1989 AMC 12 Problem 27
Attempt Problem 27 of the 1989 AMC 12 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 1989 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
27.
Let be a positive integer. If the equation has solutions in positive integers and then must be either
or
or
or
or
or
Answer: D
Small hint:
Group solutions according to
Big hint:
For fixed count the positive ordered pairs and require
Solution:
For there are positive ordered pairs and is positive when Writing the number of solutions is Setting this equal to gives Hence so or
Thus the correct answer is D.
Problem 27 in other years
- 1950 AMC 12
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- 1955 AMC 12
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