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How many ordered pairs of (m,n) integers...

How many ordered pairs of (m,n) integers satisfy `(m)/(12)=(12)/(n)`?

A

`30`

B

`15`

C

`12`

D

`10`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `(m)/(12)=(12)/(n)`
`impliesmn=144impliesn=(144)/(m)`
We want to find here total number of divisors of `144`
`144=2^(4)3^(2)`
Total divisors are `(4+1)(2+1)=15`
But negative pairs are also possible hence `=30`
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