CAT Quant Questions

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%.

How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest

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?

4 years
4.5 years
5 years
5.5 years

A certain sum of money invested at some rate of simple interest triple

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?

In a locality, two-thirds of the people have cable TV, one-fifth have VCR, and one-tenth have both

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?

23/30
2/3
17/30
19/30

In a certain village, 22% of the families own agricultural land, 18% own a mobile phone

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

20000
10000
8000
5000

A five digit number is formed using digits 1, 3, 5, 7 and 9 without repeating any one of them

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?

6666666
6666600
6666660
6666000

A man has 9 friends: 4 boys and 5 girls. In how many ways can he invite them

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?

Consider the five points comprising of the vertices of a square and the intersection point of its diagonals

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?

Boxes numbered 1, 2, 3, 4 and 5 are kept in a row, and they which are to be filled

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?

How many five-digit numbers can be formed using the digits 2, 3, 8, 7, 5 exactly

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?

In a six-node network, two nodes are connected to all the other nodes

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?

In how many ways can eight directors, the vice chairman and chairman of a firm be seated at a round table

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?

9! × 2
2 × 7!
2 × 8!
2 × 6!

Let S be the set of five-digit numbers formed by digits 1, 2, 3, 4 and 5

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?

Ten points are marked on a straight-line and 11 points are marked on another straight-line

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?

495
550
1045
2475

There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2

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?

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

Quant PnC

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

During the essay writing stage of MBA admission process in a reputed B-School

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

3540340
2874590
2903040
None of the above

In the board meeting of a FMCG Company, everybody present in the meeting shakes hand with everybody else

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

Ramesh plans to order a birthday gift for his friend from an online retailer

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?

0.004
0.006
0.216
0.994
0.996

If a 4 digit number is formed with digits 1, 2, 3 and 5. What is the probability

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?

1/12
1/6
1/8
1/4

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

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

One card is drawn from a pack of 52 cards

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

There are 4 red & 5 green balls in bag A and 5 red & 6 green balls in bag B

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?

The internal evaluation for Economics course in an Engineering programme is based on the score of four quizzes

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?

12/1024
11/1024
11/256
12/256

A dice is rolled twice. What is the probability that the number

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?

5/36
8/36
15/36
21/36
None of the above

Consider the system of linear equation: x1 + 2x2 + x3 = 3

Linear Equations

Consider the system of linear equation

x₁ + 2x₂ + x₃ = 3

2x₁ + 3x₂ + x₃ = 3

3x₁ + 5x₂ + 2x₃ = 1

The system has

Infinite no. of solutions
No solution
Unique solution
Exactly 3 solutions

The number of solutions of the equation 2x + y = 40 where both x and y

Linear Equations

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

Three times the first of three consecutive odd integers is 3 more than twice

Linear Equations

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

Which one of the following conditions must p, q and r satisfy so that the following system

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

5p - 2q - r = 0
5p + 2q + r = 0
5p + 2q - r = 0
5p - 2q + r = 0

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

Linear Equations

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

A solution for -59 < y < -56
No solution for x > 250 and y > -100
A solution for 250 < x < 300
No solution for x < 300 and y < 0

Using only 2, 5, 10, 25, and 50 paisa coins, what will be the minimum number of coins

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?

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

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.

2
-2
-1
1

Two oranges, three bananas and four apples cost Rs.15. Three oranges, two bananas

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?

Rs 8
Rs 10
Rs 12
Rs 15

In 2004, Rohini was thrice as old as her brother Arvind

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?

1984
1986
1995
2000

A firm is thinking of buying a printer for its office use for the next one year

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

5000
10000
15000
18000

Hari’s family consisted of his younger brother (Chari), younger sister (Gouri)

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.

5 years
6 years
7 years
8 years
9 years

A car owner buys petrol at Rs. 7.50, Rs. 8 and Rs. 8.50 per litre

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?

Rs. 8.50
Rs. 9
Rs. 8
Rs. 7.98

A grocer has a sale of Rs.6435, Rs.6927, Rs.6855, Rs.7230 and Rs.6562 for 5 consecutive months

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?

Rs. 4991
Rs. 5991
Rs. 6001
Rs. 6991

A library has an average of 510 visitors on Sundays and 240 on other days

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

A student took five papers in an examination, where the full marks were the same

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

The average marks of a student in 10 papers are 80. If the highest

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.

The average monthly income of P and Q is Rs. 5050. The average monthly income

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

3500
4000
4050
5000

The captain of a cricket team of 11 members is 26 years old and the wicket keeper

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?

22 years
23 years
24 years
25 years

In the first 10 overs of a cricket game, the run rate was only 3.2

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?

6.25
6.5
6.75
7

Page 2 of 5