Question

A survey of 100 families showed that 35 had a dog: 28 had a cat: 10 had a dog and a cat: 42 had neither a cat nor a dog nor a parakeet: 0 had a cat, a dog, and a parakeet. How many had a parakeet only? A. 20 B. 15 C. 5 D. 10

Answer 1

Option: C is the correct answer.

C. 5

Explanation:

We will solve the following problem with the help of the Venn diagram.

Based on the Venn diagram we are asked to find the value of v i.e. those who have parakeet only.

From the information that:

• 35 had a dog we have:

x+y+10=35

i.e.

x+y=25

Also, based on the information :

• 28 had a cat we have:

u+z+10=28

i.e.

u+z=18

Also, 42 had neither a cat nor a dog nor a parakeet.

This means it cover the outer region of the three circles.

Total 100 families were surveyed it means that:

42+x+y+10+u+z+v=100

i.e. 42+25+10+18+v=100

i.e. 95+v=100

i.e. v=100-95

i.e. v=5

Hence, the number of families who have only parakeet are: 5