Difference between revisions of "2002 AMC 10A Problems/Problem 4"

(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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==Solution==
 
==Solution==
We quickly see that for n=1, we have <math>m\le{m}</math>, so (m,1) satisfies the conditions for all m. Our answer is <math>\text{(E)}</math> Infinite
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We quickly see that for n=1, we have <math>m\le m+1</math>, so (m,1) satisfies the conditions for all m. Our answer is <math>\boxed{\text{(E) Infinite}}</math>.
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==See Also==
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{{AMC10 box|year=2002|ab=A|num-b=3|num-a=5}}
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[[Category:Introductory Algebra Problems]]

Revision as of 18:12, 26 December 2008

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 $m\le m+1$, so (m,1) satisfies the conditions for all m. Our answer is $\boxed{\text{(E) Infinite}}$.

See Also

2002 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions