2002 AMC 10A Problems/Problem 4: Difference between revisions
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... |
see also and stuff |
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==Solution== | ==Solution== | ||
We quickly see that for n=1, we have <math>m\le | 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>. | ||
==See Also== | |||
{{AMC10 box|year=2002|ab=A|num-b=3|num-a=5}} | |||
[[Category:Introductory Algebra Problems]] | |||
Revision as of 17:12, 26 December 2008
Problem
For how many positive integers m is there at least 1 positive integer n such that 
?
Infinite.
Solution
We quickly see that for n=1, we have 
, so (m,1) satisfies the conditions for all m. Our answer is 
.
See Also
| 2002 AMC 10A (Problems • Answer Key • Resources) | ||
| 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 | ||
