CAT Quantitative Ability Questions | CAT Permutation, Combination and Probability questions

CAT/2022.1(Quantitative Ability)

Question. 1

The number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is

CAT/2021.1(Quantitative Ability)

Question. 2

The number of groups of three or more distinct numbers that can be chosen from 1, 2, 3, 4, 5, 6, 7, and 8 so that the groups always include 3 and 5, while 7 and 8 are never included together is

CAT/2021.2(Quantitative Ability)

Question. 3

A box has 450 balls, each either white or black, there being as many metallic white balls as metallic black balls. If 40% of the white balls and 50% of the black balls are metallic, then the number of non-metallic balls in the box is

CAT/2021.2(Quantitative Ability)

Question. 4

The number of ways of distributing 15 identical balloons, 6 identical pencils and 3 identical erasers among 3 children, such that each child gets at least four balloons and one pencil, is

CAT/2020.3(Quantitative Ability)

Question. 5

How many integers in the set {100, 101, 102, ..., 999} have at least one digit repeated?

CAT/2018.2(Quantitative Ability)

Question. 6

In a tournament, there are 43 junior level and 51 senior level participants. Each pair of juniors play one match. Each pair of seniors play one match. There is no junior versus senior match. The number of girl versus girl matches in junior level is 153, while the number of boy versus boy matches in senior level is 276. The number of matches a boy plays against a girl is 

CAT/2017.1(Quantitative Ability)

Question. 7

In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers?

CAT/2017.2(Quantitative Ability)

Question. 8

In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?

CAT/2017.2(Quantitative Ability)

Question. 9

How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position?

CAT/2008(Quantitative Ability)

Question. 10

How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed?

Comprehension

The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town.

 

 

 

 

 

CAT/2008(Quantitative Ability)

Question. 11

Neelam rides her bicycle from her house at A to her office at B, taking the shortest path. Then the number of possible shortest paths that she can choose is

Comprehension

The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town.

 

 

 

 

 

CAT/2008(Quantitative Ability)

Question. 12

Neelam rides her bicycle from her house at A to her club at C, via B taking the shortest path. Then the number of possible shortest paths that she can choose is

CAT/2008(Quantitative Ability)

Question. 13

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

CAT/2006(Quantitative Ability)

Question. 14

A group of 630 children is arranged in rows for a group photograph session. Each row contains three fewer children than the row in front of it. What number of rows is not possible?

CAT/2006(Quantitative Ability)

Question. 15

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?

CAT/2005(Quantitative Ability)

Question. 16

Three Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. Theyneed to exchange these secrets over person-to-person phone calls so that eventually each person knows all six secrets. None ofthe Frenchmen knows English, and only one Englishman knows French. What is the minimum number of phone calls needed forthe above purpose?

CAT/2005(Quantitative Ability)

Question. 17

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

CAT/2005(Quantitative Ability)

Question. 18

Let n! = 1 × 2 × 3 × ..... × n for integer n≥1. If p = 1! + (2 × 2!) + (3 × 3!) + ..... + (10 × 10!), then p + 2 when divided by 11! leavesa remainder of

CAT/2005(Quantitative Ability)

Question. 19

Let S be a set of positive integers such that every element n of S satisfies the conditions

1. 1000 ≤ n ≤ 1200

2. every digit of n is odd

Then how many elements of S are divisible by 3?

CAT/2005(Quantitative Ability)

Question. 20

In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every other student. It was found that in 45 games both the players were girls, and in 190 games both were boys. The number of games in which one player was a boy and the other was a girl is

CAT/2005(Quantitative Ability)

Question. 21

For which value of k does the following pair of equations yield a unique solution of x such that the solution is positive?

x² – y² =  0

(x – k)² + y² = 1

CAT/2004(Quantitative Ability)

Question. 22

N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other,sings a two-minute song one pair after the other. If the total time taken for singing is 28 minutes, what is N?

