1997 AMC 12 Problem 28
Attempt Problem 28 of the 1997 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 1997 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
28.
How many ordered triples of integers satisfy
Answer: E
Small hint:
Set , so , and split according to the sign of
Big hint:
When , rewrite the resulting equations as products equal to
Solution:
If substitution and factoring lead to no pair consistent with the required sign of Thus so and If then producing the unordered pairs If then producing Each unordered pair has two orders, giving triples. The correct answer is E.
Problem 28 in other years
- 1950 AMC 12
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