WORD PROBLEMS ON SETS AND VENN DIAGRAMS 2 CIRCLES WORKSHEET

Problem 1 :

Out of 20 members in a family, 11 like to take tea and 14 like coffee. Assume that each one likes at least one of the two drinks. How many like only tea and not coffee?

a) 9      b) 5      c) 11      d) 6

Solution

Problem 2 :

In a group of 20 adults, there are 8 males and 9 vegetarians. Find the number of female nonvegetarians, if the group contains 5 male vegetarians?

a) 4      b) 8       c) 12       d) 10

Solution

Problem 3 :

The Venn diagram alongside shows the number of people in a sporting club who play tennis (T) and hockey (H). Find the number of people:

(a) in the club        (b) who play hockey

(c) who play both sports       (d) who play neither sport

(e) who play at least one sport

(f) who play tennis but not hockey

Solution

Problem 4 :

In a group of 20 boys: 6 have blue eyes. 13 have fair hair. 4 have fair hair and blue eyes. 5 have neither blue eyes nor fair hair.

(a) Copy and complete the Venn Diagram with this information.

(b) How many boys have blue eyes but not fair hair?

Solution

Problem 5 :

1 In a group of 24 girls, 18 like oranges, 7 like bananas and 4 like neither oranges nor bananas.

(a) Draw a Venn diagram to illustrate this information.

(b) How many girls like both fruit?

Solution

Problem 6 :

24 out of class of 32 students study History or Geography, or both. 15 study History but not Geography. 5 study Geography but not History.

(a) Draw a Venn diagram to illustrate this information.

(b) number of students who studies both History and Geography

(c) number of students who does not study History

Solution

Problem 7 :

In a class of 30 students, 19 study Physics, 17 study Chemistry, and 15 study both of these subjects.

(a) Display this information on a Venn diagram.

(b) Find the number of students who study

(i) both subjects     (ii) at least one of the subjects

(ii) Physics but not Chemistry

(iv) exactly one of the subjects.

Solution

Answer Key

1)  Number of members they like tea but not coffee = 6.

2)  the number of female non vegetarians = 8.

3)  a) Number of people in the club = 75

b) Number of people who play hockey = 53

(c) who play both sports = 27

(d) who play neither sport = 7

(e) who play at least one sport  = 68

(f) who play tennis but not hockey = 15

4)  Number boys who has blue eyes but not fair hair = 2

5)  

a)

b)  the number of girls who like both fruit is 1.

6)  a)

b) x = 4

c) 13

7)  a)

b)  (i) Number of students who study both subjects = 15

(ii) Number of students who study at least one of the subjects

= 22

(ii) Number of students who study Physics but not Chemistry

= 4

(iv) Number of students who study exactly one of the subjects

= 6