2002 AMC 12A Problem 6

Problem 6 of 25EasierAlgebra

For how many positive integers

m

does there exist at least one positive integer

n

such that

m \cdot n \le m + n?

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Solution

Taking

n = 1,

the inequality becomes

m \le m + 1,

which holds for every positive integer

m.

So every positive integer

m

works, and there are infinitely many. Thus, the correct answer is E.

Concepts: inequality · small cases

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