.85C will be the cost price for YY sold this same set at a profit of 10% to ZSo, he must have sold it at a price of 1.1*(0.85C)Given that Z pays $9350 to Y=> 1.1*(0.85C) = 9350=> C = 9350/(1.1*0.85)Now amount Y pays to X = 0.85C = 0.85*[9350/(1.1*0.85)] = 9350/1.1 = 8500Hence both the columns are equal
4. Given few numbers like 2, 5, 6, 7, 9. Find the number of ways of arranging a five digit even number from the given numbers?
Solution: Let the five digit number be ABCDELast digit E can take only 2 and 6 from given 5 numbers (Since then only the number will be aneven number)We need to know whether repetition is allowed or not.If repetition is not allowed thenD can take 4 values after selecting a digit for Eand C can take 3 values after selecting a digit for E and Dand B can take 2 values after selecting a digit for E, D and Cand A can take only one value after selecting for the other digitsSo the total possibilities are: 2*4*3*2 = 48But if repetition is allowed then last digit E can be selected in 2 ways and the others in 5 waysSo the answer will be 2*5*5*5*5
5. In how many ways, 7 gents and 4 ladies can be arranged circularly in a meeting?
Solution: We can arrange 11 people in a ciruclar table in (11-1)!/2 if the order of clockwise and anticlockwise is not important and it will be (11-1)! if the order of clockwise and anti clockwise isimportantSo, there is a possibility for 10!/2 also.They will be more specific in the question about the order. So no need to worry.
6. Given 1 < x < 2 < y < 3 < z < 4
Col A: x + y + zCol B: some value (xx)
Solution: x < 2y < 3z < 4=> x + y + z < 9Similarly,x > 1y > 2z > 3=> x + y + z > 6So the value of x + y + z lies between 6 and 9If the value in Column B is lesser than 6 then column A will be greater than Column BIf the value in Column B is greater than 9 then Column A will be greater than Column BIf the value in Column B is in between 6 and 9 then the relation cannot be determined
7. Given that there are two light poles, one pole is having bulb A and another is having bulb B such that the first pole is 60ft and second pole is 100 ft height. If the distance between two poles is 30 ft, then find the distance between A and B?
Solution: 50
8. Given a sequence like x, w, y, z, 0, 1, 1, 2, 3. Find the value of x?Solution:Sequence is nothing buta3 = a2 + a1y = x + wz = w + y0 = y + z1 = 0 + z=> z = 1y = -z = -1w = z – y = 1 - (-1) = 2x = y – w = -1 – 2 = -3So the sequence will be -3, 2, -1, 1, 0, 1, 1, 2, 3
9. Col A: (10)^-2Col B: 0
Solution:Column A = 0.01 is greater than Column B = 0
10. From the set of numbers: {1, 2, 3, 4, 5, 6}, how many different sums can be formed by summing up any two numbers in the set?
Solution:Minimum value will be 1 + 2 = 3Maximum value will be 5 + 6 = 11So total numbers will be {3, 4, 5, 6, ....11}which will be 9
11. Given a figure of a square like above. Find the area of the shaded region?
Solution: Total area = 15*15 = 225Area of the unshaded triangle = (1/2)x^2So shaded area = 225 – (1/2)x^2 – (1/2)x^2 = 225 – x^2
JAN 4TH:1. A circle is inscribed in a square, which is inscribed in another circle. Find the ratio of areas of smaller circle to the larger circle?
Solution:For the smaller circle the diameter will be a (which is the length of the square)So the area will be = Pi*a^2For the bigger circle the diameter will be a√2 (which is the diagonal of the square)So the area will be = Pi*(a√2)^2 = 2*Pi*a^2So the ratio will be = [Pi*a^2]/[2*Pi*a^2] = ½
2. Given a point on the x-axis (-k, 0) at point 'R' and another point S (m,0) on x-axis which is not shown in the figure is given. If RS = k^4, thenCol A: mCol B: 0Solution:Given a point on the x-axis (-k, 0) at point 'R' That means definitely it cannot take a value of 0.And also given that RS = k^4=> k + m = k^4=> m = k^4 – kNow depending on the value of k the value of m will depend
If k lies between 0 and 1 then k^4 > k and m will be lesser than 0.If k is other value then k^4 will be greater than kHence relation cannot be determined is the correct answer
3. Given the age of a person ‘X’ as four times the age of his son. After ten years, if the age of X is twice the age of his son, then what is the present age of his son?
Solution:Let the age of X be x and sons be sNow given that x = 4sAfter 10 years their age will be s + 10 and x + 10Given that x + 10 = 2(s + 10)=> 4s + 10 = 2s + 20=> 2s = 10=> s = 5Hence present age of son is 5 years
5. A certain sum of amount P, increases at r% from 1990 to 1995 and 1995 to 2000. If the total amount is (7/5) p at the end of 2 terms, then what is the rate of interest?
Solution:Total amount = (7/5)p = p + (2/5)pSince it contains 2 terms we can write the above one asp + 2*(1/5)pSince total amount will be = P + Ptr/100Hence the rate of interest will be 100/5 = 20%
6. If x < y < z, thenCol A: xyCol B: yz
Solution: x < y=> xy < y^2z > y=> yz > y^2Hence yz will be greater than xySo Column B will be greater than Column A
7. When a number is divided by 12, the remainder is 5. What is the remainder when the square of that number is divided by 8?Solution:Given that when k is divided by 12 it leaves a remainder of 5.So, k will be of the formk = 12m + 5Now k^2 = 144m^2 + 25 + 120m = 8(18m + 15) + 25So, if k^2 is divided by 8 it will leave a remainder which is equal to the remainder when 25 is
dividedby 8 (Since first term is a multiple of 8 and so it leaves a remainder of 0)=> Remainder when 25 is divided by 8 is 1Hence the remainder is 1.
JAN 6TH:
1. If 4y – 1 > 9, thenCol A: yCol B: 3Solution: Given that 4y – 1 > 9=> 4y > 10=> y > 10/4=> y > 5/2Hence relation cannot be determined
2. Col A: 0.2% of 4Col B: 1/500 of 4
Solution: Col A = 0.2/100*4 = 0.8/100 = 0.008Col B = 4/500 = 0.008Hence both the columns are equal
3. A square is formed by joining midpoints of another square as shown in figure. If the perimeter of larger square is X, thenCol A: Perimeter of smaller squareCol B: X/2
Solution: Given that the perimeter of the bigger square as X=> Length of the square = a = X/4Length of the smaller square will be a/√2 = (X/4)/√2 = X/4√2So perimeter will be X/√2 = √2(X/2) = 1.4*(X/2)Hence Column A is greater than Column B
4. Given that in a pack of plates, 1/3 plates are damaged, 2/3 plates are cracked and 1/3 of them are damaged and cracked. If 80 are not hampered, then what is the number of total plates?
Solution:Let X be the number of plates in a packn(damaged) = X/3n(cracked) = 2X/3n(damaged and cracked) = X/3Now, total number of plates = X/3 + 2X/3 – X/3 + 80 = X=> 2X/3 + 80 = X=> X/3 = 80=> X = 240Hence the number of plates are 240
5. In a set of numbers from 1 to 10. If two numbers are to be selected from these 10 numbers with replacement, then what is the probability that at least one of them is even?Solution:P(Atleast one of them even) = P(1 even and 1 odd) + P(both are even)P(Atleast one of them even) = P(1 even)*P(1 odd) + P(1 even)*P(1 even)Since repetition is allowed these will be independent eventsTotal number of possibilities of selecting 1 number out of 10 = 10From the given list 2, 4, 6, 8, 10 are even numbers (total in 5)and 1, 3, 5, 7, 9 are odd numbers (total in 5)We can select 1 odd in 5 waysand even number in 5 waysNow P(1 even) = 5/10 and P(1 odd) = 5/10 = 1/2Hence P(Atleast one of them even) = (1/2)*(1/2) + (1/2)*(1/2) = ½
6. Given ‘d’ as the standard deviation of set:{ x, y, z}, thenCol A: The standard deviation of x +2, y+2 and z+2Col B: d + 2Solution:Given that standard deviation of set:{ x, y, z} as dmean will be (x + y + z)/3 = kSo stand dev = sqrt [(x-k)^2 + (y-k)^2 + (z-k)^2]/3Now consider x +2, y+2 and z+2mean = k + 2So stand dev = sqrt [(x-2-k+2)^2 + (y-2-k+2)^2 + (z-2-k+2)^2]/3=> sqrt [(x-k)^2 + (y-k)^2 + (z-k)^2]/3 = dHence column A = dSo Column B is greater than Column A
GRE QUANT DATABASE updated by Mohan on January 4th
1) A plant grows 1/7,1/8,1/9,1/10,1/11,1/12,1/13 each year for 6 years. another plant grows 3/4 for 6 years.colA:height of ist plant in 6 yearscolB:height of 2nd plant in 6 years
Solution:Something wrong with respect to the question. Since they said that each year the plant grows 1/7,1/8, 1/9, 1/10, 1/11, 1/12 and 1/13 for 6 years but there are 7 values.
2) Given the perimeter of sector as 'pi' and area of sector as 3pi/2. find the radius of the circle.Solution:I guess it has to be arc length and not the perimeter of the sectorSee perimeter of a sector = 2r + rθ
And if we proceed it with this value we are getting some complex values for r and θHence it must be rθGiven rθ = π -->(1)And area of the sector = (1/2)r^2*θ = 3π/2 -->(2)(2)/(1)=> r = 3/2
3) Given (x-1/x)/(1+1/x)=99find the value of (x-1/x)/(1-1/x)?Solution: (x-1/x)/(1+1/x)=99=> (x^2 -1)/(x+1) = 99=> (x-1) = 99=> x = 100Now take,(x-1/x)/(1-1/x)=> (x^2 – 1)/(x-1)=> (x +1) = 100 + 1 = 101
4)
Column A: Area of shaded region in AColumn B: Area of shaded region in BSolution:In figure A,Diagonal of the square is 2rHence the length of the square = diagonal length/√2=> Length of the square = 2r/√2 = r√2So area of the square = length^2 = (r√2)^2 = 2r^2Area of the circle = πr^2
Shaded area in A = Area of circle – Area of square=> (π – 2)r^2
In figure B,Length of the square = 2rSo area of the square = length^2 = (2r)^2 = 4r^2Area of the circle = πr^2
Shaded area in A = Area of square – Area of circle=> (4 – π)*r^2
Hence Column A is greater than Column B
5) Given a fig , with label A representing three bars on it, label B representing five bars on it,label C representing three bars on it and the label D representing 2 bars on it. if each bar represents 5 units , then in which class the median lies.Solution:
If we arrange all these in ascending order we will get as:
2 (D) 3 (A) 3 (C) 5 (B)
For even numbers the median will be the average of middle two terms.That means it can lie in any of the class A or CHence answer is cannot be determined
6) Given that 'S' represents the mean of a set of variables whose mean is 56 and 'S' lies between 80th and 85th percentile, and T represents mean of set of numbers whose mean is 56 and T lies between 85th and 90th percentile.colA:ScolB:TSolution:I guess what ever may be the variables or numbers for S and T the mean will remain same.Hence both the values S and T which are nothing but the means of set of numbers and set of variables they will be 56Hence both the columns are equal
8) From a city M a person travels to city P of 500 miles at a uniform speed of 400miles/h and travels back from city P to city M at a uniform speed 500m/h. what is the average speed of a person in a round trip.Solution:Average speed of trip = (Total distance of the trip)/(Total time)Time while travelling = 500 miles/(400 miles/hr) = 5/4 hrsTime while returning = 500 miles/(500 miles/hr) = 1 hr
So average speed of the whole trip = (500 + 500)/(5/4 + 1)=> 1000/(9/4)=> 4000/9 miles/hr
9) On a particular day X member of people go to the post office. Of whom 7 people mailed letters, 9 people buy stamps and 10 people mailed packages but didn't buy stamps or mail letters.Column A: The number of people who buy stamps and mailed lettersColumn B: The number of people who mailed packages but didn't buy stamps or mailed letters.Solution:
Let A correponds to Mailing lettersB corresponds to buying stamps and C corresponds to Mailing packages
Given thatc = The number of people who mailed packages but didn't buy stamps or mailed letters = 10Hence Column B = 10
Also given that the number of people who buy stamps = f + b + h + e = 9 -->(1)Now the number of people who buy stamps and mailed letters = f + hFrom (1) we can get f + h = 9 – b – e < 9Hence Column A will be lesser than 9And Column B is 10
Therefore, Column B will be greater than Column A
10) There is a square PQRS it is tilted 90 degrees anticlockwise, so as to reach another point R' S' what is the distance covered by the square if it's length is 2.Solution:
We can find out the distance traveled by a point R
which is nothing but the length of the arc of radius = length of the square and angle of the arc as 90Distance traveled = πr/2 = π2/2 = π
11)
AC is the ladder and AB is the wall. If the ladder slided downwards against the wall AB, then Column A: xColumn B: ySolution:It completely depends on the slope of the lineSo the answer will be relation cannot be determined
12) Given a triangle ABC, D is the midpoint of AC, BD is the altitude. if one of the angles in the triangles can be 90 degrees which of the following could be true.a)<Ab)<Bc)<Cd)any one of theseSolution:In a right angled triangle,It is possible to draw an altitude from the right angled vertex to the opposite side which will be the midpoint of the opposite sideHence the right angled side will be B
13) In the year 1995, a company gets 'y' profit. in 1999 , the profit is $2.6y then what is the average of profit from 1995 to 1999 in terms of 1995 profit.Solution:This question is not very clear
Here is the possible solution for this questionAverage = (y + 2.6y)/2 = 3.6y/2 = 1.8yAverage will be 1.8 times of 1995 profit
14) There are 'n' seats in an auditorium and there are 6 indentical rows. The last row chairs are pulled out and equal number of chairs is placed in each of remaining rows such that each row appears in dentical after the whole transaction what is the minimum value of n?Solution:Given that there are n seats in an auditoriumAnd there are 6 rows arranged with equal number of seatsSo each row will have n/6 seatsNow these n/6 seats are distributed equally among 5 rowsSo each row will get (n/6)/5 = n/30 seats So, in total every row will have n/6 + n/30This value has to be a proper integer value since chairs cannot exist in fractionsSo the least possible value for which this becomes an integer will be 30Hence the minimum value of n will be 30
16) The water flows into a cylinder at 1000cubic inches/min. if the rise in the water lavel in the tank is 0.1 inches/min. what is the radius of the cylinder.Solution:Water flows into a cylinder at 1000 cubic inches/minIn 1 minute, 1000 cubic inches of volume will be filledAnd also given that in 1 minute it water level rises by 0.1 inch which is nothing but the heightSo, find out the volume in 1 min = π(r^2)h=> π(r^2)*(0.1) Since height raised by 0.1 inch in 1 minBut we know that in 1 min the volume raised is 1000=> π(r^2)*(0.1) = 1000=> π(r^2) = 10000=> r = 100/sqrt(π)
17)
As shown above two lengths of the rectangle are 2x and x. If the circumference of the circle is 4πsqrt(5), what is the area of the rectangle?Solution:Diameter of the circle = √[(2x)^2 + x^2] = x√5Now circumference of the circle = πd
=> π(x√5)Given that the circumference of the circle as 4πsqrt(5)=> 4πsqrt(5) = π(x√5)=> x = 4Now area of rectangle = x(2x) = 2x^2 = 2*(4*4) = 32
18) Given the probability of raining on each of five days is 1/6 , excepts on the first day it is 2/5 and on the last day it is 4/5 what is the probability that the rain will occur on at least one of the five days.Solution:
P(raining on first day) = 2/5=> P(It won't rain on first day) = 3/5
P(raining on second day) = 1/6=> P(It won't rain on second day) = 5/6
P(raining on third day) = 1/6=> P(It won't rain on third day) = 5/6
P(raining on fourth day) = 1/6=> P(It won't rain on fourth day) = 5/6
P(raining on fifth day) = 4/5=> P(It won't rain on fifth day) = 1/5
P(it rains atleast on one of the five days) = 1 – P(It wont rain at all on five days)
Now,P(It wont rain at all on five days) = P(Won't rain on 1st day)*P(Won't rain on 2nd day)*P(Won't rain on 3rd day)*P(Won't rain on 4th day)*P(Won't rain on 5th day)
=> P(It wont rain at all on five days) = (3/5)*(5/6)*(5/6)*(5/6)*(1/5) = 25/72P(it rains atleast on one of the five days) = 1 – P(It wont rain at all on five days)=> 1 – 25/72=> 47/72
19) There is a series 's' and 'n' positive integers where mod(n-5)<5Column A: Mean of integersColumn B: MEDIAN OF SERIESSolution:Given that, |n-5| < 5=> n will take values from 1, 2, 3, 4 and 5 which satisfies the above relationSo, S = {1,2,3,4,5}Mean of the integers = 3Median of the series will be also 3
Hence both the columns are equal
20) Given six teams like instrument 1.instrument2.. and so on in a musical competition with 5 judges and their respective scores are 31,24,14,10,43,47. what is the minimum number of teams which must get 7 or more than 7 score from any of judges.Solution:First of all we need to know what is the minimum and maximum scores that each judge can award for any of the teamsWith out those values we cannot solve this one outI hope there needs some additional information required
21) What is the probability of selecting an odd number from 1,2.....n , such that n is odd number greater than 50 Solution:
First of all we need to know whether n is greater than 50 or not.If it is not greater than 50 then the probability will be 0.
Now upto 1,2,3...n will have n/2 odd numbers if n is even and (n+1)/2 when n is odd.
If it greater than 50 then it takes different value depending on whether n is even or oddLet n is an odd numberNow we know that upto n we have (n+1)/2 odd numbers from which we need to subtract all odd numbers lesser than 50 (which are 25)Hence total number of odd numbers greater than 50 are (n+1)/2 – 25 = (n – 49)/2So when n is odd then required probability = [(n – 49)/2]/n = (n – 49)/2n
Similarly,Let n is an even numberNow we know that upto n we have n/2 odd numbers from which we need to subtract all odd numbers lesser than 50 (which are 25)Hence total number of odd numbers greater than 50 are n/2 – 25 = (n – 50)/2So when n is even then required probability = [(n – 50)/2]/n = (n – 50)/2n
GRE QUANT DATABASE updated by Mohan on January 2nd
1) If 7 workers worked 140 hours extra than usual. four workers spend x hours extra , 3 workers spend 2x hours extra. find the difference between median and meanSolution:This question is not very clear...
2) There are X members in a meeting , in how many ways a group is formed such that A members are always excluded and B members are always included.Solution:
Here is my explanation for this question. Question is not very clear but we can approach it in the following way
Total members = XOut of which A members should always be excluded andB members should always be included
So the point is all about the other people X – A – B We are not sure about the size of the group.We can select 0 from X – A – B and all members from BWe can select 1 from X – A – B and all members from BSimilarly, we can select 2 from X – A – B and all members from BSimilarly, we can select 3 from X – A – B and all members from Band so onSimilarly, we can select all members from X – A – B and all members from B
So the total number ways will be = (X – A – B)C1 + (X – A – B)C1 + (X – A – B)C2 + (X – A – B)C2 + (X – A – B)C3 +.....+ (X – A – B)C(X – A – B)
Formula: nc0 + nc1 + nc2 + .. + ncn = 2^n
=> (X – A – B)C1 + (X – A – B)C1 + (X – A – B)C2 + (X – A – B)C2 + (X – A – B)C3 +.....+ (X – A – B)C(X – A – B) = 2^(X – A – B)So, i guess the final answe is 2^(X – A – B)
3)
What is the value of AD?Solution:First we need to assume that <ABC and <CED as 90 degrees since nothing is mentioned about thatin the question and with out that we cannot solve the problemWe need to find out the value of ADObserve that CDE and ABC are similar right angled triangles
Now, x/(6-x) = 6/1=> x = 36 – 6x=> 7x = 36=> x = 36/7Now AD = CD + ACCD = sqrt(1^2 + (6/7)^2) = sqrt(85/49)AC = sqrt(36 + (36/7)^2)Hence the value of AD.It's coming out with some absurd square root value.Might be the values are not proportionate
4) Given an event , every number of a community exchange cards with every other number if the post man delivers 420 cards then how many members are there in communitySolution:Here the order is important.Let N be the members in the community=> NP2 = 420=> N(N-1) = 420=> N = 21
5) Given that, if the area of the triangle STR is 1/9th area of the equilateral triangle PQR, then what is the ratio of QT/TR?A. 1:3B. 3:1C. 2:1& so on…..
