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2002 AMC 10A Problems/Problem 4

Revision as of 17:10, 26 December 2008 by Xpmath (talk | contribs) (New page: ==Problem== For how many positive integers m is there at least 1 positive integer n such that <math>mn \le m + n</math>? <math>\text{(A)}\ 4 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 9 \qqu...)
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Problem

For how many positive integers m is there at least 1 positive integer n such that $mn \le m + n$?

$\text{(A)}\ 4 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 9 \qquad \text{(D)}\ 12 \qquad \text{(E)}$ Infinite.

Solution

We quickly see that for n=1, we have $m\le{m}$, so (m,1) satisfies the conditions for all m. Our answer is $\text{(E)}$ Infinite

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