1991 AMC 8 Problem 9
Attempt Problem 9 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).
9.
How many whole numbers from through are divisible by either or or both?
Answer: B
Small hint:
Count the multiples of and the multiples of separately
Big hint:
Numbers divisible by both and are multiples of and get counted twice, so subtract them once
Solution:
There are multiples of and multiples of up to The multiples of (namely ) were counted twice.
By inclusion-exclusion, the count is
Thus, the correct answer is B .
Problem 9 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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