Solution:
Let PQ = QR = PR = aLet SR = ST = TR = b
Area of equilateral triangle PQR = (√3/4)a^2 andArea of equilateral triangle RST = (√3/4)b^2
Given that [√3/4)b^2]/[(√3/4)a^2] = 1/9
a = 3bNow QT = QR – TR = a – b = 2bTR = b
Hence QT/TR = 2
6) Given P=x(x+1)(x+2)(x+3); where x is a positive integer , thencolA:the remainder where P is divided by 3colB: 1Solution:When a number is divided with 3 it can leave a remainder of wither 0 or 1 or 2If it leaves a remainder 0 then it will be divisible by xIf it leaves a remainder 1 then it will be divisible by x + 2If it leaves a remainder 2 then it will be divisible by x + 1
Hence what ever be the remainder that x leaves when it is divided by 3 it leaves a remainder of 0 when x(x+1)(x+2)(x+3) is divided by 3Therefore, Column A = 0Column B = 1Column A is greater than Column B
7) In an equation x/7+w/28 =1 find the number of the integer solutionsSolution:Integers can be positive and negative.If we consider negative numbers also then we might end up at infinite numbers.So it might be positive integers
x/7+w/28 =1 => 4x + w = 28So total possible values are:(0,28) (1,24) (2,20) (3,16) (4,12) (5,8) (6,4) (7,0)
8)
Given a figure of a sector of circle, with radius as 5cm and RT length as 1 cm, thenCol A: QSCol B: 6Solution:Given that the radius of the circle as 5 cm (PT)Assuming that PT passes through RRT = 1 cmPR = 5 – 1 = 4
Now PRS is a right angled triangleWe know PS = 5 and PR = 4Hence by pythagoras theorem RS = 3Hence QS = QR + RS = 3 + 3 = 6Hence both the columns are equal
9) Given that there are three hooks and 5 paintings. in how many ways , can these paintings be arranged among the three hooksSolution:Here order is importantTherefore, it will be 5P3 ways (Selecting three from 5)
10) Given that the probability of hapening an event a is 0.80 and event b is 0.60 ColA: the probability of hapening event A or BColB: 0.92Solution:Assuming both the events are independent to each otherP(A or B) = P(A) + P(B) – P(A)*P(B) => P(A or B) = 0.8 + 0.6 – 0.8*0.6=> P(A or B) = 1.4 – 0.48 = 0.92Hence Both the columns are equal
11)Given that L1 and L2 are two tangents to the circle and point (3,4) is the centre of the circle
Column A: Slope of the line lColumn B: 1Solution:
I think the option is D is the correct answer.Since we don't know the x and y-axis
If we can assume L1 and L2 as x and y-axis (for simplicity)Now slope of line l is same as slope between (3,4) and (0,0)Hence slope = 4/3=> Column A is greater than Column B
12) ColA: 1/97+1/98+1/99+1/100 ColB: 1/25these questions are appering frequently , is there any shortcut for doing this to save the timeSolution:It's very simple to solve these problems.Here is the simple trick
1/97 > 1/1001/98 > 1/1001/99> 1/100Add all the above inequalities
=> 1/97 + 1/98 + 1/99 > 1/100 + 1/100 + 1/100=> 1/97 + 1/98 + 1/99 +1/100 > 1/100 + 1/100 + 1/100 + 1/100=> Column A > 4/100=> Column A > 1/25=> Column A > Column B
13)Find the y-intercept of the line
Solution:Find out the equation of the line and write in the form of x/a + y/b = 1Then b will be the y intercept
14) How many cubes with least possible dimensions can be formed from a rectangular cuboid of dimensions 7*6*5?SolutionThis is possible if the dimension is a multiple of 7, 6 and 3Since we need the least possible dimension and that will be the LCM of 7, 6 and 3LCM of 7, 6 and 3 is 42.So side of cube (least) will be 42.=> Volume of cube is=42*42*42Volume of the rectangular cuboids is =7*6*3Number of cuboids=42*42*42/(7*6*3)=14*42=588Hence the number of cuboids required are 588
15) On the occasion of a certain meeting . each member exchanged shake hand with one another. if the total shake hands were 21 how many members are there in the meetingSolution:Let there be n number of people.We need to select 2 people from n number of peopleThat can be done in nC2 ways=> nC2 = 21=> n = 7
16) A painting 4.5ft*1.5ft is to be bordered with a 3 inches wide wooden strip. what is the minimum length of the strip required to border the paintingSolution:It's nothing but the perimeter of the painting=> 2(4.5 + 1.5)=> 2*6=> 12 feet
17) If 5 is added to some quantity 'k' it contributes 20% of the solution . what is 100% of the solution in terms of k?Solution:5 is added to some quantity 'k' it contributes 20% of the solution => 5/(5+k) = 0.2
=> 5 = 1 + 0.2k=> 0.2k = 4=> k = 20
GRE QUANT DATABASE updated by Mohan on December 30th
1) Given the points (5,9) ,(x,1) and (4,5) if points lie on the same line and find the value of x.Solution:
Since all three points lie on a same line then the slope of any points will be equal.First find out the slope of (5,9) and (4,5)=> (9-5)/(5-4) = 4
So, slope of (5,9) and (x,1) must also be 4=> (9-1)/(5-x) = 4=> 8/(5-x) = 4=> 5-x = 2=> x = 3
4) Given that P takes 4 hours to complete the work, Q takes 6 hours to complete the work and R takes 8 hours to complete the work. If these three work together to complete the same work. what is the percentage work done by PSolution:P takes 4 hours to complete the work=> In 1 hour P can complete ¼ th of work
Q takes 6 hours to complete the work=> In 1 hour Q can complete 1/6 th of work
R takes 8 hours to complete the work=> In 1 hour R can complete 1/8th of work
If they all work together then in 1 hour they all can do (¼ + 1/6 + 1/8)th work=> 13/24 th workLet x be the total required to complete the work if they all work together=> (13/24)x = 1=> x = 24/13 hoursHence it will take 24/13 hours to complete the work if they all work together.In this 24/13 hours P can do a work of (24/13)*(1/4) th work=> 6/13 th workHence percentage work done by P = 600/13 = 46%
5) What is the value of (x,y) ?Solution:
A(0, b) means it is at a height of b units from O=> OA = b unitsGiven that AC = k units=> OC = b – k unitsHence coordinate of D will the height Oc = b – k => y = b – k
Now, ACD and AOB are similar triangles
=> AC/AO = CD/OB=> k/b = x/a (since CD is nothing but the x coordinate of D)=> x = ak/b
Therefore, (x,y) are (ak/b, b – k)
6) In an apartment 92% have cars and 14% have bikes and everyone in the apartment have either bike or carColumn A: Fraction of the people having a car as well as bikeColumn B: 1/10 Solution:In the figure provided let A corresponds to Car and B corresponds to Bike
Let total number of people be 100
=> a + b + c = 100 -->(1)=> a + c = 92 -->(2)and b + c = 14 -->(3)From (1) and (2)b = 8sub b = 8 in (3)=> 8 + c = 14=> c = 14Hence the fraction of people having both bike as well as car = 14/100 = 0.14Column A = 0.14Column B = 1/10 = 0.1
Hence Column A is greater than Column B
GRE QUANT DATABASE updated by Mohan on December 28th
1) Find the area of the circle inscribed in a square having diameter as 16sqrt(2)
Solution:First Find out the length of a square which will be the diameter of the circlea√2 = 16√2=> a = 16 = diameterSo radius = 8Area of the circle = pi*(8*8) = 64pi
2) Given mean of three numbers 2x,7x, and x^2 is 12. find the range of the numbers.here i got x=3 and -12 how can we find the range?Solution:
It's the absolute difference of these two numberswhich is 3-(-12) = 15
3) Which of the following can not be necessarily true?a) a+b+c=180b) a+b>c
c) a^2+b^2=c^2d) atleast two are acute anglesfor this C and B are not necessarily true. am i correct?
Solution:See if a, b, c in the option b) are corresponding to the sides thenwe know that sum of two sides will be always greater than third side.In that case a + b > c will be trueHence it leaves only C which is true only for right angled triangles
4) Given (x-3)/x-1)<0 where x>1 find x?Solution:
can we find x?If x takes only integer values then x can take a value of 2.But otherwise,x can take any value between 1 and 3
5) If three sides of a quadrilateral are equal and are of the x cm, then find the perimeter of quadrilateral.
here the fourth angle must be equal to x. So it is 4x.is it correct?
Solution:No since we dont know the angles between them, we cannot directly assume the value of the other side as x.
6) In a group 7 out of 15 students admitted in a university and one of them absent everyday. If 315 students were admitted last month, how many students were not absent at all?Solution:
The actual meaning of the question is “ In 7 students, one of them is absent everyday. If 315 students are admitted then how many student were not absent at all.”315 in the sense 45 times 7 .Here the given condition is one among 7 is absent everyday.So, 45 times only 6 students are present.Therefore, answer is 45 x 6 = 270
7) If a person 'A' did 1/5th of the work and another 'B' did 1/6th of the remaining work. what is the work still left?Solution:Here A did 1/5th of the work, remaining work is 1-1/5=4/5.B did 1/6th of remaining work so 1/6(1-1/5)=4/30=2/15Total work is 1Work left is 1-(1/5+2/15)=1-1/3 =2/3
8) A computer system digit code has 5 digits in that 'x' repeats once, y repeats twice and z repeats twice system accepts this code xyzyz and yyxzzcolA:the number possible for the system codecolB:xxx(some value)Solution:It's just the number of ways we can arrange 5 numbers with 2 numbers repeating twiceCol A: 5!/(2!*2!)
9) Column A: The angle AColumn B: 60 degrees
Solution:
By looking at the figure we might think that the given two squares are equal in sides.But nothing is mentioned in the question about this.So in these Quantitative comparison questions we cannot assume anything just by looking at the figures.
They clearly mention in your GRE exam that nothing is drawn to the scale, so you cannot assume it to scale, if there is any question which is drawn to the scale then we will inform it in the question.
Is it clear now?Never assume anything in these Quantitative comparison questions unless they mention it in the question.
2) If the area of right angled triangle ABC is 2, thenCol A: Area of the shaded regionCol B: π
Solution:
By the symmetry of circle, AB = BC = radius of the circleHence given triangle is an isosceles right angled triangle.So (1/2)*AB^2 = 2=> AB = BC = 2There fore the radius of the = 2Required area = (πr^2)/4 = π*4/4 = πHence both the columns are equal
3) A number 'n' when divide by 24 gives 21 as remainder. which of the following can be the quotient.a)3b)4Solution:There are given some options. i think here anyone can be the quotient because 24*3+21=some dividend 24*4+21=some dividend same for other options alsoam i correct?Yes bhargav you are correct it can take any value. I guess some additional data is missing
4)-1<r<t<0cola: r+rt^2colb: -1Solution:Column A: r(1+t^2)We know 1+t^2 will always be greater than 1
and -1<r<0
So depending on the value of r and t we choose the value of column A depends.Therefore relation cannot be determined
6) As shown in the figure above, on the triangle, they are three arcs of a circle whose radius is ‘2’. Find the length of all the three arcs together?
Solution:It's nothing but the length of an arc with an angle of 60 (Since the given triangle is an equilateral triangle)
Each arc length = r(angle) = 2*(π/6) = π/3Since total three arcs are there the length of all the three arcs = 3*( π/3) = π
8) In a shop the discounts are as follows.A 40% discount on each coat and 20% discvount on each shirt. if a person buys 2 coats and 1 shirt then wt is the total discount he gets for buying.Solution:A) i think we cannot determine answer from this, because ther cost is not mentioned hereYes bhargav you are correct some data is missing in this question
1) Find out the remainder of this expression (10^8 + 10^6 + 10^4 + 10^2)/11Solution:We can use remainder theorem for solving this question.For suppose there is a function f(x) = ax^2 + bx + cAnd if we divide it with (x – k)Then the remainder will be f(k)For example,Consider f(x) = 3x^2 - 4x + 1If we divide this with x – 2Then the remainder will be f(2)=> f(2) = 3(2^2) - 4(2) + 1=> f(2) = 12 – 8 + 1 = 5Hence the remainder will be 5 if we divide 3x^2 - 4x + 1 with x – 2Let us use the same concept of remainder theorem for this problemLet f(x) = x^8 + x^6 + x^4 + x^2 (where i just replaced 10 with x)Now this f(x) is divided by x + 1 (since we considered x as 10 and 11 can be written as 10 + 1)Hence from the remainder theorem if we divide f(x) with x – k then the remainder will be f(k)Here k = -(1)Hence the remainder is f(k) = f(-1)f(-1) = (-1)^8 + (-1)^6 + (-1)^4 + (-1)^2=>f(-1) = 1+ 1+ 1+ 1 = 4Hence the remainder is 4
2) A person spends a part of amount of $20,000 for buying .40% of remaining amount is given at 6% interest and rest of money is given at 10% interest. if the total interest of the person gets $1250 then what is the amount he used for buying?Solution:Let x be the amount of money that a person spend for buyingNow the remaining money is 20,000 – x
Now 40% of this remaining money is 0.4*(20,000 – x) is given at 6% interest
And the rest of the money which is 0.6*(20,000 – x) is given at 10% interest
I guess Interest has to be given per year or per month. Nothing has been mentioned so let us assume by the end he will get 6% and 10% respectively.
6% of 0.4*(20,000 – x) + 10% of 0.6*(20,000 – x) = 1250
0.06*0.4*(20,000 – x) + 0.1*0.6*(20,000 – x) = 1250
=> 0.024*20,000 – 0.024x + 0.06*20,000 – 0.06x = 1250=> 0.084*20,000 – 0.084x = 1250=> 0.084x = 430=> x = 5120 (app.)Hence out of 20,000 he used 5120 for buying
3) given that a set 'N1' has five different numbers and'N2' has five different numbers and none of them have common numbers. If one number is selected from N1 and one number is selected from N2 how many different combinations are possible.Solution:Given that in N1 there are 5 different numbersAnd in N2 there are 5 different number (which are distinct from the 5 numbers in N1)
We can select one number from 5 numbers in N1 in 5 ways
Similarly we can select one number from 5 numbers in N2 in 5 ways.
If we can do one thing in m ways and another thing in n ways then both do both of them in m*n ways.
So we can select a number from N1 in 5 ways and N2 in 5 ways. So altogether we can select the both in 5*5 = 25 ways
4) There are x boxes and in each of the boxes some number of balls are placed .if fewer by 3 boxes are taken and 12 balls are placed into all boxes equally, then 5 balls are left wt is the number of boxes?Solution:Given that there are X boxes (We need to assume that all X boxes will have equal number of balls each)
Now fewer by 3 boxes are taken. That means total number of boxes taken are X – 3
Now 12 balls are placed in to X – 3 boxes equally and 5 balls are left outThat means total number of balls will be 12*(X-3) + 5 = 12X – 36 + 5 = 12X – 31
But since we know that total number of balls has to be perfectly divisible by X (Since initally X boxes has equal number of balls each)
So, 12X – 31 has to be divisible by X
It will be possible only if X is a multiple of 31 (since 31 is a prime number)
=> Least possible value for X = 31
Hence the total number of boxes will be 31
5) Given a series a1,a2,........a3 if a1=4, a2= -5 and an=a(n-1)-a(n-2) find the sum of the first 100 numbers.. is there any shortcut to do this problem.Solution:
Hi bhargav, these kind of problem generally involve concepts on periodicity.
Periodicity means after some terms in the sequence same set of numbers will repeat. So we need to identify that periodicity first and need to solve it. Initially it might take some time to understand but once you are thorough with it then it won't take much time in solving these kind of problems.
Here is the explanation have a look at it and let me know if you have any doubts in this:
a1 + a2 + a3 + a4 + ... + a99 + a100=> a1 + a2 + (a2-a1) + (a3 – a2) + (a4 – a3) + .... + (a98 – a97) + (a99 – a98)=> a2 + a99We need to find out a99a3 = a2 – a1a4 = a3 – a2 = a2 – a1 – a2 = -a1a5 = a4 – a3 = -a1 – a2 + a1 = -a2a6 = a5 – a4 = -a2 - (-a1) = -a2 + a1a7 = a6 – a5 = -a2 + a1 - (-a2) = a1a8 = a7 – a6 = a1 - (-a2 + a1) = a2Hence the pattern repeats like this a1 , a2 , a2 – a1, -a1, -a2, -a2 + a1.....That is from 7th term onwards the same pattern repeats.....So, a7 will be the same as a1a8 will be the same as a2a9 will be the same as a3a10 will be the same as a4a11 will be the same as a5That is a1, a7, a13, a20, will be the same1+ (n-1)6 = 6n – 5a99 doesnot comes under this categorya2, a8, a14,...will be the same2 + (n-1)6 = 6n-4
same with here...a3, a9, a15,...so will be the same category3+ (n-1)6 = 6n – 3Yes a99 comes under this categoryBecause substitute n = 17 in 6n – 3 we will get 99Hence a99 = a3 = a2 – a1Hence the sum of all 100 terms will be = a2 + a99 = a2 + a2 – a1 = 2a2 – a1 = 2(5) - (-4) = 10 + 4 = 14Hence 14 is the final answer.
6) Given a cone , the specifications of the triangle given where two equal sides x, one side 6 formed by the two sides and perimeter of semicircle 50pi. find the perimeter of the triangle.Solution:
Perimeter of the semicircle = Pi(r) = 50Pi=> r = 50Hence the x = diameter of the semicircle = 2r = 2*50 = 100
Hence the perimeter of the triangle = x + x + 6 = 206
2)
Col A: Area of square ACol B: (4/3)*(81 – x)
Solution:
We know that x will be greater than 0=> 81 – x < 81
=> Column B < (4/3)*(81) = 108
So, Column B < 108
And Column A = 81
Since Column B < 108 it can take a value greater than 81 and lesser than 81. Hence the relation cannot be determined
So the final answer is D
3)
Given area of triangle as 12Col A: xCol B: 4Solution:Observe that (x,0) and (9,0) lie on x-axisArea of triangle will be = (1/2)*base* height
Height of this triangle is nothing but the y coordinate of (3,4) (which is the perpendicular dist. From x-axis)Base = (9-x)Height = 4Hence area = (1/2)*4*(9-x) = 18 – 2x = 12 => 2x = 6=> x = 3Hence Column B is greater than Column A
1) Find the area of any trapezium?i solved it by using 1/2(b1+b2)*hi got 3a^2 but answer is given 6a^2
Solution:Even i'm getting 3a^2. Then it might be the total area of the figure
2) Given there are 3 marrid couple and they have to b arranged in 6 seats. in how many ways they can b arrangd such that husband and wife should always be together.Solution:We can club each couple in to 1 single thing.Then there are 3 things which need to be arranged in 3 seats and that can be done in 3! ways.Each couple among themselves can be arranged in 2 ways.So, the total no.of arrangements with the given condition = 3!*2*2*2 = 6*8 = 48Hence total there are 48 ways we arrange them with the given condition
3) For a given series p1,p2,p3..........pn and n>2. if p(n+1)=5pn+4, find 'pi' such that 'i' is smallest number divisible by 7.Solution:Given P1 = 1 andP(n+1) = 5Pn + 4The smallest number divisible by 7 is 7 itself.P2 = 5P1 + 4P3 = 5(5P1 + 4) + 4 = 25P1 + 4(5+1) = 52 P1 + 4(51 + 50)P4 = 5(25P1 + 4(5+1)) = 53 P1 + 4(52 + 51) = 54-1 P1 + 4(54-2 + 54-3)So, in generalPn = 5n-1 P1 + 4(5n-2 + 5n-3)So, P7 = 57-1 P1 + 4(57-2 + 57-3) = 56 P1 + 4(55 + 54) = 15625 + 4(3125 + 625) = 15625 +4(3750)=> 15625 + 15000 = 30625
4) Find the shaded area.
Solution:
<BOC = 90 – 30 = 60
OB = OC = radius = 1
Hence corresponding angles opposite to these sides will be equal.Hence triangle BOC is an equilateral triangle.
Shaded area = Area of sector OBC – Area of triangle OBC = π/6 - (√3/4)
5) Column A: Area of triangle ABDColumn B: Area of triangle ADC
Solution:Sum of angles in a triangle = 180=> 6x = 180=> x = 30Now ABC is a right angled triangle:Let AC = a and ADC is an equilateral triangle and the area = (√3/4)a^2
Now consider triangle ABCSince the angles are in the ratio 30 : 60 : 90then the lengths opposite to these angles will be in the ratio of 1: √3: 2=> AC/1 = AB/√3 = BC/2 => a = AB/√3 = BC/2=> AB = √3aSo, area of triangle ABC = (1/2)base*height = (1/2)(AB*AC) = (1/2)(√3a*a) = (√3/2)a^2So area of triangle ABD = area of triangle ABC – area of triangle ADC=> Area of triangle ABD = (√3/4)a^2
Hence both the columns are equal.
