CAT Questions

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

Quant Probability

One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn. Find the probability that the card drawn is:

  • (i) an ace
  • (ii) red
  • (iii) either red or king
  • (iv) red and a king

Quant Probability

There are 4 red & 5 green balls in bag A and 5 red & 6 green balls in bag B. If a bag is selected at random and a ball is selected from that, what is the probability that it is red?

Quant Probability

The internal evaluation for Economics course in an Engineering programme is based on the score of four quizzes. Rahul has secured 70, 90 and 80 in the first three quizzes. The fourth quiz has ten True-False type questions, each carrying 10 marks. What is the probability that Rahul’s average internal marks for the Economics course is more than 80, given that he decides to guess randomly on the final quiz?

  1. 12/1024
  2. 11/1024
  3. 11/256
  4. 12/256

Quant Probability

A dice is rolled twice. What is the probability that the number in the second roll will be higher than that in the first?

  1. 5/36
  2. 8/36
  3. 15/36
  4. 21/36
  5. None of the above

Linear Equations

Consider the system of linear equation

x1 + 2x2 + x3 = 3

2x1 + 3x2 + x3 = 3

3x1 + 5x2 + 2x3 = 1

The system has

  1. Infinite no. of solutions
  2. No solution
  3. Unique solution
  4. Exactly 3 solutions

Linear Equations

The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x ≤ y is:

  1. 7
  2. 13
  3. 14
  4. 18

Linear Equations

Three times the first of three consecutive odd integers is 3 more than twice the third. What is the third integer?

  1. 5
  2. 9
  3. 11
  4. 15

Linear Equations

Which one of the following conditions must p, q and r satisfy so that the following system of linear simultaneous equations has at least one solution, such that p + q + r ≠ 0?

  • x + 2y - 3z = p
  • 2x + 6y - 11z = q
  • x - 2y + 7z = r
  1. 5p - 2q - r = 0
  2. 5p + 2q + r = 0
  3. 5p + 2q - r = 0
  4. 5p - 2q + r = 0

Linear Equations

If x and y are integers, then the equation 5x + 19y = 64 has

  1. A solution for -59 < y < -56
  2. No solution for x > 250 and y > -100
  3. A solution for 250 < x < 300
  4. No solution for x < 300 and y < 0

Linear Equations

Using only 2, 5, 10, 25, and 50 paisa coins, what will be the minimum number of coins required to pay exactly 78 paise, 69 paise and Rs. 1.01 to three different persons?

  1. 17
  2. 18
  3. 19
  4. 20

Linear Equations

What is the value of k for which the following system of equations has no solution: 2x –- 8y = 3 and kx + 4y = 10.

  1. 2
  2. -2
  3. -1
  4. 1

Linear Equations

Two oranges, three bananas and four apples cost Rs.15. Three oranges, two bananas and one apple cost Rs.10. I bought 3 oranges, 3 bananas and 3 apples. How much did I pay?

  1. Rs 8
  2. Rs 10
  3. Rs 12
  4. Rs 15

Linear Equations

In 2004, Rohini was thrice as old as her brother Arvind. In 2014, Rohini was only six years older than her brother. In which year was Rohini born?

  1. 1984
  2. 1986
  3. 1995
  4. 2000

Linear Equations

A firm is thinking of buying a printer for its office use for the next one year. The criterion for choosing is based on the least per-page printing cost. It can choose between an inkjet printer which costs Rs. 5000 and a laser printer which costs Rs. 8000. The per-page printing cost for an inkjet is Rs. 1.80 and that for a laser printer is Rs. 1.50. The firm should purchase the laser printer, if the minimum number of a pages to be printed in the year exceeds

  1. 5000
  2. 10000
  3. 15000
  4. 18000

Linear Equations

Hari’s family consisted of his younger brother (Chari), younger sister (Gouri), and their father and mother. When Chari was born, the sum of the ages of Hari, his father and mother was 70 years. The sum of the ages of four family members, at the time of Gouri’s birth, was twice the sum of ages of Hari’s father and mother at the time of Hari’s birth. If Chari is 4 years older than Gouri, then find the difference in age between Hari and Chari.