CAT/2004(Quantitative Ability)

Question. 23

Suppose n is an integer such that the sum of the digits of n is 2, and 10¹⁰ < n < 10¹¹. The number of different values for n is

CAT/2004(Quantitative Ability)

Question. 24

Each family in a locality has at most two adults, and no family has fewer than 3 children. Considering all the families together, thereare more adults than boys, more boys than girls, and more girls than families. Then the minimum possible number of families inthe locality is

CAT/2004(Quantitative Ability)

Question. 25

In the adjoining figure, the lines represent one-way roads allowing travel only northwards or only westwards. Along how manydistinct routes can a car reach point B from point A?

CAT/2004(Quantitative Ability)

Question. 26

A new flag is to be designed with six vertical stripes using some or all of the colours yellow, green, blue and red. Then, the numberof ways this can be done such that no two adjacent stripes have the same colour out is

CAT/2003(Quantitative Ability)

Question. 27

Twenty-seven persons attend a party. Which one of the following statements can never be true?

CAT/2003(Quantitative Ability)

Question. 28

How many three digit positive integers, with digits x, y and z in the hundred’s, ten’s and unit’s place respectively, exist such that x<y, z< y and x≠0?

CAT/2003(Quantitative Ability)

Question. 29

There are 6 boxes numbered 1,2,.........6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 boxcontains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which thiscan be done is

CAT/2003(Quantitative Ability)

Question. 30

A graph may be defined as a set of points connected by lines called edges. Every edge connects a pair of points. Thus, a triangleis a graph with 3 edges and 3 points. The degree of a point is the number of edges connected to it. For example, a triangle is agraph with three points of degree 2 each. Consider a graph with 12 points. It is possible to reach any point from any other pointthrough a sequence of edges. The number of edges, e, in the graph must satisfy the condition

Comprehension

Directions for questions: Read the information given below and answer the questions that follow :

A string of three English letters is formed as per the following rules :

(a) The first letter is any vowel.

(b) The second letter is m, n or p

(c) If the second letter is m then the third letter is any vowel which is different from the first letter

(d) If the second letter is n then the third letter is e or u.

(e) If second letter is p then the third letter is the same as the first letter

CAT/2003(Quantitative Ability)

Question. 31

How many strings of letters can possibly be formed using the above rules?

Comprehension

Directions for questions: Read the information given below and answer the questions that follow :

A string of three English letters is formed as per the following rules :

(a) The first letter is any vowel.

(b) The second letter is m, n or p

(c) If the second letter is m then the third letter is any vowel which is different from the first letter

(d) If the second letter is n then the third letter is e or u.

(e) If second letter is p then the third letter is the same as the first letter

CAT/2003(Quantitative Ability)

Question. 32

How many strings of letters can possibly be formed using the above rules such that the third letter of the string is e?

CAT/2003(Quantitative Ability)

Question. 33

There are 12 towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone linessuch that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct lineotherwise. How many direct telephone lines are required?

CAT/2003(Quantitative Ability)

Question. 34

An intelligence agency forms a code of two distinct digits selected from 0, 1, 2, ............ , 9 such that the first digit of the code isnonzero. The code, handwritten on a slip, can however potentially create confusion when read upside down –– for example, thecode 91 may appear as 16. How many codes are there for which no such confusion can arise?

CAT/2002(Quantitative Ability)

Question. 35

10 straight lines, no two of which are parallel and no three of which pass through any common point, are drawn on a plane. Thetotal number of regions (including finite and infinite regions) into which the plane would be divided by the lines is

Comprehension

Directions for questions: Read the information given below and answer the questions that follow :

Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters.Other letters in the alphabet are asymmetric letters.

CAT/2002(Quantitative Ability)

Question. 36

How many four-letter computer passwords can be formed using only the symmetric letters (no repetition allowed)?

Comprehension

Directions for questions: Read the information given below and answer the questions that follow :

Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters.Other letters in the alphabet are asymmetric letters.

CAT/2002(Quantitative Ability)

Question. 37

How many three-letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?

CAT/2002(Quantitative Ability)

Question. 38

In how many ways is it possible to choose a white square and a black square on a chess board so that the squares must not liein the same row or column?

CAT/2002(Quantitative Ability)

Question. 39

How many numbers greater than 0 and less than a million can be formed with the digits of 0, 7 and 8?

