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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

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Answer:

Option: C is the correct answer.

                    C.    5

Step-by-step 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

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