  1. 5 years
  2. 6 years
  3. 7 years
  4. 8 years
  5. 9 years

Averages

A car owner buys petrol at Rs. 7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?

  1. Rs. 8.50
  2. Rs. 9
  3. Rs. 8
  4. Rs. 7.98

Averages

A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?

  1. Rs. 4991
  2. Rs. 5991
  3. Rs. 6001
  4. Rs. 6991

Averages

A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is

  1. 250
  2. 276
  3. 280
  4. 285

Averages

A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is

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

Averages

The average marks of a student in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest.

  1. 55
  2. 60
  3. 62
  4. 64

Averages

The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is

  1. 3500
  2. 4000
  3. 4050
  4. 5000

Averages Linear Equations

The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

  1. 22 years
  2. 23 years
  3. 24 years
  4. 25 years

Averages

In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?

  1. 6.25
  2. 6.5
  3. 6.75
  4. 7

Averages

Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight-member joint family is nearest to

  1. 21 years
  2. 22 years
  3. 23 years
  4. 24 years

Averages

The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is

  1. Rs. 19
  2. Rs. 19.50
  3. Rs. 18
  4. Rs. 18.50

Averages

The average weight of 10 apples is 0.4 kg. If the heaviest and lightest apples are taken out, the average is 0.41 kg. If the lightest apple weights 0.2 kg, what is the weight of heaviest apple?

Averages Quant Sets

In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?

  1. 30
  2. 25
  3. 20
  4. 15
  5. None of the above

Averages

The average height of 22 toddlers increases by 2 inches when two of them leave this group. If the average height of these two toddlers is one-third the average height of the original 22, then the average height, in inches, of the remaining 20 toddlers is

  1. 30
  2. 28
  3. 32
  4. 26

Percentages

A report consists of 20 sheets each of 55 lines and each such line consist of 65 characters. This report is retyped into sheets each of 65 lines such that each line consists of 70 characters. The percentage reduction in number of sheets is closest to

  1. 5
  2. 20
  3. 30
  4. 35

Percentages

If a quantity is increased by 20% and then decreased by 10%, then what is the net increase or decrease?

  1. 10% Decrease
  2. 10% Increase
  3. 8% Increase
  4. 8% Decrease

Percentages

In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 95% of the products of M3 are not defective. What is the percentage of defective in the stockpile?

  1. 5%
  2. 4%
  3. 3%
  4. 2.5%

Percentages

The pre-paid recharge of Airtel gives 21% less talk time than the same price pre-paid recharge of Vodafone. The post-paid talk time of Airtel is 12% more than its pre-paid recharge, having the same price. Further, the post-paid talk time of same price of Vodafone is 15% less than its pre-paid recharge. How much percent less / more talk time can one get from the Airtel post-paid service compared to the post-paid service of Vodafone?

  1. 3.9% more
  2. 4.7% less
  3. 4.7% more
  4. 2.8% less

Percentages

As a strategy towards retention of customers, the service centre of a split AC machine manufacturer offers discount as per the following rule: for the second service in a year, the customer can avail of a 10% discount; for the third and fourth servicing within a year, the customer can avail of 11% and 12% discounts respectively of the previous amount paid, Finally, if a customer gets more than four services within a year, he has to pay just 55% of the original servicing charges. If Rohan has availed 5 services from the same service centre in a given year, the total percentage discount availed by him is approximately

  1. 16.52
  2. 20.88
  3. 22.33
  4. 24.08

Percentages

Out of the shirts produced in a factory, 15% are defective, while 20% of the rest are sold in the domestic market. If the remaining 8840 shirts are left for export, then the number of shirts produced in the factory is

  1. 13600
  2. 13000
  3. 13400
  4. 14000

Percentages

In a village, the production of food grains increased by 40% and the per capita production of food grains increased by 27% during a certain period. The percentage by which the population of the village increased during the same period is nearest to 

  1. 16
  2. 13
  3. 10
  4. 7