Venn Diagrams

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**Practice Problems**

Question 1: Identify the diagram that best represents the relationship among the given classes: Country, State and City.

Question 2: In the given figure, how many cardboard boxes are not white?

A: 6

B: 13

C: 7

D: 9

Question 3: In the given figure, how many people study only 2 subjects?

A: 11

B: 23

C: 12

D: 40

Question 4: In the given figure, how many people like cricket and tennis both?

A: 17

B: 32

C: 15

D: 27

Question 5: Which one of the following diagrams represents the correct relationship among Manager, Labour Union and Worker?

Question 6: Which of the diagrams given in the alternatives correctly represent the relationship among Sharks, Whales, and Turtles?

Question 7: In the given figure, how many books are only fictions?

A: 23

B: 12

C: 53

D: 41

Question 8: In a class, there are 80 students who study both Computer Science and Electronics. While 100 students study Computer Science, 120 Students study Electronics, How many of them study Computer Science only?

A: 100

B: 40

C: 180

D: 20

Question 9: An interview of 60 persons to know whether they play Tennis, Chess or Carom was conducted. The data so obtained has been summarized in a pictorial diagram as shown. Study the diagram and answer the question. How many persons do not play any game?

A: 28

B: 57

C: 4

D: 3

Question 10: In the following diagram, police officer represents circle, corrupt represents triangle, poet represents square and married represents rectangle.

Which number represents unmarried police officers who are not corrupt but are poets?

A: 8

B: 9

C: 2

D: 4

Answers and Solutions

1:- D

Solution:

2:- A

Solution: The number of cardboard and boxes which are not white means the number of cardboards which are only boxes. So, the number of cardboard boxes which are not white is 6.

3:- B

Solution: The number of people who study only Mathematics & Physics = 5. The number of people who study only Mathematics & Chemistry = 6. The number of people who study only Chemistry & Physics = 12. Total number of people who study only two subjects = (5+6+12) = 23.

4:- B

Solution: The number of people who like cricket and tennis is (17+15) = 32.

5:- A

Solution: Manager is different from worker and labour union Worker belongs to labour union.

6:- C

Solution: Sharks belong to class fishes, Whale is a mammal and a Turtle belongs to class reptile.

7:- B

Solution: The number 12 represents the books which are only about the fiction.

8:- D

Solution: Diagram of Computer Science & Electronics students:

There are 100 students in Computer Science which include students from electronics too. Therefore, number of students opting for Computer Science only is, 100 – 80 = 20.

9:- D

Solution: The number of persons who play one game, two games and all the three games = 9 + 8 + 10+ 12+ 11+ 7 = 57. Therefore, number of persons who do not play any game = 60 – 57 = 3.

10:- A

Solution: The required regions should be common to the circle and square but outside the triangle and rectangle. So, number 8 represents unmarried police officers who are not corrupt but are poets.

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