venn diagram

Question

A survey is conducted among $106$ people. Among them $47$ people have dogs, $58$ people have cats and $38$ people have parrots. $16$ people have both a dog and cat, $15$ people have both cat and parrot and $17$ people have both a parrot and dog. Each of them has at least one of the pets.

 

How many people have people have either a dog or a parrot but not a cat?

• A. $37$
• B. $15$
• C. $23$
• D. $20$

Answer 1

Here according to the question they asked us to find people have either a dog or parrot but not cat,so by drawing a venn diagram let's assume that people who have only dogs be X, people who have only cats be Y and people who have only parrots be Z and intersection of all the pets be W.Total population is 106. So X+Y+Z+W+16+17+15=106.

From cats we can write it as Y+W+16+15= 58. From this we will get Y+W as 27. Try to substitute it on the above equation we get X+Z=48 i.e people who have  either dog or parrot but not cat.