Venn Diagram - Previous Year CAT/MBA Questions

The best way to prepare for Venn Diagram is by going through the previous year Venn Diagram CAT questions. Here we bring you all previous year Venn Diagram CAT questions along with detailed solutions.

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1. CAT 2024 QA Slot 3 | Venn Diagram CAT Question

In a group of 250 students, the percentage of girls was at least 44% and at most 60%. The rest of the students were boys. Each student opted for either swimming or running or both. If 50% of the boys and 80% of the girls opted for swimming while 70% of the boys and 60% of the girls opted for running, then the minimum and maximum possible number of students who opted for both swimming and running, are

(a)
75 and 90, respectively
(b)
72 and 80, respectively
(c)
75 and 96, respectively
(d)
72 and 88, respectively

2. CAT 2022 QA Slot 1 | Venn Diagram CAT Question

In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks is

(a)
52
(b)
47
(c)
48
(d)
53

3. CAT 2020 QA Slot 2 | Venn Diagram CAT Question

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

(a)
21
(b)
20
(c)
19
(d)
22

4. CAT 2020 QA Slot 3 | Venn Diagram CAT Question

How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

(a)
42
(b)
41
(c)
40
(d)
43

5. CAT 2019 QA Slot 1 | Venn Diagram CAT Question

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

(a)
45
(b)
43
(c)
32
(d)
38

6. CAT 2018 QA Slot 1 | Venn Diagram CAT Question

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

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7 8 9 4 5 6 1 2 3 0 . -

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7. CAT 2018 QA Slot 1 | Venn Diagram CAT Question

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

(a)
26
(b)
96
(c)
93
(d)
23

8. CAT 2006 QA | Venn Diagram CAT Question

A survey was conducted of 100 people to find out whether they had read recent issues of Golmal, a monthly magazine. The summarized information regarding readership in 3 months is given below:

Only September: 18; September but not August: 23; September and July: 8; September: 28; July: 48; July and August: 10; None of the three months: 24.

What is the number of surveyed people who have read exactly two consecutive issues (out of the three)?

(a)
7
(b)
9
(c)
12
(d)
14
(e)
17

Answer the following question based on the information given below.

New Age Consultants have three consultants Gyani, Medha and Buddhi. The sum of the number of projects handled by Gyani and Buddhi individually is equal to the number of projects in which Medha is involved. All three consultants are involved together in 6 projects. Gyani works with Medha in 14 projects. Buddhi has 2 projects with Medha but without Gyani and 3 projects with Gyani but without Medha. The total number of projects for New Age Consultants is one less than twice the number of projects in which more than one consultant is involved.

9. CAT 2003 QA - Leaked | Venn Diagram CAT Question

What is the number of projects in which Gyani alone is involved?

(a)
Uniquely equal to zero
(b)
Uniquely equal to 1
(c)
Uniquely equal to 4
(d)
Cannot be determined uniquely

10. CAT 2003 QA - Leaked | Venn Diagram CAT Question

What is the number of projects in which Medha alone is involved?

(a)
Uniquely equal to zero
(b)
Uniquely equal to 1
(c)
Uniquely equal to 4
(d)
Cannot be determined uniquely

11. CAT 2003 QA - Retake | Venn Diagram CAT Question

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 and
3 had all three options.

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

(a)
4
(b)
3
(c)
1
(d)
2

12. CAT 2002 QA | Venn Diagram CAT Question

Each question is followed by two statements A and B. Answer each question using the following instructions:

Answer (1) if the question can be solved by any one of the statements, but not the other one.
Answer (2) if the question can be solved by using either of the two statements.
Answer (3) if the question can be solved by using both the statements together and not by any one of them.
Answer (4) if the question cannot be solved with the help of the given data and more data is required.

Members in a club either speak French or Russian or both. Find the number of members in a club who speak only French.

A. There are 300 members in the club and the number of members who speak both French and Russian is 196.
B. The number of members who speak only Russian is 58.

(a)
1
(b)
2
(c)
3
(d)
4

13. CAT 2000 QA | Venn Diagram CAT Question

Choose 1; if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
Choose 2; if the question can be answered by using either statement alone.
Choose 3; if the question can be answered by using both statements together, but cannot be answered using either statement alone.
Choose 4; if the question cannot be answered even by using both statements together.

How many people are watching TV programme P?

Number of people watching TV programme Q is 1000 and number of people watching both the programmes, P and Q, is 100.
Number of people watching either P or Q or both is 1500.

(a)
1
(b)
2
(c)
3
(d)
4

14. CAT 1999 QA | Venn Diagram CAT Question

In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III.

50% of those asked favoured proposal I, 30% favoured proposal II and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one of the three proposals?

(a)
10
(b)
12
(c)
17
(d)
22

Direction: Answer the questions based on the following information.

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.

