Venn Diagrams Practice Test for Verbal Reasoning -- Free Practice

Question 1

Study the diagram below and answer the question.

a Venn diagram of three overlapping circles labelled Swimmers, Cyclists and Runners, with a number in each of the seven regions

a Venn diagram of three overlapping circles labelled Swimmers, Cyclists and Runners, with a number in each of the seven regions

How many swimmers are neither cyclists nor runners?

A

13✓✗

B

21✓✗

C

29✓✗

D

26✓✗

Explanation

The number in the part of the Swimmers circle that lies outside the other two circles is 21.

Question 2

Study the diagram below and answer the question.

a Venn diagram of three overlapping circles labelled Swimmers, Cyclists and Runners, with a number in each of the seven regions

How many cyclists are neither swimmers nor runners?

A

18✓✗

B

21✓✗

C

16✓✗

D

13✓✗

Explanation

The number in the part of the Cyclists circle that lies outside the other two circles is 13.

Question 3

Study the diagram below and answer the question.

a Venn diagram of three overlapping circles labelled Swimmers, Cyclists and Runners, with a number in each of the seven regions

How many swimmers are cyclists?

A

5✓✗

B

15✓✗

C

7✓✗

D

21✓✗

Explanation

Swimmers who are cyclists are in the overlap of those two circles, which has two parts: 5 (not runners) and 2 (also runners). Total = 5 + 2 = 7.

Question 4

Study the diagram below and answer the question.

a Venn diagram of three overlapping circles labelled Swimmers, Cyclists and Runners, with a number in each of the seven regions

How many runners are both cyclists and swimmers?

A

5✓✗

B

2✓✗

C

3✓✗

D

8✓✗

Explanation

Those who belong to all three groups are in the centre, where all three circles overlap. That number is 2.

Question 5

Study the diagram below and answer the question.

a Venn diagram of three overlapping circles labelled Swimmers, Cyclists and Runners, with a number in each of the seven regions

How many runners are neither swimmers nor cyclists?

A

17✓✗

B

25✓✗

C

3✓✗

D

30✓✗

Explanation

The number in the part of the Runners circle that lies outside the other two circles is 17.

Question 6

Study the diagram below and answer the question.

a Venn diagram of three overlapping circles labelled Singers, Dancers and Actors, with a number in each of the seven regions

a Venn diagram of three overlapping circles labelled Singers, Dancers and Actors, with a number in each of the seven regions

How many singers are neither dancers nor actors?

A

19✓✗

B

14✓✗

C

22✓✗

D

20✓✗

Explanation

The number in the part of the Singers circle that lies outside the other two circles is 14.

Question 7

Study the diagram below and answer the question.

a Venn diagram of three overlapping circles labelled Singers, Dancers and Actors, with a number in each of the seven regions

How many dancers are neither singers nor actors?

A

25✓✗

B

14✓✗

C

28✓✗

D

19✓✗

Explanation

The number in the part of the Dancers circle that lies outside the other two circles is 19.

Question 8

Study the diagram below and answer the question.

a Venn diagram of three overlapping circles labelled Singers, Dancers and Actors, with a number in each of the seven regions

How many singers are dancers?

A

6✓✗

B

18✓✗

C

10✓✗

D

14✓✗

Explanation

Singers who are dancers are in the overlap of those two circles, which has two parts: 6 (not actors) and 4 (also actors). Total = 6 + 4 = 10.

Question 9

Study the diagram below and answer the question.

a Venn diagram of three overlapping circles labelled Singers, Dancers and Actors, with a number in each of the seven regions

How many actors are both dancers and singers?

A

6✓✗

B

4✓✗

C

9✓✗

D

8✓✗

Explanation

Those who belong to all three groups are in the centre, where all three circles overlap. That number is 4.

Question 10

Study the diagram below and answer the question.

a Venn diagram of three overlapping circles labelled Singers, Dancers and Actors, with a number in each of the seven regions

How many actors are neither singers nor dancers?

A

11✓✗

B

19✓✗

C

9✓✗

D

32✓✗

Explanation

The number in the part of the Actors circle that lies outside the other two circles is 11.

Question 11

Which of the following diagrams indicates the best relation between Pilot, Carpenter and Teacher?

four Venn diagram options A to D showing different relations between three groups

four Venn diagram options A to D showing different relations between three groups

A

A✓✗

B

B✓✗

C

C✓✗

D

D✓✗

Explanation

All three are different professions, so no circle overlaps another. Three separate circles are shown in diagram C.

Question 12

Which of the following diagrams indicates the best relation between Hospital, Medicines and Doctors?

four Venn diagram options A to D showing different relations between three groups

A

A✓✗

B

B✓✗

C

C✓✗

D

D✓✗

Explanation

Medicines and Doctors are different from each other, but both are found in a Hospital. So two separate circles lie inside one larger circle, as in diagram D.

