Difference between revisions of "2012 AMC 10B Problems/Problem 10"
(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) (→Solution) |
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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 18:54, 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