CAT/2002(Quantitative Ability)

Question. 40

If there are 10 positive real numbers n1 < n2 < n3 ... < n10. How many triplets of these numbers (n1, n2, n3), (n2, n3, n4), ... can begenerated such that in each triplet the first number is always less than the second number, and the second number is always lessthan the third number?

CAT/2002(Quantitative Ability)

Question. 41

If there are 10 positive real numbers n₁ < n₂ < n₃ ...... < n10. How many triplets of these numbers (n₁, n₂, n₃), (n₂, n₃, n₄), ..... canbe generated such that in each triplet the first number is always less than the second number and the second number is alwaysless than the third number?

CAT/2001(Quantitative Ability)

Question. 42

A red light flashes 3 times per minute and a green light flashes 5 times in two minutes at regular intervals. If both lights startflashing at the time, how many times do they flash together in each hour?

CAT/2001(Quantitative Ability)

Question. 43

Ashish is given Rs. 158 in one rupee denominations. He has been asked to allocate them into a number of bags such that anyamount required between Re. 1 and Rs. 158 can be given by handing out a certain number of bags without opening them. Whatis the minimum number of bags required?

CAT/2001(Quantitative Ability)

Question. 44

The figure below shows the network connecting cities A, B, C, D, E and F. The arrows indicate permissible direction of travel.What is the number of distinct paths from A to F?

CAT/2001(Quantitative Ability)

Question. 45

Let n be the number of different 5 digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5, and 6, no digit being repeated in thenumbers. What is the value of n?

CAT/2000(Quantitative Ability)

Question. 46

Sameer has to make a telephone call to his friend Harish Unfortunately he does not remember the 7- digit phone number. But he remembers that the first 3 digits are 635 or 674, the number is odd and there is exactly one 9 in the number. The minimum number of trials that Sameer has to make to be successful is

CAT/2000(Quantitative Ability)

Question. 47

There are three books on table A which has to be moved to table B. The order of the book on Table A was 1, 2, 3, with book 1 at the bottom. The order of the book on table B should be with book 2 on top and book 1 on bottom. Note that you can pick up the books in the order they have been arranged. You can’t remove the books from the middle of the stack. In how many minimum steps can we place the books on table B in the required order?

CAT/2000(Quantitative Ability)

Question. 48

X is an odd integer such that 100 < x < 200 and x is divisible by 3 but not 7. The possible number of values of x is

CAT/2000(Quantitative Ability)

Question. 49

One red, three white and two blue flags are to be arranged in such a way that no two flags of the same colour are adjacent and theflags at the two ends are of different colours. The number of ways in which this can be done is

Comprehension

Directions for questions: Read the information given below and answer the questions that follow :

The tournament for ABC Cup is arranged as per the following rules: in the beginning 16 teams are entered and divided in 2 groupsof 8 teams each where the team in any group plays exactly once with all the teams in the same group. At the end of this round topfour teams from each group advance to the next round in which two teams play each other and the losing team goes out of thetournament. The rules of the tournament are such that every match can result only in a win or a loss and not in a tie. The winnerin the first round takes one point from the win and the loser gets zero. In case of tie on a position the rules are very complex andinclude a series of deciding measures.

CAT/2000(Quantitative Ability)

Question. 50

What is the total number of matches played in the tournament?

Comprehension

Directions for questions: Read the information given below and answer the questions that follow :

The tournament for ABC Cup is arranged as per the following rules: in the beginning 16 teams are entered and divided in 2 groupsof 8 teams each where the team in any group plays exactly once with all the teams in the same group. At the end of this round topfour teams from each group advance to the next round in which two teams play each other and the losing team goes out of thetournament. The rules of the tournament are such that every match can result only in a win or a loss and not in a tie. The winnerin the first round takes one point from the win and the loser gets zero. In case of tie on a position the rules are very complex andinclude a series of deciding measures.