Question 13

Which of the following diagrams indicates the best relation between Men, Fathers and Doctors?

four Venn diagram options A to D showing different relations between three groups

A

A✓✗

B

B✓✗

C

C✓✗

D

D✓✗

Explanation

All fathers are men, so the Fathers circle lies inside the Men circle. Some fathers and some men may be doctors, so the Doctors circle overlaps both the Fathers circle and the Men circle (and also extends outside Men, since not all doctors are men). This is diagram B.

Question 14

Which of the following diagrams indicates the best relation between Income, Salary and Interest?

four Venn diagram options A to D showing different relations between three groups

A

A✓✗

B

B✓✗

C

C✓✗

D

D✓✗

Explanation

Salary and Interest are different from each other, but both of them are parts of Income. So two separate circles lie inside one larger circle, as in diagram A.

Question 15

Which of the following diagrams indicates the best relation between Passengers, Aeroplane and Ship?

four Venn diagram options A to D showing different relations between three groups

A

A✓✗

B

B✓✗

C

C✓✗

D

D✓✗

Explanation

Aeroplane and Ship are different from each other (their circles do not overlap), but some passengers travel by aeroplane and some travel by ship, so the Passengers circle overlaps both. This is the chain of three overlapping circles in diagram C.

Question 16

Out of a total of 150 students, 45 passed in Accounts, 45 in Economics and 50 in Maths, 30 in both Accounts and Maths, 32 in both Maths and Economics, 35 in both Accounts and Economics, and 25 students passed in all three subjects. Find the number who passed in at least one of the subjects.

A

63✓✗

B

68✓✗

C

73✓✗

D

None of these✓✗

Explanation

Using the inclusion-exclusion principle: Passed at least one = 45 + 45 + 50 - 30 - 32 - 35 + 25 = 68

Question 17

A town has a total population of 50,000. Out of it, 28,000 read the newspaper X and 23,000 read Y while 4,000 read both the papers. The number of persons not reading X and Y both is

A

2,000✓✗

B

3,000✓✗

C

2,500✓✗

D

none of these✓✗

Explanation

Reading at least one paper = 28,000 + 23,000 - 4,000 = 47,000
Not reading either paper = 50,000 - 47,000 = 3,000

Question 18

Out of 1000 persons, 25 per cent were industrial workers and the rest were agricultural workers. 300 persons enjoyed World Cup matches on TV. 30 per cent of the people who had not watched World Cup matches were industrial workers. What is the number of agricultural workers who had enjoyed World Cup matches on TV?

A

230✓✗

B

250✓✗

C

240✓✗

D

260✓✗

Explanation

Industrial workers = 250, Agricultural workers = 750.
Non-watchers = 1000 - 300 = 700. Industrial among non-watchers = 30% of 700 = 210.
So industrial watchers = 250 - 210 = 40.
Agricultural watchers = Total watchers - Industrial watchers = 300 - 40 = 260

Question 19

There are 40 students; 30 of them passed in English, 25 of them passed in Maths and 15 of them passed in both. Assuming that every student passed at least in one subject, how many students passed in English only but not in Maths?

A

15✓✗

B

20✓✗

C

10✓✗

D

25✓✗

Explanation

English only = Total English - Both = 30 - 15 = 15

Question 20

In a survey of 300 companies, the number of companies using different media -- Newspapers (N), Radio (R) and Television (T) -- are as follows:
n(N) = 200, n(R) = 100, n(T) = 40, n(N∩R) = 50, n(R∩T) = 20, n(N∩T) = 25, and n(N∩R∩T) = 5.
Find the number of companies using none of these media.

A

20 companies✓✗

B

250 companies✓✗

C

30 companies✓✗

D

50 companies✓✗

Explanation

|N∪R∪T| = |N| + |R| + |T| - |N∩R| - |R∩T| - |N∩T| + |N∩R∩T|
= 200 + 100 + 40 - 50 - 20 - 25 + 5 = 340 - 95 + 5 = 250
Companies using none = 300 - 250 = 50

Question 21

In a town of 20,000 families, it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then the number of families which buy A only is:

A

6600✓✗

B

6300✓✗

C

5600✓✗

D

600✓✗

Explanation

|A| = 8000, |A∩B| = 1000, |A∩C| = 800, |A∩B∩C| = 400 (all out of 20,000 families)
A only = |A| - |A∩B| - |A∩C| + |A∩B∩C|
= 8000 - 1000 - 800 + 400 = 6600

Question 22

Out of total 150 students, 45 passed in Accounts, 45 in Economics and 50 in Maths, 30 in both Accounts and Maths, 32 in both Maths and Economics, 35 in both Accounts and Economics, 25 students passed in all the three subjects. Find the number who passed at least in any one of the subjects:

A

63✓✗

B

68✓✗

C

73✓✗

D

None✓✗

Explanation

By the inclusion-exclusion principle: |A ∪ E ∪ M| = |A| + |E| + |M| - |A ∩ M| - |M ∩ E| - |A ∩ E| + |A ∩ E ∩ M| = 45 + 45 + 50 - 30 - 32 - 35 + 25 = 140 - 97 + 25 = 68