15. CAT 1997 QA | Venn Diagram CAT Question

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

(a)
12.5%
(b)
8.5%
(c)
15%
(d)
Data insufficient

Answer: Option B

Text Explanation :

Here, a + b + c + d + e + f + g = 200 ...(i)
80% of the people watch DD implies
c + d + f + g = 160 ...(ii)
22% of the people watch BBC implies
a + d + e + g = 44 ...(iii)
15% of the people watch CNN implies
b + e + f + g = 30 ...(iv)
(ii) + (iii) + (iv) gives
a + b + c + 2(d + e + f) + 3g = 234
Subtracting (i) from this equation,
d + e + f + 2g = 34 ...(v)

To maximize g, in equation (v), we put d = e = f = 0
∴ Maximum value of g = $\frac{34}{2}$ = 17

∴ Required percentage = $\frac{17}{200}$ × 100 = 8.5%

Hence, option (b).

16. CAT 1997 QA | Venn Diagram CAT Question

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

(a)
2%
(b)
5%
(c)
8.5%
(d)
Cannot be determined

Answer: Option A

Text Explanation :

5% of people watch DD and CNN implies
f + g = 10 ...(vi)
10% of people watch DD and BBC implies
d + g = 20 ...(vii)
(v) – (vi) – (vii) gives
e = 4
∴ Required percentage = $\frac{4}{200}$ × 100 = 2%

17. CAT 1997 QA | Venn Diagram CAT Question

Referring to the previous question, what percentage of people watched all the three channels?

(a)
3.5%
(b)
0%
(c)
8.5%
(d)
Cannot be determined

18. CAT 1996 QA | Venn Diagram CAT Question

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?

(a)
$\frac{19}{30}$
(b)
$\frac{2}{3}$
(c)
$\frac{17}{30}$
(d)
$\frac{23}{30}$

Answer: Option D

Video Explanation

Text Explanation :

Probability of people having cable-TV = 2/3
Probability of people having VCR = 1/5
Probability of people having both = 1/10

∴ Probability of people having cable TV or VCR = $\frac{2}{3} + \frac{1}{15} - \frac{1}{10}$ = $\frac{20 + 6 - 3}{30}$ = $\frac{23}{30}$

Hence, option (d).

Answer the next 3 questions based on the information given below:

Ghoshbabu is staying at Ghosh Housing Society, Aghosh Colony, Dighospur, 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 Dighospur is 52 and 200 respectively. Number of persons who read Ganashakti in Aghosh Colony and Dighospur is 33 and 121 respectively; while the persons who read Anand Bazar Patrika in Aghosh Colony and Dighospur are 32 and 117 respectively.

19. CAT 1994 QA | Venn Diagram CAT Question

Number of persons in Dighospur who read only Ganashakti is

(a)
121
(b)
83
(c)
79
(d)
127

20. CAT 1994 QA | Venn Diagram CAT Question

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

(a)
13
(b)
20
(c)
19
(d)
14

21. CAT 1994 QA | Venn Diagram CAT Question

Number of persons in Aghosh Colony who read only one paper

(a)
29
(b)
19
(c)
39
(d)
20

22. CAT 1993 QA | Venn Diagram CAT Question

Out of 100 families in the neighbourhood, 45 own radios, 75 have TVs, 25 have VCRs. Only 10 families have all three and each VCR owner also has a TV. If 25 families have radio only, how many have only TV?

(a)
30
(b)
35
(c)
40
(d)
45

23. CAT 1993 QA | Venn Diagram CAT Question

Amar, Akbar, and Anthony came from the same public school in the Himalayas. Every boy in that school either fishes for trout or plays frisbee. All fishermen like snow while no frisbee player likes rain. Amar dislikes whatever Akbar likes and likes whatever Akbar dislikes. Akbar likes rain and snow. Anthony likes whatever the other two like. Who is a fisherman but not a frisbee player?

(a)
Amar
(b)
Akbar
(c)
Anthony
(d)
None

24. CAT 1991 QA | Venn Diagram CAT Question

Fifty college teachers are surveyed as to their possession of colour TV, VCR and tape recorder. Of them, 22 own colour TV, 15 own VCR and 14 own tape recorders. Nine of these college teachers own exactly two items out of colour TV, VCR and tape recorder; and, one college teacher owns all three. How many of the 50 teachers own none of the three, colour TV, VCR or tape recorder?

(a)
4
(b)
9
(c)
10
(d)
11

Answer the following questions based on the information given below:

There were a hundred schools in a town. Of these, the number of schools having a play – ground was 30, and these schools had neither a library nor a laboratory. The number of schools having a laboratory alone was twice the number of those having a library only. The number of schools having a laboratory as well as a library was one fourth the number of those having a laboratory alone. The number of schools having either a laboratory or a library or both was 35.

25. CAT 1991 QA | Venn Diagram CAT Question

How many schools had none of the three viz., laboratory, library or play – ground?

(a)
20
(b)
5
(c)
30
(d)
35

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Venn Diagram - Previous Year CAT/MBA Questions

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