Difference between revisions of "2012 AMC 10B Problems/Problem 10"

Line 33: Line 33:
<math>\boxed{\textbf{(D)}\ 9}</math>
<math>\boxed{\textbf{(D)}\ 9}</math>
{{MAA Notice}}

Revision as of 12:15, 4 July 2013

Problem 10

How many ordered pairs of positive integers (M,N) satisfy the equation $\frac {M}{6}$ = $\frac{6}{N}$

$\textbf{(A)}\ 6\qquad\textbf{(B)}\ 7\qquad\textbf{(C)}\ 8\qquad\textbf{(D)}\ 9\qquad\textbf{(E)}\10$ (Error compiling LaTeX. ! Undefined control sequence.)



$\frac {M}{6}$ = $\frac{6}{N}$

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.


$\boxed{\textbf{(D)}\ 9}$ The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Invalid username
Login to AoPS