Bunuel wrote:

The question should read:

If t and u are positive integers, what is the value of t^{-2}*u^{-3}?

(1) t^{-2}*u^{-3} = \frac{1}{36} --> \frac{1}{t^{2}*u^{3}}=\frac{1}{36} --> t^{2}*u^{3}=36 --> since t and u are positive integers, then only possible case is t^{2}*u^{3}=6^2*1^3 (u cannot be any other positive integer but 1, since 36 doesn't have a prime factor in power of 3) --> t=6 and u=1. Sufficient.

(2) t*(u^{-1}) = \frac{1}{6} --> \frac{t}{u}=\frac{1}{6} --> infinite number of values are possible for t and u (1, and 6, 2 and 12, 3 and 18, ...), thus infinite number of values are possible for t^{-2}*u^{-3}. Not sufficient.

Answer: A.

Hope it's clear.

You have corrected the error. Thanks once again.

The question now makes sense.

In the original question the answer I got was C

PS: I have edited the question again, as question stem and A have become same.