CAT Quant Questions

Progressions

Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3, ... will be

  1. 164√3
  2. 188√3
  3. 248√3
  4. 192√3

Averages

In an apartment complex, the number of people aged 51 years and above is 30 and there are at most 39 people whose ages are below 51 years. The average age of all the people in the apartment complex is 38 years. What is the largest possible average age, in years, of the people whose ages are below 51 years?

  1. 27
  2. 28
  3. 26
  4. 25

Quant Sets

If among 200 students, 105 like pizza and 134 like burger, then the number of students who like only burger can possibly be

  1. 93
  2. 26
  3. 23
  4. 96

Geometry

In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is

  1. √12
  2. √14
  3. √13
  4. √11

Mixtures Alligation

A trader sells 10 litres of a mixture of paints A and B, where the amount of B in the mixture does not exceed that of A. The cost of paint A per litre is Rs. 8 more than that of paint B. If the trader sells the entire mixture for Rs. 264 and makes a profit of 10%, then the highest possible cost of paint B, in Rs. per litre, is

  1. 26
  2. 16
  3. 20
  4. 22

Logarithms

If log log2 (5 + log3 a) = 3 and log5 (4a + 12 + log2 b) = 3, then a + b is equal to

  1. 67
  2. 40
  3. 32
  4. 59

Time Distance

Point P lies between points A and B such that the length of BP is thrice that of AP. Car 1 starts from A and moves towards B. Simultaneously, car 2 starts from B and moves towards A. Car 2 reaches P one hour after car 1 reaches P. If the speed of car 2 is half that of car 1, then the time, in minutes, taken by car 1 in reaching P from A is

Numbers

Given that x2018y2017 = 1/2 and x2016y2019 = 8, the value of x2 + y3 is

  1. 35/4
  2. 37/4
  3. 31/4
  4. 33/4

Time Work

A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hours when 5 filling and 6 draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on?

Progressions

Let x, y, z be three positive real numbers in a geometric progression such that x < y < z. If 5x, 16y, and 12z are in an arithmetic progression then the common ratio of the geometric progression is:

  1. 3/6
  2. 3/2
  3. 5/2
  4. 1/6

Divisibility

56 - 1 is divisible by

  1. 5
  2. 13
  3. 31
  4. None of these

Divisibility

If n is any odd number greater than 1, then n(n2 - 1) is

  1. divisible by 24 always
  2. divisible by 96 always
  3. divisible by 48 always
  4. None of these

Divisibility

Let N = 553 + 173 - 723. N is divisible by

  1. both 3 and 17
  2. both 7 and 13
  3. both 3 and 13
  4. both 17 and 7

Remainders

After the division of a number successively by 3, 4 and 7, the remainders obtained are 2, 1 and 4 respectively. What will be the remainder if 84 divides the same number?

  1. 53
  2. 75
  3. 41
  4. 80

Remainders

When 2256 is divided by 17, the remainder would be

  1. 1
  2. 14
  3. 16
  4. None of these

Remainders Divisibility

What will be remainder when (6767 + 67) is divided by 68?

  1. 67
  2. 63
  3. 66
  4. 1

Remainders Divisibility

Find the minimum integral value of n such that the division 55n/124 leaves no remainder

  1. 124
  2. 123
  3. 31
  4. 62

Remainders Divisibility

Let k be a positive integer such that k+4 is divisible by 7. Then the smallest positive integer n, greater than 2, such that k+2n is divisible by 7 equals

  1. 7
  2. 5
  3. 9
  4. 3

Remainders

Let N = 1421 × 1423 × 1425. What is the remainder when N is divided by 12?

  1. 0
  2. 9
  3. 6
  4. 3

Remainders

On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5?

  1. 0
  2. 1
  3. 2
  4. 4

Remainders

What is the sum of all two-digit numbers that give a remainder of 3 when they are divided by 7?

  1. 676
  2. 777
  3. 683
  4. 666

Remainders

The remainder obtained when a prime number greater than 6 is divided by 6 is

  1. 1 or 3
  2. 1 or 5
  3. 3 or 5
  4. 4 or 5

Remainders

The remainder when 784 is divided by 342 is

  1. 0
  2. 1
  3. 49
  4. 341

Remainders

The smallest number which when divided by 4, 6 or 7 leaves a remainder of 2, is

  1. 86
  2. 80
  3. 62
  4. 44

Remainders

What is the remainder when 496 is divided by 6?

  1. 0
  2. 2
  3. 3
  4. 4

Remainders

If x = (163 + 173 + 183 + 193), then x divided by 70 leaves a remainder of

  1. 0
  2. 1
  3. 35
  4. 69

Remainders LCM HCF

Which is the least number that must be subtracted from 1856, so that the remainder when divided by 7, 12, and 16 is 4.

  1. 137
  2. 140
  3. 172
  4. 1361

LCM HCF

What is the greatest number which exactly divides 110, 154 and 242?

LCM HCF

What is the highest 3 digit number which is exactly divisible by 3, 5, 6 and 7?

