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2002 AMC 12A Problem 6

Problem 6 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

Taking n=1,n = 1, the inequality becomes m≤m+1,m \le m + 1, which holds for every positive integer m.m. So every positive integer mm works, and there are infinitely many. Thus, the correct answer is E.
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Tagged: inequality · small cases

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