6)given a centre of circle (3,1) and one point in the circumference is given asked find out the radius.Solution:i think radius is the distanc between given points. is it correct?Yes bhargav you are correct
7) In a class 500 students, the marks prcentile as given if 'f' is 20% , 'g' is 40% and 'h' is 60% colA:the percentile by with g is more than f colB:the percentile by which h is more than gSolution:First let us find out the values for f, g and hf = 20% of 500 = (0.2)*500 = 100g = 40% of 500 = (0.4)*500 = 200h = 60% of 500 = (0.4)*500 = 300
Col A: Percentile by with g is more than f=> (f-g)/g*100 = 100/100*100 = 100%
Col B: Percentile by which h is more than g=> (h-g)/g*100 = 100/2 = 50%
Hence Col A is greater than Col B
8) For a match ,5100 tickets were sold and if profit is $205,000. if there are $30 ticket and $50 tickets , how many $50 tickets were sold?Solution:Let x be the $30 ticketsand 5100 – x will be $50 tickets
Total profit = 30x + (5100 – x)50 [Considering the profit as the total amount recieved on all the tickets]
=> 30x + 255000 – 50x = 205000=> 50000 = 20x=> x = 2500Hence the total tickets of $50 will be 5100 – 2500 = 2600
9)if 5^3X+5^2Y+5Z+P=264 where x,y,z,p are non zero lss than 5 find the value of X+Y+Z+P?
Solution:Given that x, y, z and p all are non zero integers less than 5.So possible values we can assign for x, y, z and p are 4, 3, 2, 1, -1, -2, -3.....There is no particular method to solve it but only by trial and error method.First find out any combination for x, y, z and p which satisfies the above equation.Start with x = 2 (simple since 125*2 will be 250 which is close to 264)
=> 125*2 + 25y + 5z + p = 264=> 25y + 5y + p = 14Let y = 1=> 25 + 5y + p = 14=> 5y + p = -11So, take y = -2 and p = -1=> -10 – 1 = -11Hence one set of combinations which will satisfy the given equation are:x = 2, y = 1, z = -2 and p = -1But the fact is that we will get mutliple answers by taking different combinations.That is if we take other combination as x = 2, y = 1 , z = -3 and y = 4Here the total sum is 4So, i guess there must be some mistake in the question.
11) Given the dimensions of a triangle 5,6,and 8.if the angls opposite to sides 5 and 6 are x and y then colA:third angle colB:90Solution:Observe the below figureAccording to the pythagoras theorem,ABC will be a right angled triangle with angle ACB = 90
Since 5^2 + 6^2 = 61
Triangle that we are discussing in the question is ADC.Since sqrt(64) is greater than sqrt(61)The third angle DCA will be greater than 90 (Try observe the graph carefully you will understand the logic behind that)
GRE QUANT DATABASE November 25th questions given by one of my student updated by Mohan
1) Find the value of x. polygon has 8 sides.
Solution:Given polygon is a regular octagonHence x = 360/8 = 45
3) Above is a square. Side is 100. it is divided into 2 parts the bigger is double the area of the smaller one. X=2Y so what is the length of ‘a’
Solution:
Area of the bigger rectangle = 100aArea of the smaller rectangle = 100*(100 – a)Given that,100a = 200*(100 – a)100a = 20000 – 200a300a = 20000a = 200/3Hence the value of a is 200/3
4) The slope is some value. Then coordinate x is (7,12) the the other is y coordinate has value in which the x coordinate is greater than the x coordinate by 7. and the value of the other coordinate is 8. so what is the value of the horizontal value of y.Solution:
Questions needs some additional information in order to solve it.Let me tell you the possible interpretation that we can interpret from the above questions.Given X (7,12)Y (x,y)
Given that x is greater than the x coordinate by 7
So, possible x = 7 + 7 = 14
and other coordinate is 8
So, Y (14, 8)Horizontal value of Y is nothing but x coordinate which is 14
5) The perimeter of a triangle is A (a,b-3) , B (a,b), C (a-4,b-3). What is the perimeter.Solution:
First find out the length of each side.
AB = 3BC = 5AC = 4Hence the perimeter will be 3 + 4 + 5 = 12
6) A truck carries some goods. It takes 10 rounds to carry them . in the last round it does not go fully loaded. What can be the total number of goods. (something like this)Solution:It depends on the options given
Let the maximum load that the truck can carry on each day be L and k be the load that the truck carried in the last round.
So the total goods will be 10L + k (where k will be lesser than k)
Finally question turns out to be a remainder problem that is when a number is divided by 10 leaves a remainder k. What is the number is the final question.
I guess the final answer will be the one from the options which is not a multiple of 10
7) There are some people in the elevator, 20 people. Some average 140 pounds some avg 210 pounds. The max the elevator can bear is 2400. how many are 140 pounds and how many are 210 pounds. (something like this)Solution:
Given that the number of people in the elevator as 20
From which let x people have an average of 140 pounds and the rest of all have an average of 210 pounds
Total weight of x people = 140x and Total weight of 20 – x people = 210*(20 – x)Hence the total weight of the people = 140x + 210*(20 – x)Given that the maximum weight that the elevator can weigh = 2400=> 140x + 210*(20 – x) <= 2400=> 4200 – 70x <= 2400=> 70x >= 2400=> x >= 5.71Since x corresponds to the total number of people it cannot be in fractionSo, x = 6Therefore, 6 people have an average of 140 pounds and the rest of 14 have an average of 210 pounds
8) Keri will randomly select one of the 16 candies in a dish. There are 3 red , 5 purple and 8 blue candies in the dish col A: the probability that kerri will select a blue candy
col B : the probability that Kerri will select a candy that is either red or purple Solution:
Col A: The probability that kerri will select a blue candy = No.of blue candys/Total no.of candies=> Col A = 8/16
Col B: The probability that Kerri will select a candy that is either red or purple = P(Kerri selecting Red candy) + P(Kerri selecting Purple candy)Note that selecting a red candy and purple candies are independent of each other.
Col B: 3/16 + 5/16 = 8/16Hence both the columns are equal
GRE QUANT DATABASE updated by Mohan on December 1st
1) Find out the remainder of this expression (10^8 + 10^6 + 10^4 + 10^2)/11Solution:
We can use remainder theorem for solving this question.
For suppose there is a function f(x) = ax^2 + bx + cAnd if we divide it with (x – k)Then the remainder will be f(k)For example,Consider f(x) = 3x^2 - 4x + 1If we divide this with x – 2Then the remainder will be f(2)
=> f(2) = 3(2^2) - 4(2) + 1=> f(2) = 12 – 8 + 1 = 5Hence the remainder will be 5 if we divide 3x^2 - 4x + 1 with x – 2
Let us use the same concept of remainder theorem for this problem
Let f(x) = x^8 + x^6 + x^4 + x^2 (where i just replaced 10 with x)Now this f(x) is divided by x + 1 (since we considered x as 10 and 11 can be written as 10 + 1)Hence from the remainder theorem if we divide f(x) with x – k then the remainder will be f(k)Here k = -(1)Hence the remainder is f(k) = f(-1)
f(-1) = (-1)^8 + (-1)^6 + (-1)^4 + (-1)^2=>f(-1) = 1+ 1+ 1+ 1 = 4
Hence the remainder is 4
2) The water flows into a cylinder at 1000 cubic inches/min. If the rise in the water level in the tank is 0.1 inches/min, find the radius of the cylinder?Solution:
Water flows into a cylinder at 1000 cubic inches/minIn 1 minute, 1000 cubic inches of volume will be filled
And also given that in 1 minute it water level rises by 0.1 inch which is nothing but the heightSo, find out the volume in 1 min = π(r^2)h=> π(r^2)*(0.1) Since height raised by 0.1 inch in 1 min
But we know that in 1 min the volume raised is 1000=> π(r^2)*(0.1) = 1000=> π(r^2) = 10000
=> r = 100/sqrt(π)
3) The best way to find out quickly the SD of two sets ex: set A: {15,19,20,21,25} B={15,18,20,22,25} Solution:
First find out the mean for both the sets
=> Mean A = 20 and Mean B = 20
So, both the means are equal.
Observe that if there is a series {a, b, c, d, e} and mean m
then SD = sqrt([(a-m)^2 + (b-m)^2 + (c-m)^2 +(d-m)^2 +(e-m)^2]/6 )
It's just the difference between the number and the mean
If we observe the given two sets all the numbers are equal except {19, 21} in the first set and {18, 22}
Other terms contribute to the same value in the numerator since the mean same.
If there is any difference then it must be because of these terms
(19 – 20)^2 + (21 – 20)^2 = 1 + 1 = 2 (for first set)
(18 – 20)^2 + (22 – 20)^2 = 4 + 4 = 8 (for second set)
Hence SD for the second set will be more
It's just the square of difference between the number and it's mean by which you investigate to find
out which one is greater
4) Col A: Area of rectangle whose perimeter 20Col B: Area of rectangle whose perimeter 24Solution:
If it is Square then Column B is greater than Column A but when it comes rectangle then any thing is possible if we take for perimeter 24 = 1 + 23 where the area of this is 23 and 20 = 10 + 10 then the area of this is 100Hence we cannot conclude it. The final answer is Option D5) Given a series a1, a2.......an. If a1 =-4, a2 =5 and an = a(n-2)-a(n-1), then find the sum of first 100 numbers in the series?[NOTE: 1, 2, (n- 2), (n-1) and n in the above question are subscripts].Solution:
a1 + a2 + a3 + a4 + ... + a99 + a100=> a1 + a2 + (a2-a1) + (a3 – a2) + (a4 – a3) + .... + (a98 – a97) + (a99 – a98)=> a2 + a99We need to find out a99a3 = a2 – a1a4 = a3 – a2 = a2 – a1 – a2 = -a1a5 = a4 – a3 = -a1 – a2 + a1 = -a2a6 = a5 – a4 = -a2 - (-a1) = -a2 + a1a7 = a6 – a5 = -a2 + a1 - (-a2) = a1a8 = a7 – a6 = a1 - (-a2 + a1) = a2Hence the pattern repeats like this a1 , a2 , a2 – a1, -a1, -a2, -a2 + a1.....That is from 7th term onwards the same pattern repeats.....
So, a7 will be the same as a1a8 will be the same as a2a9 will be the same as a3a10 will be the same as a4a11 will be the same as a5That is a1, a7, a13, a20, will be the same1+ (n-1)6 = 6n – 5a99 doesnot comes under this categorya2, a8, a14,...will be the same2 + (n-1)6 = 6n-4same with here...a3, a9, a15,...so will be the same category3+ (n-1)6 = 6n – 3Yes a99 comes under this categoryBecause substitute n = 17 in 6n – 3 we will get 99Hence a99 = a3 = a2 – a1Hence the sum of all 100 terms will be = a2 + a99 = a2 + a2 – a1 = 2a2 – a1 = 2(5) - (-4) = 10 + 4 = 14
Hence 14 is the final answer.
6) Given Q = 968*18
Col A: Q + 968Col B: 968*19
Answer: Both the columns are equal
7) 20 bulbs , 2- are defective , 2 bulbs r chosen at random , whats the probability that neither of bulbs chosen are defective? Answer: 18c2/20c2
8) If N = 5^9 + 7^10, thenCol A: The least factor of 'N' greater than 1Col B: 3Solution:
N = 5^9 + 7^10Now Last digit of 5^9 is 5 and last digit of 7^10 is 9 (Left for you to find it)Hence the last digit of the N will be 5 + 9 = 14 which is 4Hence any number with last digit equal to 4 will have a factor of 2Hence 2 is the least factor greater than 1.
Hence column B is greater than Column A
9) Given y = 2x + 5 and x^2 = 4.Col A: yCol B: 3Solution:
x^2 = 4=> x = +2 or -2y = 2*2 + 5 = 9 and y = 2(-2) + 5 = 1Hence y = 1 and 9Hence Option D) relation cannot be determined
10) There are certain events in which two persons compete and there is a trophy for each game. If one looses a game, he gives trophy to the other player and if he wins he gets 1 trophy. At the end, if one has won 4 games, then other has 8 more trophies than the number of trophies he had at the start, assuming there is no tie in any of the games, find the number of games they played?Solution:
Suppose A and B participating against each other.
Let A won 4 games.And B won x games.
So total number of games played will be x + 4We need to find out the value of x.
Now consider B, he won x matches and lost 4 matches.So additional more trophies that B will have at end when compared to the start will be= x - 4 (Since he won x matches and lost 4 matches and every win he will get one trophy and for every loss he will lose one trophy)
Given that the B had 8 more additional trophies at the end when compared to the beginning.=> x - 4 = 8=> x = 12Hence B won 12 matches.So, total matches played between A and B will be x + 4 = 12 + 4 = 16
11) If the number of possible sets for choosing 4 things out of 6 things is 15, then find the possible number of sets for choosing 3 things out of 7?Answer is 35
12) Given initial ratio of men to total number of people in a team as 1: 3. If two women leave the team then the ratio becomes 2: 5. What is the total number of people in the team?Solution:
Let the Men be M and Women be WSo total will be M + W
Given that M/(M+W) = 1/3
=> 3M = M + W=> 2M = W
If two women leave then, women will be = W – 2 and total people will be M + W – 2
So the new ratio is M/(M+W – 2) = 2/5
=> 5M = 2(M + W – 2)=> 5M = 2M + 2W -4=> 3M = 2W – 4but W = 2M
=> 3M = 4M – 4 => M = 4
=> W = 8
The total people = 4 + 8 = 12
13) If 1 < y < 2 and 1 < xy < 4, then what would be the value of x?Col A: xCol B: 2Solution:
Given 1 < y < 2 and 1 < xy < 4
Consider y = 1.1Then 1< x(1.1) < 4=> 0.9 < x < 3.63
Hence the relation cannot be determined since 2 lies between 0.9 and 3.63Hence option D is the correct answer
14) Three persons x, y and z altogether complete a work in 9 hours. If y and z together takes 12 hours to complete then x alone will take how much time to complete the same work?Solution:
Given that X, Y and Z altogether completes a work in 9 hours
Let x, y and z be the work X, Y and Z they can work in 1 hour respectively.
If they all work for 1 hour they can do x + y + z work
In 9 hours if all the three work together then they can do 9(x + y + z) = 1 Since it completes the whole work.
=> x + y + z = 1/9 --->(1)
In 12 hours y and z can complete the work=> 12(y + z) = 1
=> y + z = 1/12 --->(2)
(1) – (2)=> x = 1/9 – 1/12
=> x = 1/36
=> 36x = 1Hence it will take 36 hours to complete the work if X alone works.
15) Given X = {25, 26, 27, 28} and Y = {7, 8, 9, 10, 11}. How many distinct values can be produced by (x + y)?Solution:
Given X = {25, 26, 27, 28} and Y = {7, 8, 9, 10, 11}
We need to find out distinct values for x + y25 + 7 = 3226 + 7 = 3327 + 7 = 3428 + 7 = 3525 + 8 = 3326 + 8 = 3427 + 8 = 3528 + 8 = 3625 + 9 = 3426 + 9 = 3527 + 9 = 3628 + 9 = 3725 + 10 = 3526 + 10 = 3627 + 10 = 3728 + 10 = 3825 + 11 = 3626 + 11 = 3727 + 11 = 3828 + 11 = 39
So tell me what are the distinct values for x + y
32, 33, 34, 35, 36, 37, 38, 39So, total 8.
No need to do all these calculations instead find out 25 + 7 = 32 (minimum sum) and 28 + 11 = 39 (maximum sum)Hence the required number will be all the values between 32 to 39 which is 8
GRE QUANT DATABASE updated by Mohan on November 25th
1. Which of the following is greatest? A. 10^100 + 2^ 100 B. 100^10 + 2^ 10 C. (100+2) ^10 D. (10+2)^ 100 & so on……
Solution:
But observe option D
(10 + 2)^100
=> 10^100 + 100C1*(10)^99*2 + 100C2*(10)^98*2^2 + ....... + 2^100=> 10^100 + 2^100 + .........Hence option D is greater
2. If 2^(x^2 +5x) =2, then what is the value of x? Solution:Answer is [ { -5(+&-) root 29 } / 2 ]
4. There is a bag which consists of 10 bulbs, out of which 2 is defective. If 3 bulbs are chosen at random without replacement, then what is the probability that none of the three bulbs selected are defective? Solution:Total Number of bulbs = 10
Out of which 2 bulbs are defective
Total number of bulbs which are not defective = 10 – 2 = 8
Now we need to select three bulbs from 8 non defective bulbs (since there is a condition that all the three bulbs must be non-defective)
From 8 bulbs we can select 3 bulbs in 8C3 ways. (No.of favourable outcomes)
Total no.of possible outcomes = 10C3 (since total there are 10 bulbs out of which we need to select 3)
Probaility = No.of favourable outcomes/Total no.of possible outcomes
=> Required probability = 8C3/10C3
5. In a Isosceles triangle STU, the sides ST = SU and ‘p’ is any point on UT, then which of the following might be true? I. ST > PS II. PU > ST III. PS > PT A. Only I B. Only II C. Only III D. Only I and II
& so on………Solution:No matter how the triangle look I ST > PS always true.With respect to other two they might be true but not always.If they ask in the question to find out which of them might be true then all the three be the correct answer.If they ask in the question to find out which of them always true then only one be correct.
7. Given Set P = {1.3, 0.9, 1.5, 1.1} and Set Q = {1.3x, 0.9x, 1.5x, 1.1x}, then Col A: Standard deviation of P Col B: Standard deviation of Q Solution:
No option D is the correct answer.
Since in the standard deviation of Q it includes the value of x.
Since we don't know the range of x, the relation cannot be determined
8. Given that there are 3 hooks and 5 pictures, find the numbers of ways to select 3 picture combinations? Solution:
Answer is 60.....Since selection is important so 5P3
4. Given [x * (y)^2] < 450 and if x and y are prime numbers greater than 3, then what is the maximum possible value of y?Solution:Answer is 7 (by considering the number as 441= 7^2 * 9) Correct me if i am wrongy to be maximum, x should be minimum
=> The minimum value that x can take is 5 (since the least prime number greater than 3 is 5)Sub x = 5=> y^2 < 90Hence the greatest value of y which satisfies the above inequality is 9That is 8^2 = 81 < 90Hence the maximum possible value is 9Does that make sense?
5. Given that a vending machine dispenses gumballs in a regularly repeating cycle of ten different colors. If a quarter buys 3 gumballs, what is the minimum amount of money that must be spent before three gumballs of the same color are dispensed?Solution:
Since the vending machine dispenses gumballs in a regular cycle of ten colors, there are exactly nine other gumballs dispensed between each pair of gumballs of the same color.
For example, gumballs one and eleven must be the same color,
Similarly, two and twelve must be the same color
forty-twofifty-two, etc.
To get three gumballs all of the same color, we get one of the chosen color, then nine of another color before another of the chosen color, then nine of another color before the third of the chosen color.
That's a total of 1 + 9 + 1 + 9 + 1 = 21 gumballs to get three matching ones.
Given that a quater buys three gumballs
means $0.25 buys 3 balls=> 1 ball costs $0.25/3
So, in order to buy 27 balls we need 27*(0.25/3)
=> $7*0.25 = $1.75
Hence it costs $1.75 before three gumballs of the same color are dispensed
GRE QUANT DATABASE (UPDATED TILL November 9th) updated by Mohan
1. Given that a salesman gets 12% commission on the sales upto $500 and he gets 20% commission on further sales amount on that day. If the salesman’s total commission is $380 on that day, then how much amount did he sell on that day?Solution:Let x (> 500 assume it to be greater than 500) be the amount that salesman sell on that day.=> 500(0.12) + (x – 500)*0.2 = 380 (Since up to 500 the commission is 12% and after that it is 20%)Now find out the value of x.=> 60 + 0.2x – 100 = 380=> 0.2x = 420=> x = 2100
2. Col A: 10% [sqrt(573.28 )]Col B: sqrt(57.328)Solution:Col A = 0.1*sqrt(573.28)
Col B = sqrt(57.328)=> Col B = sqrt(57.328) = sqrt(573.28*0.1) = sqrt(0.1)*sqrt(573.28)
Clearly sqrt(0.1) is greater than 0.1Hence Col B is greater than Col A.
