Question #N284

A survey of 100 students found that 60 students like to play basketball, 40 students like to play soccer, and 20 students like to play both. How many students like to play only basketball?
A. 20
B. 40
C. 60
D. 80

Correct Answer is: B

We can use a Venn diagram to visualize the problem. Let $B$ represent the set of students who like basketball and $S$ represent the set of students who like soccer. We are given that $n(B)=60$, $n(S)=40$, and $n(B \cap S) = 20$. We are asked to find $n(B \setminus S)$. Since $n(B \cup S) = n(B) + n(S) - n(B \cap S)$, we know $n(B \cup S) = 60 + 40 - 20 = 80$. Therefore, the number of students who like to play only basketball, $n(B \setminus S) = n(B \cup S) - n(S) = 80 - 40 = 40$.