Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2002 AMC 12A Problems/Problem 6"

(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...)
(No difference)

Revision as of 18:35, 6 October 2008

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2002_AMC_12A_Problems/Problem_6&oldid=28163"