3. Given m=(2)^(-3) * (3)^(-4) * (5)^(-5), then what is the value of (2)^(-6) * (3)^(-8 ) * (5)^(-10) in terms of m?.Solution:
Answer is m^2
4. If|3x+2| = 8Col A: |X|Col B: 3Solution:
3x + 2 = 8 or -8=> 3x + 2 = 8 or 3x + 2 = -8=> 3x = 6 or 3x = -10=> x = 2 or x = -3.33Now |x| = 3.33 or 2Hence the relation cannot be determined
5. Given that three persons X, Y and Z working together, takes 9 hours to complete a work. If ‘Y’ and ‘Z’ working together takes 12 hrs to finish the same job, then how much would ‘X’ take to finish that same work alone?Solution:
Let x , y and z be the work done by each of X, Y and Z respectively in 1 hr.Let k be the effort needed to complete the whole work.=> 9*(x + y + z) = 1 => x + y + z = 1/9Similarly,12*(y +z) = 1=> y + z = 1/12x = (x + y + z) – (y + z) = 1/9 - 1/12=> x = 1/36=> 36x = 1So, it takes 36 hours to complete the whole work by x.
6. Col A: 2/[(1/3)/(1/3)]Col B: 2/[1/(3/(1/3))]Solution:
Col A = 2Col B = 18
8. Given a line which has slope -5/8 and passes through the points (4, 3) and (2, k). Find the value of K?Solution:The two point formula for slope = (Y2 – Y1 ) / (X2 – X1)Where, (X1 , Y 1) = ( 2, k)(X2 , Y 2) = ( 4 , 3)( 3 – k ) / ( 4 – 2 ) = -5/83 – k = -5/4=> 12 – 4k = -5=> 4k = 17=> k = 17/4
9. If a Rectangular plate can hold 3 cubic feet, thenCol A: The number of cubic yards that 100 such plates can holdCol B: 13Solution:
10. There is a series of numbers 5, 12, 26.........till 100 terms. Which of these cannot be a term of the series?A. 57B. 75C. 96D.89E. 47Solution:
11. Given 1 < xy < 4 and 1 < y < 2,Col A: xCol B: 2Solution:
12. If 0 < t < u < v, thenCol A: Median of t, u, vCol B Mean of t, u, vSolution:
13. Given k and n are two positive even integersCol A: The remainder when k^(2) + n is divided by 2Col B: The remainder when k^(n + 2) + 2 is divided by 2Solution:Given that k and n are two positive even integers
=> Hence k^(2) + n and k^(n + 2) + 2 will be even positive integersAny even number divided by 2 will leaves a remainder 0Hence Both the columns will be equal to 0
Therefore, option c is the correct answer.
14. Given RST as an isosceles triangle and RS = ST. ‘P’ is a point on RT. Which of the following is true?I. SP<RSII. SP>RTIII. SP < PTA. Only IB. Only IIIC. I and II& so on………..Solution:
15. Given two sets X1 = {7, 8, 9, 10, 11} and X2 = {25, 26, 27, 28}. For X1 + X2, how many different numbers will be generated?Solution:
16. Col A: 1/2 + 1/3 + 1/4Col B: 1/1Solution:
17. A rectangular sheet is divided into unequal squares with total number of rows in the rectangle ‘n’ and columns ‘n+2’. If the minimum value of n is 21, thenCol A: The area of the square present in the 15th row and 18th columnCol B: n^2Solution:Case 1)First let us assume the length and breadth of the rectangular sheet be 21 and 23The maximum square that we can draw in this rectangular sheet is 21*21Hence any square will be always lesser than 21*21 (if we draw a square of 21 length then there is no possibility of drawing the other columns)Hence in this case Column B (=21^2) is greater than Column A
Case 2)
Let the us take the length and breadth of the rectangular sheet be 42 and 46Then if we apply same logic Any square will be lesser 42*42So, Column A < 4*21^2Column B is 21^2In this case the relation cannot be determinedFrom these two cases we can conclude that the relation cannot be determined
It will be more meaningful to solve this problem if they provide the dimensions of the rectangular sheet (which will surely turn out to be the best problem with a good logic)With out the dimensions the question seems to be a bit vague. There might be some information missing in this question
18. Two spheres have their volumes as 4Y and 3y, where y is some integer.Col A: The ratio of their radiusCol B: 4/3Solution:
First observe whether the given volumes include the same y or not.If Y and y are the actual variables involved in the volumes then the answer is D.If both are same y's then Then Column A = (4/3)^(1/3)
Hence in this case Column B is greater than Column A
GRE QUANT DATABASE (UPDATED TILL November 5 th ) updated by Mohan
1. Which of the following is greatest?A. 10^100 + 2^ 100B. 100^10 + 2^ 10C. (100+2) ^10D. (10+2)^ 100& so on……
2. If 2^(x^2 +5x) =2, then what is the value of x?
3. If m = (2)^(-3) * (3)^(-4) * (5)^(-5), then what is the value of (2)^(-6) * (3)^(-8 ) * (5)^(-10)?
4. There is a bag which consists of 10 bulbs, out of which 2 is defective. If 3 bulbs are chosen at random without replacement, then what isthe probability that none of the three bulbs selected are defective?
5. In a Isosceles triangle STU, the sides ST = SU and ‘p’ is any point on UT, then which of the following might be true?I. ST > PSII. PU > STIII. PS > PTA. Only I
B. Only IIC. Only IIID. Only I and II& so on………
6. There are 67 children in a community. If 52 like biking, 21 like skating and 12 like both, then number of children who like neither biking nor skating?(Similar to this)
7. Given Set P = {1.3, 0.9, 1.5, 1.1} andSet Q = {1.3x, 0.9x, 1.5x, 1.1x}, thenCol A: Standard deviation of PCol B: Standard deviation of Q(Similar to this)
8. Given that there are 3 hooks and 5 pictures, find the numbers of ways to select 3 picture combinations?(Similar to this)
GRE QUANT DATABASE (UPDATED TILL November 2 nd ) updated by Mohan
1. If m = (2)^(-3) * (3)^(-4) * (5)^(-5) then what is the value of (2)^(-6) * (3)^(-8 ) * (5)^(-10)?
2. A box contains 10 bulbs, out of which 2 are defective. If 3 bulbs are chosen at random, then what is the probability that at least one of these is defective?
3. Given that A, B and C working together completes a work in 9 days. If B and C working together completes the same work in 12 days, then in how many days A alone can complete the work?
4. Given [x * (y)^2] < 450 and if x and y are prime numbers greater than 3, then what is the maximum possible value of y?
5. Given that a vending machine dispenses gumballs in a regularly repeating cycle of ten different colors. If a quarter buys 3 gumballs, what is the minimum amount of money that must be spent before three gumballs of the same color are dispensed?(Similar to this)
6. Col A: Standard Deviation of x1, x2, x3, x4, x5Col B: Standard Deviation of x1 + 5, x2 + 5, x3 + 5, x4 + 5, x5 + 5
GRE QUANT DATABASE (UPDATED TILL OCTOBER 22ND) updated by MohanQuant:1. The reflection of a positive integer is obtained by reversing the digits. For example, 321 is the reflection of 123. The difference between a five-digit integer and its reflection must be divisible by which of the following?A. 2 B. 4 C. 5 D. 6 E. 9
Solution:Let the five digit number N be abcde=> N= 10000a + 1000b + 100c + 10d + eNow the reflection N1 will be 10000e + 1000d + 100c + 10b + aN-N1 = 10000(a-e) + 1000(b-d) + 10(d-b) + e-a=> N-N1 = (a-e)*(10000-1) + (b-d)(1000-10)=> N-N1 = (a-e)*(9999) + (b-d)*(990)=> N-N1 = (a-e)*(9*1111) + (b-d)*(9*110)=> N-N1 = 9[1111(a-e) + 110*(b-d)]Hence it is divisible by 9
2. Figure missingCol A: x + yCol B: 180
3. What is the remainder of the expression (7^0 + 7^1 + 7^2 + ………… + 7^20) when divided by 14?Solution:
Remainder when 7^0 is divided by 14 is 1Remainder when 7^1 is divided by 14 is 7Remainder when 7^2 is divided by 14 is 7Remainder when 7^3 is divided by 14 is 7So the pattern continues upto 7^20So, the total remainder will be 1 + 7(20 times)=> 1 + 140 = 141If we divide 141 with 14 the remainder will be 1
Hence the remainder of the given expression when it is divided by 14 is 1
4. Figure missing
Find the value of x?(Similar to this)
5. Figure missing
As shown in the figure above, on the triangle, they are three arcs of a circle whose radius is ‘2’. Find the length of all the three arcs together?(Similar to this)
6. Given slope and y-intercept of a line and asked to find the perpendicular slope of a line?Figure missing
7. If (3)^(2x) =(3)^(2) * (3)^(x), what is the value of x?Solution:
=> (3)^(2x) =(3)^(2 + x)=> 2x = 2 + x=> x = 2
8.Given a train ‘P’ travelling a distance ‘s’ km at an average speed of x km/hr and another train ‘T’ travels a distance ‘z’ at a speed of y km/hr. If the time taken by train ‘P’ is less than the train ‘T’, find the equation which satisfies the above problem?Solution:
Train P travels Distance s km at an average speed of x km/hrTime taken to travel s km iss/x hrs
Train T travels z km at an average speed of y km/hrTime taken to travel z km isz/y hrs
Time taken by train p is less than train T=> s/x < z/y=> sy – zx < 0
9. Given three sets R1 = {-1, -2, -3}, R2 = {1, 2, 3} and R3 = {-3, -2, -1, 1, 2, 3}. And Standard Deviation of R1 is S1, Standard Deviation of R2 is S2 and Standard Deviation of R3 is S3.I. S1 > S2II. S2 < 0III. S3 = 0
A. Only IB. Only IIC. Only IIISolution:
S1 = Standard deviation of R1First find out the mean for all the three sets.Mean of R1 = -6/3 = -2Mean of R2 = 6/3 = 2Mean of R1 = 0/3 = 0S1 = Sqrt {[(-1 - (-2))2
+ (-2 - (-2))2 + (-3 - (-2))2]/3} = Sqrt {[12
+ 02 + (-1)2]/3} = sqrt (2/3)
S2 = Sqrt {[(1 - 2)^2 + (2 - 2)^2 + (3 - 2)^2]/3} = Sqrt {[(-1)^2 + 0^2 + 1^2]/3} = sqrt (2/3)S3 = Sqrt {[(-3)2 + (-2)2 + (-1)2 + 12 + 22 + 32 ]/6} = sqrt(28/6)I S1 > S2 is wrong since S1 = S2II S2 < 0 is wrong since S2 = sqrt(2/3)III S3 = 0 is also wrongHence none of the above is the correct answer
10. Given that there are 10 balls and 10 bags and 3 balls are of same kind. In how many ways these ‘10’ balls can be arranged in 10 bags, such that no bag should be left empty?Solution:
We need to observe that no bag has to be left empty.That means every bag will get one ball each.We need to arrange 10 balls in 10 places with 3 balls being identical.This can be done in 10!/3!
11. In a shop, the discounts are as follows. A 40% discount on each coat and 20% discount on each shirt. If a person buys 2 coats and 1 shirt, then what is the total discount he gets on buying?Solution:
Some data is missing in this question
12. A person has 'W' kg of food for one week to feed some dogs. If each dog consumes 'x' kg per day thenCol A: Number of dogsCol B: 7w/xSolution:
Let the no.of dogs be D.Each dog consumes x kg/dayIn a week total all dogs require 7*D*x kgsGiven that w kg is sufficient to feed=> 7Dx = w=> D = w/7x
Hence Column B (7w/x) is greater than Column A (w/7x)
GRE QUANT DATABASE (UPDATED TILL OCTOBER 21ST) updated by Mohan
1. The value of [Sqrt(15.987) * 601.146]/[15.78 * 301.124] is …………………. ?Solution:
For these kind of problems we need to round off each number [Sqrt(15.987) * 601.146]/[15.78 * 301.124]=> [Sqrt(16) * 602]/[16 * 301]=> 4 * 602/(16*301)=> 8/16 = 0.5Hence the value will be closer to 0.5Try calculating this value with the help of calculator you will get exact value as 0.5058 which is almost close to 0.5
4. Given that there are 3 married couple and they have to be arranged in 6 seats. In how many ways they can be arranged, such that husband and wife should always be together?Solution:
We can club each couple in to 1 single thing.Then there are 3 things which need to be arranged in 3 seats and that can be done in 3! ways.Each couple among themselves can be arranged in 2 ways.So, the total no.of arrangements with the given condition = 3!*2*2*2 = 6*8 = 48Hence total there are 48 ways we arrange them with the given condition
5. For a given series P1, P2, P3……....Pn; P1= 1. And for n>=2, if P(n+1) = 5Pn + 4, find Pi such that ‘i' is the smallest number divisible by 7?Note: 1, 2, 3, i, n and n+1 are suffixes.Solution:
Given P1 = 1 andP(n+1) = 5Pn + 4The smallest number divisible by 7 is 7 itself.P2 = 5P1 + 4P3 = 5(5P1 + 4) + 4 = 25P1 + 4(5+1) = 52 P1 + 4(51 + 50)P4 = 5(25P1 + 4(5+1)) = 53 P1 + 4(52 + 51) = 54-1 P1 + 4(54-2 + 54-3)So, in generalPn = 5n-1 P1 + 4(5n-2 + 5n-3)So, P7 = 57-1 P1 + 4(57-2 + 57-3) = 56 P1 + 4(55 + 54) = 15625 + 4(3125 + 625) = 15625 +4(3750)=> 15625 + 15000 = 30625
6. Given that set A consists of positive odd numbers less than 100, set B consists of positive even numbers less than 5 and if set C consists of product of set A and set B. Find the number of numbers
possible in set C?Solution:
That is A = { 2n + 1} where n = 0, 1, 2.....49 [total 50 terms]Set B = {2, 4}Now the product of A and B will beA1 = {2*(2n + 1)} = {4n + 2} where n = 0, 1, 2.....49 [total 50 terms]A2 = {4*(2m + 1)} = {8m + 4} where m = 0, 1, 2,....49. [total 50 terms]Now we need to find out that in the two sets will there be any common terms.If there is any common term then we will get total number of elements will be less than 100If there are no common term then we will get the total number of elements as 100.Let us see whether there exists any common terms.For common term to exist it must satisfy both the forms=> 4n + 2 = 8m + 4=> 4n = 8m + 2=> 2n = 4m + 1We need to find out all m and n's which satisfy the above condition with all m,n 0, 1, 2...49But observe that RHS will always an odd number, agree?Because 4m will always an even number and even number + 1 will always be an odd number.But LHS will always be an even number that is 2*any number will be always an even numberSince even number cannot be equal to odd number, we cannot find any values for m and n whichsatisfies the expression 2n = 4m + 1Hence there are no common terms in them.So, the total number of elements in the required set will be 100
GRE QUANT DATABASE(UPDATED TILL OCTOBER 19TH) updated by Mohan
1. If (5^3) x + (5^2) y + (5) z + p = 264; where x, y, z, p are all non-zero integers less than 5, find the value of x + y + z + p?A. 10 B. 12 & so on………….Solution:
Given that x, y, z and p all are non zero integers less than 5.So possible values we can assign for x, y, z and p are 4, 3, 2, 1, -1, -2, -3.....There is no particular method to solve it but only by trial and error method.First find out any combination for x, y, z and p which satisfies the above equation.Start with x = 2 (simple since 125*2 will be 250 which is close to 264)=> 125*2 + 25y + 5z + p = 264=> 25y + 5y + p = 14Let y = 1=> 25 + 5y + p = 14=> 5y + p = -11So, take y = -2 and p = -1=> -10 – 1 = -11Hence one set of combinations which will satisfy the given equation are:
x = 2, y = 1, z = -2 and p = -1But the fact is that we will get mutliple answers by taking different combinations.That is if we take other combination as x = 2, y = 1 , z = -3 and y = 4Here the total sum is 4So, i guess there must be some mistake in the question.
2. When ‘k’ is divided by 12 it gives remainder 5, what will be remainder when k^2 is divided by 8?Solution:
Given that when k is divided by 12 it leaves a remainder of 5.So, k will be of the form k = 12m + 5Now k^2 = 144m^2 + 25 + 120m = 8(18m + 15) + 25So, if k^2 is divided by 8 it will leave a remainder which is equal to the remainder when 25 is divided by 8 (Since first term is a multiple of 8 and so it leaves a remainder of 0)=> Remainder when 25 is divided by 8 is 1Hence the remainder is 1.
3. Given x < 2-yCol A: yCol B: 2Solution:
Given, x < 2 – y=> -x > y – 2=> 2 – x > y=> y < 2 – xHence Column B is greater than Column A
4. Given a train ‘p’ travelling a distance ‘s’ km at an average speed of r km/hr and another train ‘t’ travels a distance ‘y’ at a speed of z km/hr. Find the equation which satisfies the above problem?A.sr - yz > 0 B. sz - yr > 0 C. yz – sr > 0 D. ry.sz > 0 E. sy – rz > 0Solution:
Train P travels Distance s km at an average speed of x km/hrTime taken to travel s km iss/x hrs
Train T travels y km at an average speed of z km/hrTime taken to travel z km isz/y hrs
Time taken by train p is less than train T=> s/x < z/y=> sy – zx < 0
5. Given that there are 600 communities and the average annual income of the communities comes around $600 of which f is 20 %, g is 40% and h is 60 %.Col A: The amount of ‘g’, greater than ‘f’Col B: The amount of ‘h’, greater than ‘g’
6. If 3/5 = x/y, thenCol A: x - 3Col B: y – 5Solution:
Given that 3/5 = x/y=> 5x = 3y=> x = 3y/5Column A = x – 3 = 3y/5 – 3=> 3(y – 5)/5 = (3/5)(y – 5)=> Column A = (3/5)* Column B Hence Column B is greater than Column A
7. The value of (14^10 + 7^2)^2 - (14^10 - 7^2)^2 is ……..?Solution:
Use the formula a^2 – b^2 = (a +b)(a-b)Here a = 14^10 + 7^2 andb = 14^10 – 7^2Now, (1410
+72)2 – (1410-72)2
= (1410 +72
+ 1410-72 )*(1410
+72 -1410
+ 72)=> 2*1410*2* 72
=> 2*(2*7)10*2*72
=> 2*210*710*2*72
=> 212 *712
=> (2*7)12
=> 1412 Is the correct answer
8. Given x > 0Col A: (10)^(-2) * (x)^(-1)Col B: (10)^(2) * xSolution:
Column A = 0.01/x and Column B = 100xSince x > 0 means 0 < x < 1 and x >=1Case 1) Let x lies between 0 and 1 So assume it to be 0.001=> Column A = 0.01/ 0.001 = 10Column B = 100*0.001 = 0.1In this case Column A is greater than Column B.
Case 2) x >=1Assume x = 10Column A = 0.01/10 = 0.001Column B = 100*10 = 1000In this case Column B is greater than Column A.
Hence from 1 and 2 cases the relation between these two columns cannot be determined
9. Given slope of a line as -3 and the points are located at (3, k) and (-2, m).Col A: k – mCol B: -15Solution:
Given that the slope of a line as -3Kindly note that is the points (3, k) and (-2, m) lie on this line then they will have the same slope as -3(It has to be clearly mentioned in the question that they lie on the same line)If they lie on the same line then,
k-m3+2 = -3
=> (k-m) = -3*5 = -15
Hence both the columns are equal.
GRE QUANT DATABASE(UPDATED TILL OCTOBER 16TH)Quant:
1. Col A: (1/25+1/26 + 1/27 + 1/28 + 1/29 +1/30)Col B: 0.2Solution:
Given that Column B = 0.2=> Column B = 20/100 = 1/5 = 6/30=> Column B = 1/30 + 1/30 + 1/30 + 1/30 + 1/30 + 1/30
So, both in Column A and Column B there are 6 terms and corresponding each term like 1st term of Column A with 1st term of Column B, 2nd term of Column A with 2nd term of Column B and so on..
Clearly 1st term of Column A (1/25) is greater than 1st term of Column B(1/30) and2nd term of Column A (1/26) is greater than 2nd term of Column B(1/30)3rd term of Column A (1/27) is greater than 3rd term of Column B(1/30)4th term of Column A (1/28) is greater than 4th term of Column B(1/30)5th term of Column A (1/29) is greater than 5th term of Column B(1/30)Exclude 6th terms as they are equal.
