Problem:
The Pythagoras High School band has female and male members. The Pythagoras High School orchestra has female and male members. There are females who are members in both band and orchestra. Altogether, there are students who are in either band or orchestra or both. The number of males in the band who are NOT in the orchestra is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are females in the band, in the orchestra, and in both. Thus, there are females in at least one of the groups. Since the total is , then there are males in at least one of the groups. There are males in band and males in orchestra, thus to find the number of males in both, . There are in both. Finally, the number of males in band who are not in orchestra is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions