Difference between revisions of "2005 AMC 12A Problems/Problem 8"
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Latest revision as of 21:19, 3 July 2013
Problem
Let 
, and 
be digits with
![\[(100A+10M+C)(A+M+C) = 2005\]](http://latex.artofproblemsolving.com/7/a/7/7a75ad55ea64bc7187afbbb55619c09c380827f7.png)
What is 
?
Solution
Clearly the two quantities are both integers, so we check the prime factorization of 
. It is easy to see now that 
works, so the answer is 
.
See also
| 2005 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 7 |
Followed by Problem 9 |
| 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 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