Hence if we add all five terms we can conclude thatColumn A is greater than Column B
2. Given a1 = -9, a2 = -4, such that an = a(n-1) - a(n-2). Calculate sum of first 100 terms?Note: (Here 1, 2, (n – 1) and (n – 2) are suffixes)Solution:
Sum of first 100 terms will bea1 + a2 + a3 + a4 + ... + a99 + a100=> a1 + a2 + (a2-a1) + (a3 – a2) + (a4 – a3) + .... + (a98 – a97) + (a99 – a98)=> a2 + a99We need to find out a99a3 = a2 – a1a4 = a3 – a2 = a2 – a1 – a2 = -a1a5 = a4 – a3 = -a1 – a2 + a1 = -a2a6 = a5 – a4 = -a2 - (-a1) = -a2 + a1a7 = a6 – a5 = -a2 + a1 - (-a2) = a1a8 = a7 – a6 = a1 - (-a2 + a1) = a2Hence the pattern repeats like this a1 , a2 , a2 – a1, -a1, -a2, -a2 + a1.....That is from 7th term onwards the same pattern repeats......So, a7 will be the same as a1a8 will be the same as a2a9 will be the same as a3a10 will be the same as a4a11 will be the same as a5That is a1, a7, a13, a20, will be the same1+ (n-1)6 = 6n – 5a99 doesn't comes under this categorya2, a8, a14,...will be the same2 + (n-1)6 = 6n-4same with here...a3, a9, a15,...so will be the same category3+ (n-1)6 = 6n – 3Yes a99 comes under this categoryBecause substitute n = 17 in 6n – 3 we will get 99Hence a99 = a3 = a2 – a1Hence the sum of all 100 terms will be = a2 + a99 = a2 + a2 – a1 = 2a2 – a1 = 2(-4) - (-9)-8 + 9 = 1Hence 1 is the final answer.
3. If (1/(x + y)) – 1 + (1/(x - y)) -1= 4, then which one of the following must be true?I. x = 2II. y = 0III. y = -1
& so on…..
Guess some thing is missing?
4. If x = k^2 and y = k^3, thenCol A: x^9Col B: y^6
5. There is a micro chip. Each side is extended by 0.1 millimeters. If surface area of one face increases to 0.75 mm, find the original length of the edges?Solution:
Let the length and breadth of the micro chip be l (assume it to be a square).This surface area is l^2Now new length will be l + 0.1 and breadth l + 0.1Now the new area will be (l + 0.1)*(l + 0.1) = 0.75(l + 0.1)^2 = 0.75=> l + 0.1 = sqrt(0.75) = 0.866 (app)=> l = 0.766 (app)With out this we cannot solve this question.
6. Given k1 = 1. The series is such that ki = 5k(n-1) + 4. Find the least possible value of ‘i' for which ki is divisible by 7?Note: 1, i and (n-1) are subscripts.Solution:Given P1 = 1 andP(n+1) = 5Pn + 4The smallest number divisible by 7 is 7 itself.P2 = 5P1 + 4P3 = 5(5P1 + 4) + 4 = 25P1 + 4(5+1) = 52 P1 + 4(51 + 50)P4 = 5(25P1 + 4(5+1)) = 53 P1 + 4(52 + 51) = 54-1 P1 + 4(54-2 + 54-3)So, in generalPn = 5n-1 P1 + 4(5n-2 + 5n-3)So, P7 = 57-1 P1 + 4(57-2 + 57-3) = 56 P1 + 4(55 + 54) = 15625 + 4(3125 + 625) = 15625 +4(3750)=> 15625 + 15000 = 30625
7. If -6 <= x <= 4 and -10 <= y <= 4, then what is the greatest value of (–x^2 + y^4)?A. 16B. 240C. 10,000D. 10,036& so on……………Solution:
For y^4 – x^2 to be maximum
=> y^4 to be maximum and x^2 must be minimum.The minimum value of square of a variable is 0 and that is for the value of 0Since 0 lies in the given interval for x i.e., -6<= x <= 4Hence minimum value of x^2 = 0
And Maximum value of y in the given interval -10 < = y <= 4 will be at x = -10 (since the power to which y is raised is an even number and -ve number to the power of an even number will be a positive number)
=> Max(y^4) = 10^4
So, Max(y^4 – x^2 ) = Max(y^4) – Min(x^2) => 10000 – 0 = 10000Hence C is the correct answer
8. Given x/y = 3/5.Col A: x – 3Col B: y – 5Solution:Given that 3/5 = x/y=> 5x = 3y=> x = 3y/5Column A = x – 3 = 3y/5 – 3=> 3(y – 5)/5 = (3/5)(y – 5)=> Column A = (3/5)* Column B Hence Column B is greater than Column A
9. Given the dimensions of a triangle as 5, 6 and 8. If the angles opposite to sides 5 and 6 are ‘x’ and ‘y’, thenCol A: The third angleCol B: 90Solution:Observe the above figureAccording to the pythagoras theorem,ABC will be a right angled triangle with angle ACB = 90Since 5^2 + 6^2 = 61
Triangle that we are discussing in the question is ADC.Since sqrt(64) is greater than sqrt(61)The third angle DCA will be greater than 90 (Try observe the graph carefully you will understand the logic behind that)
10. What is the nearest value of sqrt(171)?A. 12B. 13C. 14& so on………Solution:First find out the squares of 13 and 14=> 13^2 = 169and 14^2 = 196
Now find out whether 171 is closer to 169 or 196 (and the corresponding values square root will be nearest value of sqrt(171))
Difference between 171 and 169 is 2 where as diff. Between 196 and 171 is 25Since the diff. Between 171 and 169 is smaller there nearest value will be the sqrt(169) =13Hence 13 is the nearest value of sqrt(171)
11. Given R1: {-3, -2, -1}, R2: {-1, -2, -3}and R3: {-3, -2, -1, 1, 2, 3}. If s1, s2, s3 are defined as the Standard Deviations of R1, R2 and R3 respectively, then which one of the following is true?I. s1 < s2II. s1 = 0III. s3 = 0A. NoneB. Only IC. I and IID. II and IIIE. I and III
Solution:
S1 = Standard deviation of R1First find out the mean for all the three sets.Mean of R1 = -6/3 = -2Mean of R2 = -6/3 = -2Mean of R1 = 0/3 = 0S1 = Sqrt {[(-3 - (-2))^2 + (-2 - (-2))^2 + (-1 - (-2))^2]/3} = Sqrt [(-1)^2 + 0^2 + 1^2] = sqrt (2/3)S2 = Sqrt {[(-1 - (-2))^2 + (-2 - (-2))^2 + (-3 - (-2))^2]/3} = Sqrt [1^2 + 0^2 + (-1)^2] = sqrt (2/3)S3 = Sqrt {[(-3)^2 + (-2)^2 + (-1)^2 + 1^2 + 2^2 + 3^2 ]/6} = sqrt(28/6)I S1 < S2 is wrong since S1 = S2II S1 = 0 is wrong since S1 = sqrt(2/3)III S3 = 0 is also wrongHence none of the above is the correct answer
GRE QUANT DATABASE(UPDATED TILL July 21st) updated by Mohan
1. Given ‘x’ as a two digit number, thenCol A: Unit place of x
Col B: Unit place of x2 Solution:
The last digit of x can vary from 0 to 9
Units place of x2 = Last digit [last digit of x *last digit of x]Case 1)
If the last digit is 0 then the last digit of x2 will = Last digit[0*0] = 0Column A: 0 and Column B: 0Hence they are equalCase 2)
If the last digit is 1 then the last digit of x2 will = Last digit[1*1] = 1Column A: 1 and Column B: 1Hence they are equalCase 3)
If the last digit is 2 then the last digit of x2 will = Last digit[2*2] = 4Column A: 2 and Column B: 4Column A is lesser than column BCase 4)
If the last digit is 8 then the last digit of x2 will = Last digit[8*8] = Last digit[64] = 4Column A: 8 and Column B: 4Column A is greater than Column B
From Case 1, Case 2, Case 3, Case 4 we can conclude that the relation cannot be determined with the given information
2. If an article costs ‘S’ dollars and the tax on it is 8% of ‘S’ dollars, then what is the total cost of the article? Solution:
Article cost = S dollarsTax on the article = 8% Total cost of the artice= 1.08S
3. Given a cylinder of radius 10 inches as above and ‘w’ is the width of the label on the cylinder. If the area of the label is equal to base area of the cylinder, then what is the value of ‘w’?
Solution:
Base area of the cylinder = πr2 = π(100) = 100πNow 100π = 2πrw=> 100π = 10πw=> w = 10
4. In an Isosceles triangle, the average of the two angles is given as 65. Find the possible value of the third side? Solution:
Let the angles of an isosceles triangle be x, x, yGiven that the average of two angles = 65These two angles may be x,y or x,xCase 1) Let the two angles be x, y. Then the other angle will be x=> x+y = 65*2 = 130Other angle will be 2x+y=180=> x+130=180=> x=50 Case 2) Let the two angle be x and x. Then the other angle will be y=> 2x=130=> x=65Then the other angle y = 180-2x = 180-130 = 50From both cases the other possible angle is 50
5. For the equation x2– x – 2 <=0; how many solutions are possible?
Solution:
Consider the expression x2– x – 2=> x2– 2x +x– 2=>x(x-2)+1(x-2)=> (x-2)(x+1)Now given inequality is that (x-2)(x+1)<=0Possible solutions are -1<=x<=2Since x is not an integer it can take infinitely many values in between -1 and 3.So, the answer is infinity
But if they mention in the that x takes only the integer values then the answer will be all integers which lie between -1 and 3 including -1 and 3That means -1, 0, 1, 2, 3 total of 5
6. If m and n are positive, then
Col A:
Col B: Solution:
Column A: 25(m-n)
and Column B: (m/n)2
Consider case 1)For m=1 and n=0.5Column A: 250.5=5and Column B: 4In this case column A is greater than Column B
Now consider case 2)For m=0.5 and n=1Column A: 25-0.5=0.2Column B: 0.52 = 0.25In this case Column B is greater than Column A
So, with the given information it is not possibe to compare Column A and Column B
7. A person deposits an amount of $2000 for a certain time ‘t’. If he gets an interest of $200, then what is the rate of interest? Solution:
Let the rate of interest be iThe interest amount that person will get = 2000*i/100 = 200Then the rate of interest i = 10%
8. If the probability of number of workers in an industry is < (1/4), then
Col A: Probability of non-workers being in the industryCol B: ¾Solution:
The probability of number of workers in an industry + the probability of number of workers in an industry = 1=> The probability of number of workers in an industry = 1 - the probability of number of workers in an industry
But Prob. Of no. Of workers in an industry <(1/4)=> 1 - The probability of number of workers in an industry < (¼)=> The probability of number of workers in an industry -1 > -(¼)=> The probability of number of workers in an industry> ¾Hence Column A(>3/4) is greater than Column B (=3/4)Hence Option A is the correct answer
9.
What is the value of x? Solution:
75 + 2x + 1 = 180=> 2x = 104=> x = 52
10. If (x2+y2)/2 = xy, thenCol A: xCol B: y Solution:
(x2+y2)/2 = xy=> (x2+y2) = 2xy=> (x-y)2 = 0=> x=yHence option C is the correct answer
11Q) Given a series 3, 1, 4, 2, 3, 1, 4, 2………………………… What is the product of the 67th and 68th
term? Solution:
Given series 3 1 4 2 3 1 4 2 3 1 4 2 .......So, After every four terms the same pattern repeats.That is, t1 = t5 = t9 = ..... = 3t2= t6= t10= t14=....1t3= t7= t11= t15=....4t4 = 2, t8 = 2, t12 = 2 .....So, t67 comes in the pattern of t3 that is 4and t68 comes in the pattern of t4 that is 2Hence the product is 4*2 = 8
Simple method is to find out the remainder of the given term with 4 (Reason for finding out the remainder with 4 is that here the terms show same pattern for 4 terms. If the terms show same pattern 5 terms then find out the remainder with 5 and the rest will be same as follows)Now assign for remainder 0 the value is 2 (fourth term)For remainder 1 the value is 3 (1st term)For remainder 2 the value is 1 (2nd term)For remainder 3 the value is 4 (3rd term)Now the remainder when 67 is divided by 4 is 3 hence the value of t67 = 4 andRemainder when 68 is divided by 4 is 0 hence the value of t68 = 2Hence the answer follows
GRE QUANT DATABASE(UPDATED TILL July 3rd) updated by Mohan
1) There is a square with side 10m. On top of the square there is one semicircle with its diameter on one side of the square (diameter length = side length). One point on the semicircle is chosen and a perpendicular is drawn on to the square which divides the side of the square in 8:2. Find the length of the perpendicular? How to solve this one?Solution:
This is how you have to approach this question
If you look at the figure ABCD is the square with side = 10m and APB is the semi circle sitting on the
top of the square.We need to find out the PT valueAS = 8, SB = 2, OS = 3 (Since the point P on the semi circle divides the length of the square in the ratio 8:2. Hence the length AS =8 and SB =2)From the right angled triangle OPS,OP2 = OS2 + PS2 => 52 = 32 + PS2 => PS2 = 42
Therefore PS = 4Now, PT = PS + STWhere ST = length of the rectangle = 10Therefore, PT = 4 + 10 = 14cm
2) Given N= v * w * x * y * z - (v+w+x+y+z). If ‘N’ is an even integer, then how many of v, w, x, y, z will need to be even numbers? Solution:
Let all the numbers be oddThen A = v * w * x * y * z = Which is a product of all odd numbersHence the number A will be an odd numberNow consider B = (v+w+x+y+z) = Which is a sum of all odd numbers for odd timesHence the number B will be an odd number
Since:Sum of even total of odd numbers is even number (for example take 1 3 5 7 9 which are all odd numbers and total number is also odd that is 5 numbers. Then the sum is 25 which is an odd number) andSum of odd total of odd numbers is odd number (for example take 1 3 5 7 which are all odd numbers and total number is even that is 4 numbers. Then the sum is 16 which is an even number)
Therefore, difference of two odd numbers is an even numberHence the number of even number is 0 for the given number N to be an even number.
3) If |x| <=6; |y| <=4, then find the greatest possible value of |x/y|? Solution:
As |y| approaches 0 then |x/y| approach infinityHence the answer is infinity.
4) The probability of raining tomorrow is 0.49. Col A: The probability that it will rain tomorrow and George eats the foodCol B: 0.54 Solution:
There is no need for additional information.
Given that it will rain tomorrow = 0.49Let the prob. of George eats the food = p (<=1)Now the probability that it will rain tomorrow and George eats the food = 0.49*p (we need to multiply since "and" is used)So, the required probability = 0.49*p <= 0.49*1 <= 0.49So, Column A is always less than or equal to 0.49 and Column B is 0.54Hence Column B is greater than Column A
5) Given equation of the circle as x2+y2 = 49. If two points (0, b) and (4, a) lie on the circle, then what is the slope of the line? Solution:
There are 4 possible answers as followsLet A= (0,b) , then A= (0,7), (0,-7)B=(4,a) ,then B= (4,sqrt(33)), (4,-sqrt(33))They need to specify the quadrant in which the points lie. But if you come across these kind of problems try finding out the slopes for each and possible combination and then check with the options given.
6)
Col A: (1/2)(Remaining angles)Col B: 55° Solution:
Given angle 70 and x (=70)Now Column A = Half the sum of the remaining angles = (1/2)(360 – (70+70)) = (1/2)*(360-140) = 220/2 = 110Which is greater than Column B (=55)Hence option A is the correct answer
7) If twice the average of x, y and z, when divided by 7 gives remainder 1, then what is the remainder, when average x, y and z is divided by 7?Solution:
It will be easy to solve this by assuming a simple caseGiven that the twice the average of x, y and z when divided by 7 leaves a remainder 1=> 2(x+y+z)/3 = 7q+1Let q =1=> 2(x+y+z)/3 = 8=> x+y+z = 12
let the three numbers be 3, 4 and 5Now, (x+y+z)/3 = 4So, the remainder when (x+y+z)/3 divided by 7 is 4
Actual Procedure with out substitution method:
2(x+y+z)/3 = 7q+1 ------> (1)
Now 7q+1 will be an even number since on the LHS (x+y+z)/3 is multiplied by 2
And in the question it is asked to find out the remainder when (x+y+z)/3 is divided by 7 which means that (x+y+z)/3 is an integer.
Now if we consider 7q+1It will even if and only if 7q is an odd numberNow,7X1 = 77X2 = 147X3 = 217X4 = 28Then from the above pattern we can conclude that q must be odd numberAny odd number can written in the form of 2k+1Therefore, q = 2k+1 ------------------> (2) where (k=0, 1, 2, 3.....)Sub (2) in (1)=> 2(x+y+z)/3 = 7(2k+1)+1=> 2(x+y+z)/3 = 14k+8=> (x+y+z)/3 = 7k+4Hence when (x+y+z)/3 is divided by 7 it will a remainder 4
8)
Given the area of the circle as 16π, asked to find the perimeter of shaded region OAB? Solution:
Given area = 16π=> πr2 = 16π=> r = 4Now req circumference = r + r + length of the arclength of the arc = (90/360)2π(4) = 2πHence the perimeter of shaded region is 8+2π
9) Given arithmetic mean of p, q, r as 10. If arithmetic mean of p, q, r, x is 15, thenCol A: x/2Col B: 15 Solution:
Both the columns will be equal
GRE QUANT DATABASE(UPDATED TILL May 21st) updated by Mohan
1.If a, b and c are 0, 1 or 2 and if a.32+ b.3 + c = 25, then what is the possible value of a + b + c? Solution:
Clearly, a and b cannot be less than 2 (since either of a or b equals 0 or 2 then we cannot get a sum of 25)Possible combinations are a = 2, b = 2 and choose c accordingly=> 2(9)+3(2)+c = 25=> 24+c = 25=> c =1Therefore, a + b + c = 2 + 2 + 1 = 5
2.In a survey of voting in a election, if 55% of the voters who casted their votes supported person ‘x’ , 61% supported ‘y’ and 80% supported both of them, then what percentage of people supported neither ‘x’ nor ‘y’? Solution:
Some mistake in the questionNumber of people who support both of them cannot be greater than the number of people who support them individually
3. When point ‘A’ is displaced by ‘x’, point ‘B’ is displaced by ‘y’.Col A: xCol B: y
Solution:
Cannot be determined
4. If n > 0, then
Col A: x n+1
Col B: (x+1)n Solution:
This is how you have to come to conclusion for this questionLet us consider x+1 < 0 => x < 0
We know that (-ve number )even number = +ve number
and (-ve number)odd number = -ve numberCase 1) n is an even numberThen n+1 is an odd number
Now Column A: (-ve number)even number = +ve number
Column B: (-ve number)odd number = -ve numberTherefore for this case Column A is greater than Column B
Case 2) n is an odd numberThen n+1 is an even number
Now Column A: (-ve number)odd number = -ve number
Column B: (-ve number)even number = +ve numberTherefore for this case Column A is lesser than Column BHence from case 1) and case 2) we can conclude that the given columns cannot be compared
5. If a rectangle of length 4 and breadth 3 is divided into two smaller rectangles, thenCol A: Sum of perimeters of both the rectanglesCol B: 21Solution:
Given that a rectangle is divided into two smaller rectangles. But it is not mentioned whether it is cut length wise or breadth wiseCase 1) let the reactangle is cut length wise to make two equal partsThen the sum of perimeters = 4+4+4+4+1.5+1.5+1.5+1.5 = 22Therefore Column A:22 which is greater than Column B: 21Case 2) Rectangle is cut breadth wise to make two equal parts
Then the sum of perimeters = 4*3+4*2 = 12+8=20Column A: 20 which is lesser than Column B:21From Case 1 and Case 2 we can conclude that it cannot be determined with the given information.
6. There are five lists of 25 members. If average of 25 members in each list is a1, a2, a3, a4 and a5 and median is m1, m2, m3, m4 and m5, thenCol A: Median of a1, a2, a3, a4, a5Col B: Average of m1, m2, m3, m4, m5. Solution:
All a1, a2, a3, a4, a5, m1, m2, m3, m4 and m5 can take any values.So, the value of Column A can be greater or lesser or equal to Column B.Therefore, Cannot be determined with the given information
7.
If perimeter of the circle is 16π, then what is perimeter of the shaded region? Solution:
When ever any two sectors divided by same symbol it means that they are equal.So, you can assume that all the sectors are equal
Circle is divided into 8 equal partsGiven perimeter of the circle = 16π=> 2πr = 16π=> r = 8Now the length of the shaded arc = (3/8)*(16π) = 6πTherefore required perimeter = 6π + 2r = 16 + 6π
8. If a number, when divided by 5 gives remainder 3 and when divided by 4 gives remainder 2, then what is the remainder when the same number is divided by 10? Solution:
This is how you have to come to conclusion for this questionLet the number be 5q+3 = 4p+2=> 5q+3 = 2(2p+1) ----->(1)Since RHS is an even number which implies that LHS must also be even number=> 5q+3 is an even number(Sum of 2 odd numbers is an even number and sum of 1 odd and 1 even is an odd number)Since 3 is an odd number 5q must also be an odd numberNow 5q can be odd if and only if q is odd
Any odd number can be written in the form of 2k+1q = 2k+1 ------>(2)Now sub (2) in (1)=> 5(2k+1) + 3 = 10k+ 5 + 3=> 10k +8Hence the remainder when given number is divided by 10 is 8
GRE QUANT DATABASE(UPDATED TILL May 5th) updated by Mohan
1.If x < y < 0, thenCol A: xyCol B: y – x
Solution:
If x<0 and y<0
Then xy>0
If x<y
Then -x>-y
=>y-x>0
Since both the columns are greater than 0 the relation cannot be determined with the given information.