Interests

A man earns x% on the first Rs. 2,000 and y% on the rest of his income. If he earns Rs. 700 from income of Rs. 4,000 and Rs. 900 from if his income is Rs. 5,000, find x%.

  1. 10%
  2. 15%
  3. 20%
  4. 25%

Interests

How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

  1. 4 years
  2. 4.5 years
  3. 5 years
  4. 5.5 years

Interests

A certain sum of money invested at some rate of simple interest triple itself in 4 years. In how many years the principal will become 9 times of itself at the same rate?

Quant Sets

In a locality, two-thirds of the people have cable TV, one-fifth have VCR, and one-tenth have both. What is the fraction of people having either cable TV or VCR?

  1. 23/30
  2. 2/3
  3. 17/30
  4. 19/30

Quant Sets

In a certain village, 22% of the families own agricultural land, 18% own a mobile phone and 1600 families own both agricultural land and a mobile phone. If 68% of the families neither own agricultural land nor a mobile phone, then the total number of families living in the village is

  1. 20000
  2. 10000
  3. 8000
  4. 5000

Quant PnC

A five digit number is formed using digits 1, 3, 5, 7 and 9 without repeating any one of them. What is the sum of all such possible numbers?

  1. 6666666
  2. 6666600
  3. 6666660
  4. 6666000

Quant PnC

A man has 9 friends: 4 boys and 5 girls. In how many ways can he invite them, if there have to be exactly 3 girls in the invitees?

  1. 80
  2. 160
  3. 200
  4. 320

Quant PnC

Consider the five points comprising of the vertices of a square and the intersection point of its diagonals. How many triangles can be formed using these points?

  1. 4
  2. 6
  3. 8
  4. 10

Quant PnC

Boxes numbered 1, 2, 3, 4 and 5 are kept in a row, and they which are to be filled with either a red or a blue ball, such that no two adjacent boxes can be filled with blue balls. Then how many different arrangements are possible, given that all balls of a given colour are exactly identical in all respects?

  1. 8
  2. 10
  3. 15
  4. 22

Quant PnC

How many five-digit numbers can be formed using the digits 2, 3, 8, 7, 5 exactly once such that the number is divisible by 125?

  1. 0
  2. 1
  3. 3
  4. 4

Quant PnC

In a six-node network, two nodes are connected to all the other nodes. Of the remaining four, each is connected to four nodes. What is the total number of links in the network?

  1. 7
  2. 13
  3. 15
  4. 26

Quant PnC

In how many ways can eight directors, the vice chairman and chairman of a firm be seated at a round table, if the chairman has to sit between the the vice chairman and a director?

  1. 9! × 2
  2. 2 × 7!
  3. 2 × 8!
  4. 2 × 6!

Quant PnC

Let S be the set of five-digit numbers formed by digits 1, 2, 3, 4 and 5, using each digit exactly once such that exactly two odd position are occupied by odd digits. What is the sum of the digits in the rightmost position of the numbers in S?

  1. 192
  2. 216
  3. 228
  4. 294

Quant PnC

Ten points are marked on a straight-line and 11 points are marked on another straight-line. How many triangles can be constructed with vertices from among the above points?

  1. 495
  2. 550
  3. 1045
  4. 2475

Quant PnC

There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done?

  1. 144
  2. 180
  3. 192
  4. 360

Quant PnC

What is the number of distinct terms in the expansion of (a + b + c)20?

  1. 210
  2. 231
  3. 242
  4. 253

Quant PnC

During the essay writing stage of MBA admission process in a reputed B-School, each group consists of 10 students. In one such group, two students are batch mates from the same IIT department. Assuming that the students are sitting in a row, the number of ways in which the students can sit so that the two batch mates are not sitting next to each other, is

  1. 3540340
  2. 2874590
  3. 2903040
  4. None of the above

Quant PnC

In the board meeting of a FMCG Company, everybody present in the meeting shakes hand with everybody else. If the total number of handshakes is 78, the number of members who attended the board meeting is

  1. 7
  2. 9
  3. 11
  4. 13

Quant Probability

Ramesh plans to order a birthday gift for his friend from an online retailer. However, the birthday coincides with the festival season during which there is a huge demand for buying online goods and hence deliveries are often delayed. He estimates that the probability of receiving the gift, in time, from the retailers A, B, C and D would be 0.6, 0.8, 0.9 and 0.5 respectively.

Playing safe, he orders from all four retailers simultaneously. What would be the probability that his friend would receive the gift in time?

  1. 0.004
  2. 0.006
  3. 0.216
  4. 0.994
  5. 0.996

Quant Probability Quant PnC

If a 4 digit number is formed with digits 1, 2, 3 and 5. What is the probability that the number is divisible by 25, if repetition of digits is not allowed?

  1. 1/12
  2. 1/6
  3. 1/8
  4. 1/4

Quant Probability

An unbiased dice is thrown. What is the probability of getting

  • (i) an even number
  • (ii) a multiple of 3
  • (iii) an even number or a multiple of 3
  • (iv) an even number and a multiple of 3