1991 AMC 8 Problem 23
Attempt Problem 23 of the 1991 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1991 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
23.
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: A
Small hint:
First find how many females are in at least one group, using
Big hint:
Subtract the females from the total to get the males in at least one group, then use inclusion–exclusion to find how many males are in both groups
Solution:
Females in band or orchestra: So males in at least one group:
With males in band and in orchestra, the males in both are Hence males in band but not orchestra:
Thus, the correct answer is A .
Problem 23 in other years
- 1985 AMC 8
- 1986 AMC 8
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