2.Given that, there are two racks A and B. If 4 books from rack A are replaced to rack B, then the number of books become equal. If 7 books from rack B are replaced to A, then number of books in A is 3 times the books in B. What is the total number of books?Solution:
Let the no. Of books in rack A = a
and the no. Of books in rack B = b
After replacing 4 books from rack a
New no.of books in rack A = a-5
and in rack B = b+5
Now given that a-5 = b+5
=> a = b+10 --->(1)
From second condition,
7 books are replaced from rack B to A
Then,
New no.of books in rack A = a+7
and in rack B = b-7
Now given that, a+7 = 3(b-7)
=> a = 3b-28 -->(2)
Sub (1) in (2)=> b+10 = 3b-28
=> 2b = 38
=> b = 19
=> a = b+10
=> a = 29Therefore the total no.of books = a+b = 29+19 = 48
3.If a person moves towards west in straight line for 6m and then to north for another 16m and then to west again for another 10m, find the distance between starting and ending point?Sol:
Solution:
From the figure, Triangle RPA and Triangle RQB are similar triangles
=> x/(16-x) = 6/10
=> 10x = 96 -6x
=> 16x = 96
=> x = 6
Now Distance between A and B is sum of distances AR and BR
=> 6√2 + 10√2
=> 16√2
4. Given a coordinate system, a point P is at -5 on the x-axis, a point R is at 10 on the x-axis and another point Q is situated in between P and R, such that the ratio of distance between P and Q to the distance between R and Q is 2 is to 3.Col A: The x-coordinate of point QCol B: 0Solution:
From the given information,
P = (-5,0)
R = (10,0)
Let the distance between P and R be 5x, then PQ = 2x and QR =3x
Find out the distance between P and R = √((10+5)2+(0-0)2) = 15
Now 5x = 15
=> x = 3
Now PQ = 2x = 2*3 = 6
Since P and lie on x-axis then any point lying on the line joining P and R will also lie on x-axis
Hence the Point of Q will be of the form (a,0)
Now we know PQ = 6 = √((a-(-5))2+(0-0)2) = a+5
Hence a = 1
Column A: X-coordinate of Q = 1
Column B: 0
Therefore, Option A is the correct answer
5.If N is an integer between 200 and 300 with units digit 5 and tens digit x, thenCol A: N/5Col B: 40+2x
Solution:
N= 200 + 10x + 5 (where x can take any value from 0, 1, 2, ...,9)
Column A: N/5 = (200 + 10x + 5)/5 = 40 + 2x + 1 = 41 + 2x
Column B: 40 + 2x
Hence Column A is greater than Column B
Option A is the correct answer
6.Given a series of odd numbers from 1 to n. Find the probability, that a number selected at random will be an odd number?(provided ‘n’ is an odd number)
Solution:Number of odd numbers = (n+1)/2And number of even numbers = n-(n+1)/2 = (2n-n-1)/2 = (n-1)/2Now the probability of that a number selected at random will be an odd number = (n+1)/2/n=> (n+1)/2n
GRE QUANT DATABASE(UPDATED TILL April 21st) updated by Mohan
1) If the sum of a two digit number 'n' is n/4, thenCol A: nCol B: 36Solution:
It is given, n is a two digit number
So, Let's take n as xy
It says, if we add x + y we get, xy/2
Which means, x + y = xy/2
What is the value of n ( where n = xy)
Here , we need to do trial and error method, that is substituting different values for n
Case 1 : Let n = 36
3 + 6 = 36/4
9 = 9In case 1, we can say, both the quantities are equal.
Case 2 : Let n =24
2 + 4 = 24/4
6 = 6
In case 2, the value for n = 24 is less than 36, so column B is greater.
From both the cases, we can conclude that, “Relationship cannot be determined”.
2) If A = {5, 12, 34, 35, 56, 34, 34, 48, 3} and B = {3, 45, 3, 4, 53, 56, 93, 23, 45, 5}Col A: The standard deviation of A
Col B: The standard deviation of BSolution:
If we have equal denominator in both the columns, then we do not want to find the square root. In that case, we need to check only the numerator, If the numerator value is greater in one column, then it means, the standard deviation of that column will be greater.
This can't be done here, because, the denominator value is different, it is 9 in column A and 10 in Column B.Mean of sequence A = 29Standard deviation of A= {Sqrt [(5-29)2 + (12-29)2 + (34-29)2 + (35-29)2 + (56-29)2 + (34-29)2 + (34-29)2 + (48-29)2 + (3-29)2] /9] }= {Sqrt [(-24)2+(-17) 2 + (5) 2 + (6) 2 + (27)2+ (5)2+ (5)2+ (19) 2 + (-26) 2 ] /9 }= Sqrt [ 2742 / 9 ]= Sqrt [ 304.67]= 17.45
Mean of sequence B = 33Standard deviation of B= [ 3−33 2 45−33 2 3−33 2 4−33 2 53−33 2 56−33 2 93−33 2 23−33 2 45−33 2
3−33 2 ] /10= [ −30 2 − 122 −30 2 -29 2 20 2 23 2 60 2 -10 2 12 2 -30 2 ] /10= Sqrt [ 8458 / 10 ]= Sqrt [ 845.8 ]= 29.08
Therefore, column B is greater.
But if you feel that it will take lot of time to solve all this, then try to guess by looking at the numbers givenMean of set A is 29 and Mean of set B is 33So, find out maximum (a-mean)2 terms in both the sets (where 'a' can be any individual term which gives maximum of (a-mean)2 value)First observe Set A (a-mean)2 = (56-29)2 = 729For Set B (a-mean)2 = (93-33)2 = 602 = 3600
If we observe these two values for set B the value very much higher than that of set A. Hence in this case we can conclude that set B will have higher standard deviation.
But if the two values are close then we cannot predict by looking at these values.
NOTE: It's just a mere approximation but every time it may not give us the correct value. So, try this if you feel that the calculations cannot be done.
3) Given that, if a number x leaves remainder 7 when divided by 11 and leaves remainder 1 when divided by 5, then
Col A: Least possible value of xCol B: 40Solution:
The General equation for these type of question is Dividend = ( Divisor * Quotient) + Reminder
For this question, we will have two equations,
→ “ if a number x leaves remainder 7 when divided by 11”
x = 11 Q1 + 7 -------(1)
→ “ number x leaves remainder 1 when divided by 5”
x = 5 Q2 + 1 -------(2)
It means, 11 Q1 + 7 = 5 Q2 + 1 --------(3)
By trial and error method, find the values for Q1 and Q2, which should make the equation (3) equal.
So, we will get Q1 = 4 and Q2 = 10
Therefore, the value of x = 51. ( By substituting the value of Q1 and Q2 in equation (1) and (2) respectively )Hence, column A is greater.
4) If a line of slope -1/3 passes through the points (1, p) and (4, 5), then what is the value of p?Solution: 6 is the correct answer
5) If a1 = 2 and an+1=(an - 1)2, then find the value of a17?
Solution:
It is given a1 = 2
a 2+1 = ( a 2-1)2
a 3 = (a1)2 = (2)2 = 4 → This can be written as (2)2
a5 = (a3)2 = (4)2 = 8 → this can be written as (2)4
a 7 = (a5)2 = (8)2 = 16 → This can be written as (2)8
Like wise, we need to do...........
Then we will get, a 17 = (2)256 = 2^(2^8)
6) Two cyclists are moving towards each other at 10 miles/hour. When they are 50 miles apart, a fly starts from one cyclist and move towards other, moving to and fro till the two cyclists meet each other. If the fly is moving at the rate of 15 miles/hour, then find the total distance covered by the fly?Answer is 37.5 miles
GRE QUANT DATABASE(UPDATED TILL April 21st) updated by Saranya
1. If the sum of a two digit number 'n' is n/4, thenCol A: nCol B: 36Solution:
It is given, n is a two digit numberSo, Let's take n as xyIt says, if we add x + y we get, xy/2Which means, x + y = xy/2What is the value of n ( where n = xy)Here , we need to do trial and error method, that is substituting different values for nCase 1 : Let n = 363 + 6 = 36/49 = 9In case 1, we can say, both the quantities are equal.Case 2 : Let n =242 + 4 = 24/46 = 6In case 2, the value for n = 24 is less than 36, so column B is greater.From both the cases, we can conclude that, “Relationship cannot be determined”.
2. If A = {5, 12, 34, 35, 56, 34, 34, 48, 3} and B = {3, 45, 3, 4, 53, 56, 93, 23, 45, 5}Col A: The standard deviation of ACol B: The standard deviation of BSolution:
Mean of sequence A = 29Standard deviation of A= {Sqrt [(5-29)2 + (12-29)2 + (34-29)2 + (35-29)2 + (56-29)2 + (34-29)2 + (34-29)2 + (48-29)2 + (3-29)2] /9] }= {Sqrt [(-24)2+(-17) 2 + (5) 2 + (6) 2 + (27)2+ (5)2+ (5)2+ (19) 2 + (-26) 2 ] /9 }= Sqrt [ 2742 / 9 ]= Sqrt [ 304.67]= 17.45Mean of sequence B = 33Standard deviation of B= [3−33245−3323−3324−33253−33256−332 93−332 23−332 45−33 23−33 2 ] /10= [−302 −122 −302 -292 202 232 602 -102 122 -302 ] /10= Sqrt [ 8458 / 10 ]= Sqrt [ 845.8 ]= 29.08
Therefore, column B is greater.NOTE: If we have equal denominator in both the columns, then we do not want to find the square root. In that case, we need to check only the numerator, If the numerator value is greater in onecolumn, then it means, the standard deviation of that column will be greater.This can't be done here, because, the denominator value is different, it is 9 in column A and 10 inColumn B.
3. Given that, if a number x leaves remainder 7 when divided by 11 and leaves remainder 1when divided by 5, thenCol A: Least possible value of xCol B: 40Solution:
The General equation for these type of question isDividend = ( Divisor * Quotient) + ReminderFor this question, we will have two equations,→ “ if a number x leaves remainder 7 when divided by 11”x = 11 Q1 + 7 -------(1)→ “ number x leaves remainder 1 when divided by 5”x = 5 Q2 + 1 -------(2)It means, 11 Q1 + 7 = 5 Q2 + 1 --------(3)By trial and error method, find the values for Q1 and Q2, which should make the equation (3)equal.So, we will get Q1 = 4 and Q2 = 10Therefore, the value of x = 51. ( By substituting the value of Q1 and Q2 in equation (1) and (2)respectively )Hence, column A is greater.
4. If a line of slope -1/3 passes through the points (1, p) and (4, 5), then what is the value of p?Solution:
The two point formula for slope = (Y2 – Y1 ) / (X2 – X1)Where, (X1 , Y 1) = ( 1, p)(X2 , Y 2) = ( 4 , 5)( 5 – p ) / ( 4 – 1 ) = -1/35 – p = -1p = 6
5. If a1 = 2 and an+1=(an - 1)2, then find the value of a17?Solution:
It is given a1 = 2a 2 + 1 = ( a 2 – 1)2a 3 = (a1)2 = (2)2 = 4 → This can be written as (2)2a5 = (a3)2 = (4)2 = 8 → this can be written as (2)4a 7 = (a5)2 = (8)2 = 16 → This can be written as (2)8
Like wise, we need to do...........Then we will get, a 17 = (2)256The powers are like, 2 , 4 , 8 , 16 , 32 , 64, 128, 256...........Current values power = Previous values power * 2
6. Two cyclists are moving towards each other at 10 miles/hour. When they are 50 milesapart, a fly starts from one cyclist and move towards other, moving to and fro till the twocyclists meet each other. If the fly is moving at the rate of 15 miles/hour, then find the totaldistance covered by the fly?Solution:
Speed of the cyclist = 10 miles / hourSo, for 2 cyclist = 2 * 10 miles/hr = 20miles /hrThey are 50 miles apart, which means Distance = 50 milesTime taken by the cyclists to meet each other = Distance/Speed = 50/20 = 2.5 hoursThe question says, the fly will move to and fro till the cyclists meet each other.So, the fly will move to and fro for 2.5 hours, because, the cyclist meet only after 2.5 hours.Time taken = 2.5 hoursspeed of the fly was given as 15 miles/hourTherefore, we can find the distance covered.Distance = Speed * Time = 15 * 2.5 = 37.5 miles.
GRE QUANT DATABASE(UPDATED TILL April 17th) updated by Mohan1) The product of prime factors of 300.A. 15B. 30C. 45& so on....Solution:
We need to find out the prime factors for 300300 = 3 * 100 = 3 * 10 * 10 = 3 * 5 * 2 * 5 *2 Therefore, the product of the prime factors = 3 * 5 * 2 = 30 ( option B)
So, the answer is not the number itself
2) If 'P' is the probability of an event occurring, P* is the probability of not occurring an event and if P>0.5, thenCol A: PP*Col B: PSolution:
Given p > 0.5We know that p + p* = 1If p > 0.5
Then p* < 0.5Column A = PP* < 0.5Column B p > 0.5Hence, Column B is greater (Correct answer)
3) If (2,1) is the center of the circle and (9,1) is the point on the circumference, then what is the radius of the circle?Solution:
Distance between (2,1) and (9,1) which is 7
4) In a bottle of 3 red, 4 green and 5 blue marbles, if 2 marbles are taken out, what is the probability that two marbles are of red color?Solution:
=> 3C2/12C2
5) Given A = {6, 6, 9,10,14,15}B = {7, 9,10,11,14, 15}Col A: Standard deviation of ACol B: Standard deviation in BSolution:First find out the mean of these two setsMean for Set A = (6+6+9+10+14+15)/6 = 10Mean for Set B = (7+9+10+11+14+15)/6 = 11Here the denominators will be same, so no need to find the square root, check with the numerator, the column in which the numerator is greater, then that columns Standard deviation will be greater.
Now Numerator of Standard deviation A = (10-6)2+(10-6)2+(10-9)2+(10-10)2+(10-14)2+(10-15)2
=> (4)2+(4)2+(1)2+(0)2+(4)2+(5)2= 74and Numerator of Standard deviation B = (11-7)2+(11-9)2+(11-10)2+(11-11)2+(11-14)2+(11-15)2
=> (4)2+(3)2+(1)2+(0)2+(3)2+(4)2= 42Hence Column A is greater than Column B
6. Given a series of numbers x, y, z, 0, 1, 1, 2, 3, 5, 8??.If every number in the series is sum of the proceeding two numbers, then what is value of x?
Answer is 2
7) Given that there are two boats X and Y which start at the same point. If boat X travels due north at a rate 3miles/hr and boat Y travels due east at a rate of 4miles/hr, then at what time will the two boats be 10 miles apart?Answer is 2 h
GRE QUANT DATABASE(UPDATED TILL April 17th) updated by Saranya
1. The product of prime factors of 300.A. 15B. 30C. 45& so on....Solution:
300 = 3 * 100 = 3 * 10 * 10 = 3 * 5 * 2 * 5 *2Therefore, the product of the prime factors = 3 * 5 * 2 = 30 ( option B)
2. If 'P' is the probability of an event occurring, P* is the probability of not occurring anevent and if P>0.5, thenCol A: PP*Col B: PSolution:
It is given ,P is greater than 0.5, so it can take values from 0.6 to 1Case 1 : If P = 0.6, P* = 1 -0.6 = 0.4,Col A = (0.6)(0.4) = 0.24 ; Col B = 0.6So, for case 1 , col B is greater.Case 2 : If P = 0.8, P* = 1 -0.8 = 0.2,Col A = (0.8)(0.2) = 0.16 ; Col B = 0.8So, for case 2 , col B is greater.Case 3 : If P = 1, P* = 1 -1 = 0,Col A = (1)(0) = 0 ; Col B = 1So, for case 3 , col B is greater.From all the cases, we can conclude that, Column B is greater.
3. If (2,1) is the center of the circle and (9,1) is the point on the circumference, then what isthe radius of the circle?Solution:
The diagram is shown above.If we check the diagram, we can see, it a straight line.Therefore, we can find the radius of that circle by using, the distance formulaDistance = Sqrt [ (y2 – y1)2 + (x2 – x1)2 ]= Sqrt [ (1 -1 ) 2 + ( 9 – 2)2 ]= Sqrt [49]= 7Therefore radius = 7
4. In a bottle of 3 red, 4 green and 5 blue marbles, if 2 marbles are taken out, what is theprobability that two marbles are of red color?Solution:
Probability = favorable outcomes / possible outcomesprobability that two marbles are of red color = 3 C 2 / 12 C2 = 1 / 22
5. Given A = {6, 6, 9,10,14,15}B = {7, 9,10,11,14, 15}Col A: Standard deviation of ACol B: Standard deviation in BSolution:
It is same as the second question from the beginning, here the denominators will be same, so noneed to find the square root, check with the numerator, the column in which the numerator isgreater, then that columns Standard deviation will be greater.For this question, Column A is greater
6. Given a series of numbers x, y, z, 0, 1, 1, 2, 3, 5, 8??.If every number in the series is sum of theproceeding two numbers, then what is value of x?Solution:
Acc to the conditionz + 0 = 1, means z = 1y + 1 = 0, so y = -1x – 1 = 1 , so x = 2
Hence, x = 2
7. Given that there are two boats X and Y which start at the same point. If boat X travelsdue north at a rate 3miles/hr and boat Y travels due east at a rate of 4miles/hr, then atwhat time will the two boats be 10 miles apart? Solution:
The question says,Boat X travels 3 miles/hr and Boat Y travels 4 miles/hr.Since it forms a right angle triangle.The speed to cover 10 miles = Sqrt [ (3)2 + (4)2 ] = Sqrt [25] = 5 miles/hrTherefore, time taken to cover 10 miles = Distance / Time = 10/ 5 = 2 hours
GRE QUANT DATABASE(UPDATED TILL April 8th) updated by Saranya
1. Given that, if the area of the triangle STR is 1/9th area of the equilateral triangle PQR,then what is the ratio of QT/TR?A. 1:3 B. 3:1 C. 2:1 & so on…..
Solution:
Only with this information, we will not be able to find the ratio between QT/TR.If the question says, that both PQR and STR are equilateral triangles, we will get the answer as2 : 1If triangle POR and STR are equilateral triangles. Then we can say, both are similar triangles.
According to similar triangle property,RTQR= SRPR= STPQ=m say RT=mQR ;SR=m PR ;ST =m PQArea of equilateral triangle = ( √3 / 4 )(S^2)Therefore, Area of triangle PQR = ( √3 / 4 )(QR^2)Area of triangle STR = ( √3 / 4 )(RT^2)Since RT = m QRThe ratio of , Area of triangle PQR / Area of triangle STR = [( √3 / 4 )(QR)^2 / ( √3 / 4 )(m QR)^2 ]Area of triangle PQR / Area of triangle STR =1/ m^2Area of triangle PQR : Area of triangle STR = 1 : m^2The question says, “ area of the triangle STR is 1/9th area of the equilateral triangle PQR”.Area of Triangle STR = 1/9th Area of Triangle PQR→ m^2 = 1/9Therefore, m = 1/3→ RT/ QR = 1/3That is QT : QR = 2/3Hence, QT / RT = 2/1 = 2 : 1
2. Given a set of five numbers 27, 29, 35, 9, 25 on increasing each number by ‘K’ if the newmean of the set becomes 29.5, then what is the new median?Solution:
( 27 + k + 29 + k + 35 + k + 9 + k + 25 + k ) / 5 = 29.5( 125 + 5 k ) = 147.55 k = 22.5k = 4.5Therefore, the set of new five numbers = (27 + 4.5) , (29 + 4.5) , (35 + 4.5) , (9 + 4.5) , (25 + 4.5)= 31.5 , 33.5 , 39.5, 13.5 , 29.5To find the median , we need to arrange the values in ascending order.13.5, 29.5 , 31.5 , 33.5 , 39.5Therefore new median = 31.5
3. If a1=2 and an+1= (an-1)^2, then what is the value of a15?A. 28B. 216C. 232D. 2128E. 2256Solution:
This is same as “If a1 = 2 and an+1=(an - 1)^2, then find the value of a17?”Therefore, solution = 2128
4. Given that, if |x| = |y| and xy<0, thenCol A: x-yCol B: 0Solution:
We need to check with few cases, with different values of x and yLet's take the conditions(i) xy<0 , so it means x or y should be negative.(ii) |x| = |y| , so the numerical values of x and y should be equal.Case 1 : x = 1 , y = -1Whether it satisfies the condition ,xy<0 → (1)(-1) = -1 , which is less than 0|1| = |-1| , which means 1 = 1Conditions are satisfiedSo, Col A : x – y = 1 - (-1) = 2From Case 1, we can say, Col A is greater.Case 2 : x = -2, y = 2It will satisfy both the conditions.So, Col A : x – y = -2 -2 = -4From Case 2, we can say, Col B is greater.Therefore, we can conclude that, “relationship cannot be determined”
5. If the equation of two lines ‘L’ & ‘M’ are 7x – 4y = 1 and 10x + 5y + 3 = 0, thenCol A: Slope of the line ‘L’Col B: Slope of the line ‘M’Solution:
To find the slope, we need to arrange the equation in the general equation form.General equation : y = m x + c ( m is the slope )Equation 1 : 7x – 4y = 14y = 7x – 1Y = (7/4)x + ( - 1/4)Therefore, Slope of the line “L”= 7/4Equation 2 : 10x + 5y + 3 = 05y = -10 x – 3Y = (-10/5) x + ( - 3/5)Y = (-2)x + (- 3/5)Therefore , Slope of the line “M” = -2Hence, Col A is greater.