CAT/2000(Quantitative Ability)

Question. 51

The maximum number of matches that a team going out of the tournament in the first round itself can win is

Comprehension

Directions for questions: Read the information given below and answer the questions that follow :

The tournament for ABC Cup is arranged as per the following rules: in the beginning 16 teams are entered and divided in 2 groupsof 8 teams each where the team in any group plays exactly once with all the teams in the same group. At the end of this round topfour teams from each group advance to the next round in which two teams play each other and the losing team goes out of thetournament. The rules of the tournament are such that every match can result only in a win or a loss and not in a tie. The winnerin the first round takes one point from the win and the loser gets zero. In case of tie on a position the rules are very complex andinclude a series of deciding measures.

CAT/2000(Quantitative Ability)

Question. 52

The minimum number of matches that a team must win in order to qualify for the second round is

Comprehension

Directions for questions: Read the information given below and answer the questions that follow :

The tournament for ABC Cup is arranged as per the following rules: in the beginning 16 teams are entered and divided in 2 groupsof 8 teams each where the team in any group plays exactly once with all the teams in the same group. At the end of this round topfour teams from each group advance to the next round in which two teams play each other and the losing team goes out of thetournament. The rules of the tournament are such that every match can result only in a win or a loss and not in a tie. The winnerin the first round takes one point from the win and the loser gets zero. In case of tie on a position the rules are very complex andinclude a series of deciding measures.

CAT/2000(Quantitative Ability)

Question. 53

Which of the following statements about a team which has already qualified for the second round is true?

CAT/2000(Quantitative Ability)

Question. 54

There are five boxes each of a different weight and none weighing more than 100. Arun weights two boxes at a time and obtainsthe following readings in grams : 110, 112, 113, 114, 116, 117, 118, 119, 120, 121. What is the weight of the heaviest box?

CAT/1999(Quantitative Ability)

Question. 55

Five persons A, B, C, D and E along with their wives are seated around a round table such that no two men are adjacent to each other. The wives are three places away from their husbands. Mrs. C is on the left of Mr. A, Mrs. E is two places to the right of Mrs. B. Then, who is on the right hand side of Mr. A?

CAT/1999(Quantitative Ability)

Question. 56

There are 10 points on a line and 11 points on another line, which are parallel to each other. How many triangles can be drawn taking the vertices on any of the line?

CAT/1999(Quantitative Ability)

Question. 57

There are three boxes with 2 red, 2 white and one red and one white ball. All of them are mislabelled. You have to correct all the labels by picking only one ball from any one of the boxes. Which is the box that you would like to open

CAT/1999(Quantitative Ability)

Question. 58

Out of 2n+1 students, n students have to be given the scholarships. The number of ways in which at least one student can begiven the scholarship is 63. What is the number of students receiving the scholarship?

CAT/1998(Quantitative Ability)

Question. 59

How many numbers can be formed from 1,2,3,4 and 5 (without repetition), when the digit at the units place must be greater than that in the tenth place?

CAT/1998(Quantitative Ability)

Question. 60

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

CAT/1998(Quantitative Ability)

Question. 61

A, B, C, D, ..................X, Y, Z are the players who participated in a tournament. Everyone played with every other player exactly once. A win scores 2 points, a draw scores 1 point and a loss scores 0 points. None of the matches ended in a draw. No two players scored the same score. At the end of the tournament, the ranking list is published which is in accordance with the alphabetical order. Then

CAT/1997(Quantitative Ability)

Question. 62

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

CAT/1997(Quantitative Ability)

Question. 63

ABC is a three-digit number in which A > 0. The value of ABC is equal to the sum of the factorials of its three digits. What is the value of B?

CAT/1996(Quantitative Ability)

Question. 64

A man has nine friends – four boys and five girls. In how many ways can he invite them, if there have to be exactly three girls in the invitees?

CAT/1995(Quantitative Ability)

Question. 65

A,B,C and D are four towns any three of which are non-colinear. Then the number of ways to construct three roads each joining a pair of towns so that the roads do not form a triangle is

CAT/1995(Quantitative Ability)

Question. 66

Boxes numbered 1, 2, 3, 4 and 5 are kept in a row and they 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?

CAT/1994(Quantitative Ability)

Question. 67

I. The probability of encountering 54 Sundays in a leap year 

II. The probability of encountering 53 Sundays in a non-leap year