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2002 AMC 12A Problems/Problem 6

Revision as of 18:35, 6 October 2008 by Qntty (talk | contribs) (New page: ==Problem== For how many positive integers <math>m</math> does there exist at least one positive integer n such that <math>m \cdot n \le m + n</math>? <math> \mathrm{(A) \ } 4\qquad \math...)

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Problem

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

$\mathrm{(A) \ } 4\qquad \mathrm{(B) \ } 6\qquad \mathrm{(C) \ } 9\qquad \mathrm{(D) \ } 12\qquad \mathrm{(E) \ }$ infinitely many

Solution

$m \cdot 1 \le m + 1$ for $n=1$

$m \le m + 1$

$\Rightarrow \mathrm{(E) \ }$ infinitely many

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