Question #N859
A survey of 100 students found that 60 students like to play basketball and 40 students like to play soccer. If 20 students like to play both basketball and soccer, 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 help visualize the problem. Let $B$ represent the set of students who like basketball, and let $S$ represent the set of students who like soccer. We know that $n(B) = 60$, $n(S) = 40$, and $n(B \cap S) = 20$. The number of students who like only basketball is given by $n(B) - n(B \cap S) = 60 - 20 = 40$. [asy] unitsize(0.6 cm); label("Basketball", (2,7), E); label("Soccer", (7,2), S); draw(Circle((2,5), 2.5)); draw(Circle((6,1), 2.5)); draw((2,5)--(6,1)); label("20", (4,3.5)); label("40", (6,4.5), E); label("20", (3,1), S); [/asy]