2012 AMC 10B Problems/Problem 10
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.