6. Given that an amount of 2000$ is given for annual interest at rate of 'r'%. If 150$ is received asan interest for 1 year then find the rate of interest ‘r’%?Solution:
Principle ( P) = $2000
Rate (R) = r%Interest (I)= $150No. of years (N) = 1 yearInterest = PNR / 100150 = [ (2000)(1)(r) ] / 100r = 15000 / 2000r = 7.5 %Therefore, the rate of Interest = 7.5%
7. Given P, Q, R, S and A, B, C, D as midpoints of bigger square and smaller squarerespectively, if on joining these midpoints, if 8 trapeziums are formed as above, then findthe perimeter any one of the trapezium?
Solution:
We need to find the perimeter of one trapezium.Let's take the trapezium that is shaded.
The diagram shows you clearly the three sides of the trapezium. ( I guess, you will be clear withthe diagram)How to find the 4th side?It is the diagonal .
So, if we deduct the bigger square diagonal from the smaller square diagonal, we will get the leftout portion in the two sides, which are in red color ( do you agree ? )Diagonal of the square = √2 SDiagonal of the bigger square = √2 * 4 = 4√2Diagonal of the smaller square = √2 * 2 = 2√2Therefore the left out portion is 4√2 – 2√2 = 2√2Since, the left over is of 2 parts, but we need only one part = (2√2)/2 = √2Therefore, Perimeter of the trapezium = 1 + 1 + 2 + √2 = 4 + √28. Given volume of a cube is x3 and find the lateral surface area of the cube?Solution :The surface area of the cube is 6S2But, the lateral surface area is 2x2
GRE QUANT DATABASE(UPDATED TILL April 8th) updated by Mohan
1)
Given that, if the area of the triangle STR is 1/9th area of the equilateral triangle PQR, then what is the ratio of QT/TR?A. 1:3B. 3:1C. 2:1& so on…..Answer is C
2) Given a set of five numbers 27, 29, 35, 9, 25 on increasing each number by ‘K’ if the new mean of the set becomes 29.5, then what is the new median?Solution:
( 27 + k + 29 + k + 35 + k + 9 + k + 25 + k ) / 5 = 29.5
( 125 + 5 k ) = 147.5
5 k = 22.5
k = 4.5
Therefore, the set of new five numbers = (27 + 4.5) , (29 + 4.5) , (35 + 4.5) , (9 + 4.5) , (25 + 4.5)
= 31.5 , 33.5 , 39.5, 13.5 , 29.5
To find the median , we need to arrange the values in ascending order.
13.5, 29.5 , 31.5 , 33.5 , 39.5
Therefore new median = 31.5
3. If a1=2 and an+1= (an-1)2, then what is the value of a15?
A. 28 B. 216 C. 232 D. 2128 E. 2256
Answer is 2256
4) Given that, if |x| = |y| and xy<0, thenCol A: x-yCol B: 0Answer is relationship Cannot be determined
5) If the equation of two lines ‘L’ & ‘M’ are 7x – 4y = 1 and 10x + 5y + 3 = 0, thenCol A: Slope of the line ‘L’Col B: Slope of the line ‘M’Answer is Column A is greater
6. Given that an amount of 2000$ is given for annual interest at rate of 'r'%. If 150$ is received as an interest for 1 year then find the rate of interest ‘r’%?
Answer is 7.5%
7)
Given P, Q, R, S and A, B, C, D as midpoints of bigger square and smaller square respectively, if on joining these midpoints, if 8 trapeziums are formed as above, then find the perimeter any one of the trapezium?Answer is 4 + sqrt(2)
8) Given volume of a cube is x3 and find the lateral surface area of the cube?Solution:
The surface area of the cube is 6S2
But, the lateral surface area is 2x2
GRE QUANT DATABASE(UPDATED TILL April 3rd) updated by Saranya
1. The value of 1/5 - 1/10 =A. 0.1B. 0.2C. 0.5& so on.....Solution:
1/5 – 1/10 = 1/10 = 0.1
2. If the base length and height of a bigger triangle are 4 & 5, and if the base length and height ofsmaller triangle are 3 & 3, then what is the area of the shaded region?
Solution:
Area of the shaded region = Area of the bigger triangle – Area of the inner triangle= [ . * 4 * 5 ] - [ . * 3 * 3 ]= 20/2 – 9/2= 11/2= 5.5 Sq. units
3. Given 'n' is a positive integer. What is the least value of n, such that the product 12nshould be a perfect square of some integer?Solution:
We should have different values of n and substitute in 12n to satisfy the condition.Let , n = 112n = 12 ( It is not a perfect square)Let n = 212n = 24 ( It is not a perfect square)Let n = 3
12n = 36it is the perfect square of another integer 6.Therefore, the least value of n = 3.
4. A group can charter a particular aircraft at a fixed total cost. If 36 people charter aircraftrather than 40, then loss per person is 12$. What is cost per person if 40 people charter it?Solution:
Let the total cost be X and cost / amount per person be AThe fixed total cost will be shared among 40 people equally.It means → 40 A = X ----------equation (1)If 36 people are sharing the fixed total cost, then loss per person is 12$.It means, each person should pay 12$ in addition to “A”36 ( A + 12) = X -----------equation (2)Substitute equation (1) in equation (2)36 A + 432 = 40 A4 A = 432A = 108Therefore, cost per person if 40 people charter it = $108
5. Col A: (0.9/1.1) 2 + (1.1 /0.9)2Col B: 2Solution:
Col A : (9/11)2 + ( 11/ 9)2 = (81/121) + (121/81) = 0.67 + 1.49 = 2.16Col B : 2Therefore, Column A is greater.
6. If slope of a line XY is -1/2, thenCol A: X-intercept of LineCol B: Y-intercept of Line.Solution:
It is given slope of the line XY is -1/2The general equation is y = m x + cWhere, m is the slopey = (-1/2 ) x + c2y = -x + 2cLet x be 0, to find the value of y2y = 0 + 2 cy = cTherefore, Y intercept = c ( Col B )Let y be 0, to find the value of x0 = -x + 2cx = 2cTherefore, X intercept = 2c ( Col A)
Since, the value of c can be positive or negative, “relationship cannot be determined”
7. If the median of seven Consecutive integers is 2n+2, then find the Arithmetic mean of thesequence?Solution:
Remember : If we have an odd set of consecutive integer ( say, 3 consecutive integers or 5consecutive integers or 7 consecutive integers or 9 consecutive integers, etc.,). In this case, themean value and the median value will be same.Since, the question talks about 7 consecutive integers and the median value is given.The Arithmetic mean of the sequence = Median of the sequence.Therefore, A.M = 2n + 2
GRE QUANT DATABASE(UPDATED TILL December 10th) updated by Saranya
1) Given that, the probability that it won't rain tomorrow is 0.46Col A: The probability that it will rain tomorrow at temperature of 85degree centigradeCol B: 0.54
Solution:
p is the probability of success (probability that it will rain.)
q is the probability of failure (probability that it won't rain.)
then p + q = 1.
Given : q = 0.46
Therefore, p = 1 – 0.46 = 0.54
2) If 'N' is a 3 digit number where hundreds place is 'x' and units place is 'y' then what will be the factor for N-100x-y?A. 3 B. 4 C. 5 D. 6 E. 7 Solution:
Case 1 : Let us take N as 131, x = 1 and y = 1,
then , N-100x-y = 131 – 100-1= 30, which is a factor of 3, 5 and 6.
Case 2 : Let us take N as 456, x=4 and y = 6
then, N-100x-y = 456 – 400 – 6 = 50 , which is a factor of 5
Case 3 : Let us take N as 142, x=1and y = 2
then, N-100x-y = 142 – 100 – 2 = 40 , which is a factor of 4 and 5.
From all these cases, what we infer is, for any number of N, the factor for N-100x-y will be 5.
Answer is Option C (5)
3) If 'S' is a set of all integers that are multiples of 3 & multiples of 5, provided it should be of 2 digits, then find the range of S?A. 81 B. 77 C. 87 D. 89 E. 91 Solution:
Multiples of 3 and Multiples of 5 ( condition : it should be of 2 digits)
Multiples of 3 = { 12 , 15 , 18 , 21 ,........................., 99}
Multiples of 5 = { 10, 15, 20, 25, .............................,95}
Therefore, S = { 10,12,15,18,...........................99}
Range = Maximum number – Minimum Number
Range of S = 99 – 10 = 89
Answer : Option D (89)
4) Find the number of possible values of x & y in the expression (5+x)/(7+y), so that the resultant ratio is 5:7 where x and y lie between 12 and 29?
Solution:
(5+x)/(7+y) = 5/7
x and y should lie between 12 and 29
To Find : x and y
5+x must be a multiple of 5 , the possible values will be (5+0), (5+5), (5+10), (5+15),(5+20),(5+25), (5+30),..................
7+y must be a multiple of 7 , the possible values will be (7+0), (7+7), (7+14), (7+21),(7+28),(7+35), (7+42),..................
(5+x)/(7+y) can be (5+0)/(7+0) , (5+5)/(7+7), (5+10)/(7+14), (5+15)/(7+21) , (5+20)/(7+28) , (5+25)/(7+35) , (5+30)/(7+42)
All the above said are possible values that x and y can take, but
the condition given is x and y should lie between 12 and 29.
So , eliminating options, which does not lie in this range, we get
(5+15)/(7+21) and (5+20)/(7+28).
Answer : x = 15 and y = 21 (or) x = 20 and y = 28
Whichever option given in the question can be marked as the answer.
5) If -2 < x < -1, thenCol A: 1/x3Col B: 1/x
Solution:
In all cases except x = -1 ,
the value of 1/x3 > value of 1/x
Answer : Option A (Column A is greater)
Note : If the question given as If 2 < x < 1 , all positive values, then
In all cases except x = 1
Value of 1/x3 < value of 1/x.
GRE QUANT DATABASE(UPDATED TILL December 9 th ) updated by Saranya
1) A triangle ABC is given, in which lengths of two sides were given as BC = 12 , AC = 13 and the perimeter of the triangle is 32. Col A: Measure of angle of B Col B: 90
Solution:
AB + BC + AC = 32
BC and AC are given as 12 and 13 , therefore, AB = 7
Note : Conditions to satisfy
If angle B to be Right angle
Condition to be satisfied AB2 + BC2 = AC2
If angle B to be an Obtuse angle
Condition to be satisfied AB2 + BC2 < AC2
If angle B to be an Acute angle
Condition to be satisfied AB2 + BC2 > AC2
In this question , if we solve the values we will get as AB2 + BC2 > AC2
72 + 122 > 132, therefore, it is an acute angle
Answer : Option B ( Column B is greater )
2) Given the average of seven numbers as 35. When k is added to it, if the average of eight numbers remains 35, then what is the value of k?
Solution:
(Total of 7 numbers ) / 7 = 35
Therefore, total of 7 numbers = 245
If k is added , then the average of 8 numbers remains 35
(245 + k ) / 8 = 35
245 + k = 280
k = 35
Answer: the value of k is 35
3) Col A: 2^-1 + 1/(2)^-1 Col B: (3)^-1 + 1/(3)^-1
Solution:
Col A can be written as ½ + 2 = 5/2 = 2.5
Col B can be written as 1/3 + 3 = 10/3 = 3.33
Answer : Option B ( Colum B is greater )
4) If x > 0 and y > 0, thenCol A: sqrt(xy) Col B: sqrt(x+y)
Solution:
Case 1 : If x = 0.2 and y = 0.2
Col A = √0.04 = 0.2 and Col B = √0.4 = 0.632
In case 1, column B is greater.
Case 2 : If x = 2 and y = 3
Col A = √6 = 2.45 and Col B = √5 = 2.24
In case 2, column A is greater.
Answer : Option D ( Relation Cannot be determined )
5) Given a cuboid consisting of small tiles of dimension 1feet, the small tiles spread across length are 9 in amount, across height are 3 in amount and across width are 6 in amount{not sure}. Find the total surface area of cuboid?
Solution:
Given : length = 9 , height = 3 and width = 6 (as per the question )
Total surface Area of cuboid = 2(lw+wh+hl)
= 2 ( 54 + 18 + 27 )
= 198
Answer : Total Surface Area of Cuboid = 198 sq units
6. Given a circular flower garden with radius 'r' and a stone walk surrounds the garden whose thickness is given as half the radius of circular garden.Col A: Area of circular gardenCol B: Area of stone walk
Solution:
Col A : Area of Circular garden = Πr2
Col B : Area of stone walk = Area of outer circle – Area of the inner circle
= Π( r + r/2)2 – Πr2
= Π (9/4)r2 – Πr2
= 5/4Πr2
Answer : Option B ( Column B is greater )
GRE QUANT DATABASE(UPDATED TILL December 8 th ) updated by Saranya
1) For n/12, what is the value of n whose remainder is odd integer?
Solution:
n can take any value from { 13, 15, 17, 19, 21, 23,25,.....}
Therefore, Value cannot be determined
2) If 'x' and 'y' are integers between 12 and 30, then for (5+x)/(7+y) how many sets of x & y for the
given expression will be having same ratio?
Solution:
Same question as, “ Find the number of possible values of x & y in the expression (5+x)/(7+y), so that the resultant ratio is 5:7 where x and y lie between 12 and 29?” , Solve by the same method.
3) Given five consecutive numbers, if the highest value of them is x, then what is the average of the numbers?
Solution:
Five consecutive numbers with the highest value of x will be
(x – 4 ) , ( x – 3 ) , ( x – 2 ) , ( x – 1 ) , x
Average of these numbers = (x – 4 + x – 3 + x – 2 + x – 1 + x )/5
= (5x – 10 )/ 5
= x – 2
Answer : Average of numbers = x -2
4) Given series 1, 1, 1, 1, 1Col A: Standard Deviation of given seriesCol B: 1
Solution:
Col A : Standards Deviation of 1,1,1,1,1 = 0
Note : Always Standard deviation for a sequence of 1 will be equal to “zero”
Col B : 1
Answer : Option B ( Column B is greater )
5)
Given a figure like above i.e. a square whose side is equal to diameter of the circle, find the area of circle? Solution:
Area of the circle = Πr2 (or)Πd
As the diameter of the circle is equal to the side of the square,
Area of the circle = ΠSAnswer : With the available information, Area of the circle can be Πr2 (or) Πd (or) ΠS
6) A teacher teaches biology for a group 53 students. She can divide them into two batches P and Q. P has 7 batches of ‘n’ students each. Q has ‘x’ students of five batches; or six students with ‘y’ students in 5 batches and (y+1) students in 6th batch. Col A: x Col B: n( Question is insufficient )
7. If x is a positive number, then Col A: x^2 Col B: 1/x^2
Solution:
If x is a positive number greater than 1, then we can say x^2 > 1/x^2
but, here, 1 is also included,
if we substitute 1 in Col A and Col B , we will get x^2 = 1/x^2
Answer : Option D ( Relationship cannot be determined )
GRE QUANT DATABASE(UPDATED TILL December 5 th ) updated by Saranya
1. Given N is a positive odd integer. If the number in the tens digit is double the digit at theunits place then what is the value of N?A. n > 90B. 30 < NC. N > 50D. 30 < N < 50Solution:
If the number in the tens digit is double the digit at the units place andN is a positive odd integer.N can take only two values , 21 and 63.Answer : It does not fall in any of the options.
2. Given a series of numbers 1, -1, 2, -2, 3, -3.......Col A: The sum of the first 67 termsCol B: 34Solution:
1st No. 2nd No. 3rd No. 4th No. 5th No. 6th No. 7th No. 8th No. 9th No. 10th No.
First 10 values
1 -1 2 -2 3 -3 4 -4 5 -5
11-20 values
6 -6 7 -7 8 -8 9 -9 10 -10
21-30 values
14
31-40 values
19
41-50 values
24
51-60 values
29
61-70 values
34 (67th
value)
Sum of first 67 terms = 34 ( except 34, all the values have + sign and – sign alternatively, which will be canceled)
Answer : Option C ( Both are equal )
GRE QUANT DATABASE(UPDATED TILL December 4 th ) updated by Saranya
1. Given three seriesl: x, 2x, 3x, 4x, 5xll: x, x+1, x+2, x+3lll: 1/x,1/x+1,1/x+2,1/x+3Which of the series has same mean and median?Solution:
l: x, 2x, 3x, 4x, 5xMean = (x + 2x + 3x + 4x + 5x )/5 = 3xMeadian = (n + 1 )/2 th term = 3rd term = 3xBoth are same.ll: x, x+1, x+2, x+3Mean = (4x + 6 )/ 4 = (2x + 3 )/2Median = 2.5th term = (2nd term + 3rd term ) / 2 = [(x+1) + (x+2) ] / 2 = (2x + 3)/2Both are same.lll: 1/x,1/x+1,1/x+2,1/x+3Mean : (4 + 6x)/4x = (2 + 3x )/2xMedian : 2.5th term = (2nd term + 3rd term ) / 2= (2 + 3x )/2xBoth are sameAnswer : For all the three options mean and median are same.
2. In a class of 20 students, one half of the students are boys, if a teacher has to select 7students and the first 6 are girls. What is the probability that the 7th student is a girlSolution:
Given: Total number of students = 20.Number of boys = 10Number of girls = 10 First 6 are girls.Solution:The remaining girls = 4Total number of remaining students = 20 – 6 = 14.We need to select a girl to put in the 7th place.Probability of selecting a girl = 4C1/ 14C1 = 4 / 14 = 2 / 7.So, the probability that the 7th students is a girl = 2/ 7.Answer : The probability that the 7th student is a girl is 2/7
4. If the probability of not raining tomorrow is 0.42, thenCol A: Probability of not raining tomorrow, when temperature is above 85 centigradeCol B: 0.58Solution:
Solution already given
5. Col A: 10! + 9!Col B: 10(9!)Solution:
10(9!) is nothing but 10!Hence, it is clear Col A > Col BAnswer : Option A ( Column A is greater )
6. If x & y are the integers between 13 & 29, then for 5+x/7+y how many sets of values of x & yfor the given expression will be in same ratio?Solution:
Solution already given
7. If x/x-1 = x-2/x+1Col A: xCol B: 2/3Solution:
x/(x-1) = (x-2)/(x+1)x(x+1) = (x -2)(x-1)x2 +x = x2 -x -2x + 24x = 2x = 1/2Col A = ½ = 0.5Col B = 2/3 = 0.67
Answer : Option B ( Col B is greater )
GRE QUANT DATABASE(UPDATED TILL December 3rd) updated by Saranya
1. There are 1 badger and 1 panderer. If each badger has 6 flavors and each panderer has 3flavors, then what is the total number of ways of selecting 4 flavors from badger and 1flavor from panderer?Solution:
Total number of flavors in badger is 6.From the badger of 6 flavor, 4 flavors can be selected in 6C4 = 15 ways.Total number of falvors of panderer = 3.From the panderer of 3 flavors, 1 can be selected in 3C1 = 3 ways.The total number of ways of selecting 4 flavors from badger and 1 flavor from panderer = 15 x 3= 45 ways.Answer : The total number of ways of selecting 4 flavors from badger and 1 flavor from panderer= 45 ways
2. Given 'A' works 25mins to produce 1 ton of oil and 'B' works 30mins to produce 1 ton of oil, Ifthey work simultaneously, then in how many hours they can produce 15 tons of oil?Solution:
A works 25 minutes to produce 1 ton oil.In one minute A can produce 1 /25 tons of oil.B works 30 minutes to produce 1 ton oil.In one minute B can produce 1/ 30 tons of oil.Together can produce 1/25 + 1/30 tons of oil in one minute.1/25 + 1/30 = 55 / 750.That is, in 750 minutes, they both can produce 55 tons of oil.To produce one ton of oil, the need to work 750/ 55 minutes.To produce 15 tons of oil, the need to work 15 x 750/55 minutes.Let us convert 15 x 750/55 minutes to hours.15 x 750/55 minutes = 15 x 750/55 / 60 hours = 150/44 hrs. = 3.4091 hrs.That is, 3 hrs 24 minutes and 33 seconds.Answer : 3 hrs 24 minutes and 33 seconds.
