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2002 AMC 10A Problem 4

Problem 4 of 25EasierAlgebraProblem-Solving Techniques

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

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Solution

Take n=1.n=1. Then m⋅1≤m+1m\cdot 1\le m+1 becomes m≤m+1,m\le m+1, which holds for every positive integer m.m. So every positive integer mm works, giving infinitely many. Thus, the correct answer is E.
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Tagged: inequality · small cases

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