Difference between revisions of "2008 AMC 8 Problems/Problem 22"
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==Problem== | ==Problem== | ||
| − | <onlyinclude>For how many positive integer values of <math>n</math> are both <math>\frac{n}{3}</math> and <math>3n</math> three-digit whole numbers?</onlyinclude> | + | <!-- don't remove the following tag, for PoTW on the Wiki front page--><onlyinclude>For how many positive integer values of <math>n</math> are both <math>\frac{n}{3}</math> and <math>3n</math> three-digit whole numbers?<!-- don't remove the following tag, for PoTW on the Wiki front page--></onlyinclude> |
<math>\textbf{(A)}\ 12\qquad | <math>\textbf{(A)}\ 12\qquad | ||
Revision as of 21:05, 16 March 2015
Problem
For how many positive integer values of 
are both 
and 
three-digit whole numbers?
Solution
If is a three digit whole number, must be divisible by 3 and be 
. If is three digits, n must be 
So it must be divisible by three and between 300 and 333. There are 
such numbers, which you can find by direct counting.
See Also
| 2008 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 21 |
Followed by Problem 23 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
