CAT Quantitative Ability Questions | CAT Set Theory questions

CAT/2020.2(Quantitative Ability)

Question. 1

Students in a college have to choose at least two subjects from chemistry, mathematics and physics. The number of students choosing all three subjects is 18, choosing mathematics as one of their subjects is 23 and choosing physics as one of their subjects is 25. The smallest possible number of students who could choose chemistry as one of their subjects is

CAT/2019.1(Quantitative Ability)

Question. 2

A club has 256 members of whom 144 can play football, 123 can play tennis, and 132 can play cricket. Moreover, 58 members can play both football and tennis, 25 can play both cricket and tennis, while 63 can play both football and cricket. If every member can play at least one game, then the number of members who can play only tennis is

CAT/2018.1(Quantitative Ability)

Question. 3

Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H is

CAT/2018.1(Quantitative Ability)

Question. 4

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

CAT/2018.2(Quantitative Ability)

Question. 5

For two sets A and B, let AΔB denote the set of elements which belong to A or B but not both. If P = {1,2,3,4}, Q = {2,3,5,6,}, R = {1,3,7,8,9}, S = {2,4,9,10}, then the number of elements in (PΔQ)Δ(RΔS) is

CAT/2018.2(Quantitative Ability)

Question. 6

If A = {6²ⁿ - 35n - 1: n = 1,2,3,...} and B = {35(n-1) : n = 1,2,3,...} then which of the following is true?

CAT/2004(Quantitative Ability)

Question. 7

Consider the sets T_n = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3, ............... , 96. How many of these sets contains 6 or any integral multiple thereof (i.e. any one of the numbers 6, 12, 18,............)?

CAT/2003(Quantitative Ability)

Question. 8

Let T be the set of integers { 3, 11, 19, 27 .....451, 459, 467} and S be a subset of T such that the sum of no two elements of S is 470. The maximum possible number of elements in S is

CAT/2003(Quantitative Ability)

Question. 9

What is the smallest positive integer n such that gⁿ = e?

CAT/2003(Quantitative Ability)

Question. 10

CAT/2003(Quantitative Ability)

Question. 11

CAT/2003(Quantitative Ability)

Question. 12

A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of the three popular options — air-conditioning, radio and power windows - were already installed. The survey found

15 had air conditioning

2 had air conditioning and power windows but no radios

12 had radio

6 had air-conditioning and radio but no power windows

11 had power windows

4 had radio and power windows

3 had all three options.

What is the number of cars that had none of the options?

CAT/2003(Quantitative Ability)

Question. 13

70 per cent of the employees in a multinational corporation have VCD players, 75 per cent have microwave ovens, 80 per cent have ACs and 85 per cent have washing machines. At least what percentage of employees has all four gadgets?

CAT/2002(Quantitative Ability)

Question. 14

 If Z = (P.D) ∪ M, then

CAT/2002(Quantitative Ability)

Question. 15

If P.A = Φ and P ∪ A = D, then which of the following is true?

CAT/2001(Quantitative Ability)

Question. 16

If Y = F.(D.V), is not a null set, it implies that :

CAT/2000(Quantitative Ability)

Question. 17

CAT/2000(Quantitative Ability)

Question. 18

Let ‘f’ be a function from set A to set B for a set, XCB define f^–1 (X) = {X ∈ A : f(X) ∈ X}  Then which of the following is necessarily true for a subset U of X?

CAT/2000(Quantitative Ability)

Question. 19

Given that X = M.D is such that X = D, which of the following is true?

CAT/1999(Quantitative Ability)

Question. 20

In a political survey, 78% of the politicians favour at least one proposal. 50% of them are in favour of proposal A, 30% are in favour of proposal B and 20% are in favour of proposal C. 5% are in favour of all three proposals. What is the percentage of people favouring more than one proposal?

CAT/1997(Quantitative Ability)

Question. 21

A survey of 200 people in a community who watched at least one of the three channels — BBC, CNN and DD — showed that 80% of the people watched DD, 22% watched BBC, and 15% watched CNN.

What is the maximum percentage of people who can watch all the three channels?

CAT/1997(Quantitative Ability)

Question. 22

A survey of 200 people in a community who watched at least one of the three channels — BBC, CNN and DD — showed that 80% of the people watched DD, 22% watched BBC, and 15% watched CNN.

If 5% of the people watched DD and CNN, 10% watched DD and BBC, then what per cent of the people watched BBC and CNN only?

CAT/1997(Quantitative Ability)

Question. 23

A survey of 200 people in a community who watched at least one of the three channels — BBC, CNN and DD — showed that 80% of the people watched DD, 22% watched BBC, and 15% watched CNN.

Referring to the previous question, how many per cent of the people watched all the three channels?

CAT/1996(Quantitative Ability)

Question. 24

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 ?

CAT/1995(Quantitative Ability)

Question. 25

There are three different cable channels namely Ahead, Luck and Bang. In a survey it was found that 85% of viewers respond to Bang, 20 % to Luck, and 30% to Ahead. 20% of viewers respond to exactly two channels and 5% to none.

What percentage of the viewers responded to all three ?

CAT/1995(Quantitative Ability)

Question. 26

There are three different cable channels namely Ahead, Luck and Bang. In a survey it was found that 85% of viewers respond to Bang, 20 % to Luck, and 30% to Ahead. 20% of viewers respond to exactly two channels and 5% to none.

Assuming 20% respond to Ahead and Bang and 16% respond to Bang and Luck, what is the percentage of viewers who watch only Luck ?

CAT/1994(Quantitative Ability)

Question. 27

Ghoshbabu is staying at Ghosh Housing Society, Aghosh Colony, Dighoshpur, Calcutta. In Ghosh Housing Society 6 persons read daily Ganashakti and 4 read Anand Bazar Patrika; In his colony there is no person who reads both. Total number of persons who read these two newspapers in Aghosh Colony and Dighoshpur is 52 and 200 respectively. Number of persons who read Ganashakti in Aghosh Colony and Dighoshpur is 33 and 121 respectively; while the persons who read Anand Bazar Patrika in Aghosh Colony and Dighoshpur are 32 and 117 respectively.

Number of persons in Dighoshpur who read only Ganashakti is

CAT/1994(Quantitative Ability)

Question. 28

Ghoshbabu is staying at Ghosh Housing Society, Aghosh Colony, Dighoshpur, Calcutta. In Ghosh Housing Society 6 persons read daily Ganashakti and 4 read Anand Bazar Patrika; In his colony there is no person who reads both. Total number of persons who read these two newspapers in Aghosh Colony and Dighoshpur is 52 and 200 respectively. Number of persons who read Ganashakti in Aghosh Colony and Dighoshpur is 33 and 121 respectively; while the persons who read Anand Bazar Patrika in Aghosh Colony and Dighoshpur are 32 and 117 respectively.

Number of persons in Aghosh Colony who read both of these newspapers is

CAT/1994(Quantitative Ability)

Question. 29

Ghoshbabu is staying at Ghosh Housing Society, Aghosh Colony, Dighoshpur, Calcutta. In Ghosh Housing Society 6 persons read daily Ganashakti and 4 read Anand Bazar Patrika; In his colony there is no person who reads both. Total number of persons who read these two newspapers in Aghosh Colony and Dighoshpur is 52 and 200 respectively. Number of persons who read Ganashakti in Aghosh Colony and Dighoshpur is 33 and 121 respectively; while the persons who read Anand Bazar Patrika in Aghosh Colony and Dighoshpur are 32 and 117 respectively.

Number of persons in Aghosh Colony who read only one newspaper