2012 AMC 10B Problems/Problem 10: Difference between revisions
Created page with "== Problem 10 == How many ordered pairs of positive integers (M,N) satisfy the equation <math>\frac {M}{6}</math> = <math>\frac{6}{N}</math> <math> \textbf{(A)}\ 6\qquad..." |
Whirltwister (talk | contribs) |
||
| Line 18: | Line 18: | ||
Now you find all the factors of 36: | Now you find all the factors of 36: | ||
1 | <math>1\times36=36</math> | ||
2 | <math>2\times18=36</math> | ||
3 | <math>3\times12=36</math> | ||
4 | <math>4\times9=36</math> | ||
6 | <math>6\times6=36</math>. | ||
Now you can reverse the order of the factors for all of the ones listed above, because they are ordered pairs except for 6*6 since it is the same back if you reverse the order. | Now you can reverse the order of the factors for all of the ones listed above, because they are ordered pairs except for 6*6 since it is the same back if you reverse the order. | ||
Revision as of 17:54, 24 February 2012
Problem 10
How many ordered pairs of positive integers (M,N) satisfy the equation 
= 
$\textbf{(A)}\ 6\qquad\textbf{(B)}\ 7\qquad\textbf{(C)}\ 8\qquad\textbf{(D)}\ 9\qquad\textbf{(E)}\10$ (Error compiling LaTeX. Unknown error_msg)
Solution
=
is a ratio; therefore, you can cross-multiply.
Now you find all the factors of 36:
.
Now you can reverse the order of the factors for all of the ones listed above, because they are ordered pairs except for 6*6 since it is the same back if you reverse the order.
OR
