Question #N277

A survey of 100 people found that 60 people like apples, 45 people like bananas, and 20 people like both apples and bananas. How many people like neither apples nor bananas?
A. 15
B. 25
C. 35
D. 45

Correct Answer is: A

We can use a Venn diagram to solve this problem. Let $A$ represent the set of people who like apples, and let $B$ represent the set of people who like bananas. We are given that $n(A) = 60$, $n(B) = 45$, and $n(A \cap B) = 20$. Since $n(A \cup B) = n(A) + n(B) - n(A \cap B)$, it follows that $n(A \cup B) = 60 + 45 - 20 = 85$. Therefore, 100 – 85 = 15 people like neither apples nor bananas.