2002 AMC 10A Problem 4 — Solution | LIVE by Po-Shen Loh

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2002 AMC 10A Problem 4

Attempt Problem 4 of the 2002 AMC 10A 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 2002 AMC 10A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

4.

For how many positive integers $m$ does there exist at least one positive integer $n$ such that $m\cdot n\le m+n?$

$4$

$6$

$9$

$12$

infinitely many

Answer: E

Concepts:inequality small cases

Difficulty rating: 980

Solution:

Take $n=1.$ Then $m\cdot 1\le m+1$ becomes $m\le m+1,$ which holds for every positive integer $m.$

So every positive integer $m$ works, giving infinitely many.

Thus, the correct answer is E.

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Problem 4 in Other Years

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