2002 AMC 10A Problem 4

Problem 4 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

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.

Concepts: inequality · small cases

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