1985 AMC 12 Problem 26
Attempt Problem 26 of the 1985 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 1985 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
26.
Find the least positive integer for which is a non-zero reducible fraction.
none of these
Answer: E
Small hint:
Any common divisor of and also divides a suitable linear combination
Big hint:
Compute
Solution:
Euclid’s algorithm gives Since is prime, the nonzero fraction is reducible exactly when is a nonzero multiple of The least positive possibility is which is not among the four numerical choices.
Thus the correct answer is E.
Problem 26 in other years
- 1950 AMC 12
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