3. 1/2(10^6) =??Option A. 5*10^5 , other options not givenSolution:
1/2(10^6) = ½ ( 2)6 (5)6 = (25)(56)Answer : (25)(56) , check with the options
4. Col A: (0.02)^2Col B: (-0.05)^2Solution:
(0.02)^2 = 0.02 x 0.02 = 0.0004(-0.05)^2 = 0.05 x 0.05 = 0.0025Answer : Option B ( Column B is greater)
5. If -10 < = X < = 6, then what is the maximum possible greatest value of -X^2+X^4?Solution:
Both the powers are even.Therefore, negative values when powered with even values will turn into a positive value.Hence, -X^2+X^4 = - (-10)2 + (-10)4 = -100 + 10000 = 9900Answer : The maximum possible greatest value of -X^2+X^4 = 9900
7. If 'A' is three times of 'B' and 'B' is five times of 'C', then how many times is 'A' whencompared to 'C'?A.15B.14CC.15CD.10CSolution:
A is three times B. This can be written as A = 3B ------> 1.B is five times C. This can be written as B = 5C.Plug in B = 5C in eqn 1.A = 3(5C) = 15C.A = 15CAnswer : A is 15 times of C
GRE QUANT DATABASE(UPDATED Unknown date) updated by Saranya
Question 1 : Given a figure as above with circle inside a square, if the area of the square is 16, thenCol A: Area of circleCol B: 4PIESolution:
The figure is
Area of the square is 16 , implies that the length of the side of the square is 4. Since the circle completely lies inside the square, the diameter of the circle is less than 4. The radius of the circle is less than 2. Hence the area of the circle is less than 4π.
Col B is greater
Question 2: If 61% supports ‘X’ and 55% supports ‘Y’ and out of those who support ‘Y’ 80% also supports ‘X’ , then what percentage of people supports neither ‘X’ nor ‘Y’?Solution:
Suppose:Given that 61% support X,55% support Y and out of those who support Y, 80% also supports X.ie 80% of (55% support Y) support X .ie 80% X 55% supports both X and YThus 44% supports both X and Y, (61 – 44)% = 17% support only X and (55 – 44)% = 11% supportonly Y.Hence 17% + 11% + 44% = 72% either support X or Y and (100 – 72)% = 28% of people neithersupport X nor Y.
Question 3: If there is a series in which the first number A1 is 4 and An+1 = (An - 3)^2, then whatis the 25th number ?(Here 1, n, n+1 are suffixes)Solution:
Here we have not given information about the complete sequence.Given : A1=4 , A n1 = An−3 ^ 2Let n - 3 = 1, then n = 4Hence we can find A41 = A5=A4−3 ^ 2 =A1^2 =4^2Let n-3 = 5, then n = 8A81 = A9 = A8−3 ^ 2 = A5^2 = 4^4n – 3 = 9, then n = 12A13=4^8The sequence is 1, 5, 9, 13, 17, 21, 25,.....such that A1=4 , A5=4^2 , A9=4^4 , A13=4^8 , A17=4^16, A21=4^32 , A25=4^64
Question 4: A certain game has multiple rounds, in each round a participant receives either 2points or 4 points, the average points received by one particular participant for all the rounds is2.2Col A : 9 times the number of rounds in which the participant got 4 pointsCol B: the number of rounds in which the participant got 2 pointsSolution:
The game has N multiple rounds.In that suppose there are T games in which the participate receives 2 points. Thus in N – T games theparticipant has receive 4 points.Given the average points received by one particular participant for all the rounds is 2.22T4 N−T N =2.24N−2T=2.2 N1.8N−2T=018N−20T=0 ,9 N−T = T
Hence Col A = Col B
Question 5 : If there is a list of some numbers, whose mean is 10.8 and standard deviation is '0',thenCol A: Range of that listCol B: 0Solution:
Note that standard deviation describes the distribution of these number. In other words, it says how faris the list these numbers is away from the mean.Here standard deviation is 0 which says that all the numbers in the list must be equal to 10.8.Hence the range of the list = max value – min value = 10.8 – 10.8 = 0Answer is C
Question 6 : Given Set A = 1, 2, 3, 4, 5 ...m & Set B = 1, 2, 3 ....n where 'n' is odd and 'm' is evenCol A: Percentage of odd numbers in ACol B: Percentage of even numbers in BSolution:
Set A = 1,2,3....mNote that when m is even then Set A will have m/2 even number and m/2 odd numbers. Hence thenumber of odd numbers will be 50%Set B = 1, 2,3...nNote that when n is odd then Set B will have (n – 1)/2 even number and ((n – 1)/2 + 1) odd numbers.Hence the number of even numbers will be (n – 1)/n * 50% < 50% as (n-1)/n < 1Hence answer is column A.
Question 7 :
Given a figure like above, here PQRS is a square of length 10 and the line VT is theperpendicular to the diameter of the semicircle PQ and it is also given that PU = 2, then find thelength of VT?Solution:
Consider the following figure.
Length of the square is 10 means side of the square is 10.Hence the diameter of the semicircle is 10 and radius is 5.PU = 2 implies OU=3 and also OV = 5.where O is the center of the circle.Now, ΔVOU is an right angled triangle.By hypotenuse theorem we get VU = 4.VT = 4 + 10 = 14
Question 8 :How much interest would accrue over a $4000 loan over 3 months at 8% annual Simple Interest?
Solution:
Given : Principle(p) = $4000
Number of years (n) = 3/12
Interest ( r ) = 8%
To Find : Interest
Interest = [(p)(n)(r)] / 100
= [4000 x (3/12) x 8 ] / 100
= $ 80.
Question 9 :Dick is twice as old as he was 10 yrs ago. Jane is half as old as she will be in 10 years.
Evaluate and choose
Col A: Dick’s age
Col B: Jane’s age
Solution:
Let us Consider each case separately.
First case: Dick is twice as old as he was 10 yrs ago.
It means the present age of Dick , is 2 times the age of Dick 10years ago.
Now we can frame the equation
Let age of Dick be X
Let Y be his 10 years before, Y = X – 10
But its also given that X = 2Y
Therefore X = 2 ( X-10)
X = 2X -20
2X – X = 20
→ X = 20,
Hence age of Dick = 20 years.
Second Case: Jane is half as old as she will be in 10 years.
It means Jane's age is half the age of hers 10 years later.
Now we can form the equation.
Let age of Jane be M
Let N be the age after 10 years, N = M+10
Bit its given that M = ½ N
Therefore,M= ½ (M + 10)
2M = M + 10
2M –M = 10
M = 10,
Hence age of Jane = 10years
Therefore, answer is Option 1 ( Column A is greater )
Question 10 : The range of list-1 is 16 and range of list-2 is 10(approx values). If both the lists are combined then what will be the minimum value of their range?
Solution:
The question is incomplete, it has not given any detail with regard to list – 1 and list – 2, Hence, it cannot be computed.
Let us take 2 cases for better understanding.
Case 1 :Let list-1 contains numbers from 1 to 17 and list-2 contains 20 to 30
Here the range on list-1 is16 and range of list-2 is 10 and the minimum value of these two lists are 1 and 20 respectively.
If we combine both the lists, the minimum value will be 1 which comes from list-1.
Case 2 : Let list-1 contains value from 5 to 21 and list -2 contains value from 2 to 12
Here also the range for list-1 is 16 and the range for list-2 is 10 and the minimum values are 5 and 2 respectively.
If we combine both the lists, the minimum value will be 2 which comes from list-2.
From these two cases, we can clearly say, that both the lists can have numerous combination of numbers and their minimum value will be changing accordingly ie the minimum value may come from any list.
Hence, the question provided is insufficient to answer.
Question 11 : Given that there was about 8500 distribution numbers. If the score of 26.7 was 35th percentile and 37.1 was 50th percentile, then how many distribution parameter numbers accounted for about 50 percentile of the distribution?
Solution:
26.7 was 35th percentile → It means in a distribution of 100, 36th person will have the score of 26.7 .
37.1was 50th percentile → It means, in a distribution of 100, 51st person will have the score of 37.1.
The question is to find out how many distribution parameter numbers accounted for about 50 percentile of the distribution.
It means, in 8500 distribution where this 50 percentile will fall.
The formula is (L/N) x 100 = P
we need to find L, where N = 8500 and P = 50
L = (50 x 8500)/100
= 4250.
Therefore, 4250 distribution parameter numbers are accounted for 50th percentile of the distribution.
Question 12 : Given that, there is a field with 'r' sections in which there are 's' sub- fields in each section. It is also given that there are 5 employees for working and each one does the work equally. If there is an employee Annie who does the work of her and also 1/3 work of the other colleague, thenCol A: Work done by AnnieCol B: rs/4.
Solution:
Total work that has to be completed by all the employees = rs
This is because, we need to work in a field with 'r' sections and each of these 'r' sections have 's' sub-fields.
Now let us find the work done by each employee.
It is given that all the employees work equally
Therefore, work done by each employee = (Total work)/ (Number of employees)
= rs/5
In column A it is given as Work done by Annie
Work done by Annie = Annie's work + 1/3 work of the other employee.
= rs/5 + (1/3)(rs/5)
= rs/5 + rs/15
= (3rs + rs )/15
= 4rs/15
= rs/3.75
In Column B : rs/4
When comparing column A and column B
Column A is greater.
Question 13: PR and PQ are chords and ON a tangent to circle of centre C. Angle QRP measures 40 0.What is the measure of angle PQR ?
Solution:
Consider the diagram, line ON is tangent of the circle with center C . Angle of the arc PR will be equal to the angle PCR. Draw the line CR . CP is perpendicular to ON. Angle CPO is 900. => Angle CPR + Angle RPO = 900.=> angle CPR = 900 – angle RPO ---------------(1)
Now, consider ΔCPR, angle CRP = angle CPR
angle CRP + angle CPR + angle PCR = 1800
2(angle CRP) + angle RCP = 1800
From (1)2(900 – angle RPO) + angle RCP = 1800
angle RCP = 2 (angle RPO) ------------------(2)
Now, angle RCP = 2 (angle RQP)From (2)We have angle RPO = angle RQPsince, angle CPR = 100.(given)angle RPO = 800.=>angle RQP = 800.
Question 14 : Two lists were given: A: 12, 10, 30, 35 & 40 and B: 30, 50, 20, 10 & 60 Col A: Standard Deviation of ACol B: Standard Deviation of BSolution:
Mean of sequence A = 25.4
Standard deviation of A = 12−25.4210−25.4230−25.4 235−25.4240−25.42
5
= −13.42−15.4 24.429.4214.42
5
Mean of sequence B = 34
Standard deviation of B = 30−34250−34220−34210−34260−342
5
= 42242−142−142302
5
Clearly, numerator of standard deviation A < numerator of standard deviation B
Hence Column B is greater
Question 15 : Given one triangle whose arms are 3 and 5. If its angles are less than 90, then find the
range of other arm? Solution:
If θ is the angle between the sides of length 3 and 5. The range of θ is 0° - 90°If the angle the two arms is 0°, then the length of the third arm is (5- 3) = 2.If the angle the two arms is 90°, then the length of the third arm (by hypotenuse theorem) is 5232=34
Hence the range of third side is 2 to 34 .
Question 16 : If in a team of 100, 70 liked cricket, 80 liked football and 5 liked neither, then how many people did like cricket but not football? Solution:
Out of 100 people, 5 liked neither.Thus out of 95 students, 80 liked football and 70 liked cricket. Let x people play both cricket and football. Hence 70 – x people likes to play only cricket and 80 – x people likes to play only football.But the total number people who plays either cricket or football = 95Hence (70 – x) + x + (80 – x) = 95x = 55Hence 60 people likes to play both cricket and football. (70 – 55) = 15 likes to play only cricket.
Question 16 : There are two names given JOHNSON and TONY. If one letter is picked from both simultaneously at random, then find the probability that the letter is same? Solution:
From the words JOHNSON and TONY, the letters 'O' and 'N' occurs in both the word. What is the probability that either 'O' or 'N' is chosen?
The probability of choosing 'O' in JOHNSON is 2/7 and probability of choosing O from the letter TONY is 1/4 . Hence the probability that O is chosen from both the names = 2/7 * 1/4 = 1/14
Similarly the probability of choosing 'N' in JOHNSON is 2/7 and probability of choosing N from the letter TONY is 1/4 . Hence the probability that N is chosen from both the names = 2/7 * 1/4 = 1/14
Hence the probability that either N or O is chosen, = 1/14 + 1/14 = 1/7.
Question 17 : If a wheel 'A' has half the diameter of wheel B, thenCol A: Number of revolutions made by wheel A to cover 5000 miles
Col B: Number of revolutions made by wheel B to cover 2500 milesSolution:
If d is the diameter of wheel A , then the diameter of wheel B is 2d. Hence perimeter or circumference of wheel A is πd and the perimeter of wheel B is 2πd.
Note that the one revolution of wheel A = circumference of the wheel A.Hence the number of revolutions made by wheel A to cover 5000 miles = 5000/ πd
Similarly one revolution of wheel B = circumference of the wheel B.Hence the number of revolutions made by wheel B to cover 2500 miles = 2500/ 2πd = 1250/πd
Hence, Column A > Column B.
Question 18: A Rectangular floor is made up of 'M' rows and 'M+4' columns fully made up of square tiles.Col A : The difference between the number of tiles in the 21st row and 26th columnCol B: M^2+2M+2 Solution:
Given a rectangular floor made up of 'M' rows and 'M+4' columns fully made up of square tiles.Hence each row has M+4 tiles and each column has M tiles.Column A: The difference between the number of tiles in the 21st row and 26th column = M+4 – M = 4Hence column A = 4
Column B : M2 + 2M + 2. Since M is the positive integer. Even if M = 1 then M2 + 2M + 2 = 5Hence M2 + 2M + 2 > 4 Column A > column B
Question 19 : A girl has several pigeons and she uses 'W'kg grains to feed them for a week. If a single pigeon consumes 'K'kg per day, thenCol A: The total Number of pigeonsCol B: 7W/KSolution:
Since a pigeon consumes K kg per day. Therefore in 7 days one pigeon will consume 7K kgand suppose she has x pigeons then,7Kx = Wx = W/7KColumn A : x =W/7KColumn B : 7W/K > W/7KHence Column B is bigger
Question 20 : If x, y & z are exterior angles of a triangle, thenCol A: x+y Col B: 180-z Solution:
Let us draw the figure.x, y and z are exterior angles with respect to a, b, cHence let us see all possible equations
1) x + a = 1802) y + b = 1803) z + c = 1804) x = b + c5) y = a + c6) z = a +b
x + y = 180 – a + 180 – b = 360 – (a + b) = 360 – z
= (180 – z) + 180Hence Column A is greater
Question : If perimeter of a rectangle A is 20 & perimeter of rectangle B is 24, thenCol A: Area of the rectangle Col B: Area of the rectangle Solution:
Perimeter of rectangle A is 20. Let the length and breadth of rectangle A be 6 and 4. Then perimeter is 20 and the area is 24 .
If length and breadth of rectangle B is 10 and 2, then the perimeter is 24 and the area is 20. But if the length and breadth of rectangle B is 7 and 5 then the perimeter is 24 bu the area is 35
Since there is no information about the length and breadth of rectangle A and B and the answer is option D that the relation cannot be determined.
Sheetal Doubts
1) if y= 2x + 3 , xy < 0 value of x lies between ?Solution:
To satisfy the condition xy<0, we have two options→ If x is positive, y should be negative.It means, x > 0 and 2x + 3 < 0→ If x is negative, y should be positive.
It means , x < 0 and 2x + 3 > 0The first case will not hold good, because, if x is positive, y will also be positive and not negative. Therefore, first option is ruled out.Thus second option alone holds good,2x + 3 > 02x > -3x > -3/2 -----------(1)Thus, the second condition says, x < 0 ---------(2) , Hence from (1) and (2)
Hence the range of x is -3/2 < x < 0.
2) If integer defined as (-1)^n then which of following is applicable for integers a & b I) a+b= a*bII) (a+b) = a + bIII) a*b = (a)* (b)a) both 1 &2 b)only 1 c) only 2 d) none e) allSolution:
The question should be If n is the integer, it is defined as (-1)^n.........Then a = (-1)^a b = (-1)^ba + b = (-1)^(a+b) = (-1)^a * (-1)^b = a * b a*b = (-1)^a * (-1)^b = (-1)^(a+b) = a + b.From this we can say that, only 1 is correct.Answer : Option b
3) abc is a triangle with ac = x+5 , bc= x , ab = 20- x, angle opp to ac and bc acute , wh is value of x??15,11,8,<15Solution:
Sides of the triangles should satisfy the 3 conditions of inequalities.→ AC < AB + BC→ AB < AC + CB→ BC < AB + AC
Lets check for these conditions.
→ (x+5) < x + 20 – x x +5 < 20 x < 15 ----------(1)→ (20 – x ) < x + 5 + x 20 – x < 2x + 5
-3x < -15 3x > 15 x > 5 --------------(2)→ x < 20 – x + x + 5 x < 25--------------(3)
Hence, the value of x should satisfy all the 3 requirements.With this, we can say, x can vary from 6 to 24.
4) Standard dev and mean of a group of nos given .largest and smallest nos given . hw many nos are there in that grp of nos ?? i.e how to find n??Solution:
Only with these information, we will not be able to find out the value of n.
7 ) A teacher teaches biology in a class of 53 students. she divides them into 2 batches p and q. p has 7 batches of n each and q has x students of 5 batches or 6 students in 5 batches and ( y+1) in 6th
batch Col a - x Col b - nSolution:
Given : 53 is divided into p and qp → 7 batches of n each = 7nq → x students of 5 batches = 5x (or) 6 students in 5 batches and (y+1) in 6th batch = 30 + (y +1) we can say that 5x = 30 + y + 1 5x = 31 + y
we need to find x and nx and n can take any value , therefore, value cannot be determined. 8) A certain game has multiple rounds in each round and participants receives either 2 to 4 pts avg. avg received by 1particular participant for all rounds is 2.2col a )" 9 times no of rounds in which participant got 4 pts col b) no of rounds in which participant got 2 pts.Solution:
If in round x , the person gets 4 pointsIn round y, he gets 2 pointsand it is said that, his average in all rounds is 2.2, then
(4x + 2y) / (x+y) = 2.24x + 2y = 2.2x + 2.2y
1.8x = 0.2y18x = 2y9x =y
Col a : 9 times no of rounds in which participant got 4 pts = 9xCol b : no of rounds in which participant got 2 pts = y
From our calculation, it is said that, 9x = y
Hence, both the quantities are equal.
9) Given x1 , x2 , x3 can do a job together in 4 hrs if x1, x2 can do the same job in 6 hrs then how long it would take for x3 i do that job alone.Solution:
RATE OF X1 +X2+X3 = 1/4 -------------(1) X1+X2 = 1/6------------(2) Subtracting (20 from (1) X3 = 1/12 SO IT TAKE 12 Hrs
10) Series given -8, -3, 5, 8, 3, -5cola ) the no that would 1st time repeat 3rd time col b) 3Solution:
Every number is the sequence is the difference of last two numbers.Third term = second term – First term = -3 - (-8) = 5Fourth term = Third term – Second term = 5 - (-3) = 8
If we find the 7th term , we will get as - 8 , and the same sequence follows, hence, the number that would first repeat the third time is - 8
Therefore, Col B is greater.
11) LCM of x and y is 24 and of z and w is 30 . what is LCM of x,y,z,w.Solution:
LCM for x and y = 24 = 6 * 4 = 2 * 3 * 2 * 2LCM for z and w = 30 = 6 * 5 = 2 * 3 * 5
Therefore, LCM for x,y,z,w = 120 ( it is nothing but, 2*3*2*2*5)
5) 2^n > 10^15n .wh is value of n?Solution:
Only if n is negative, 2^n > 10^15n is possible
6)given x and y are integers . if A = 896*355*(x-1) (y+2)col a) unit digit of a col b) 0Solution:
A = 896 * 355 * (x -1 )(y-2)First consider 896 * 355The unit digit of this will be 0 . (it is because 6*5 = 30, the unit digit is 0 in this case).Hence, anything multiplied will have the unit digit as 0.
Therefore, both the columns are equal.