Question

How many ordered pairs of (m, n) integers satisfy $\frac{m}{12}=\frac{12}{n}$?

• A. $30$
• B. $15$
• C. $12$
• D. $10$

Answer 1

The correct option is B $15$

$m\times n=144$

144 can be written in multiplication of two integers in the following ways:

$1\times 144=2\times 72=3\times 48=4\times 36=6\times 24=8\times 18=9\times 16=12\times 12$

For all the factors except $(12,12)$ there would be 14 ordered pairs.

Adding one more, yields 15 possibilities