Hi abhasjha,

This question can be solved by TESTing Values and knowing a bit about factors and multiples.

We're told that A, B, K and M are POSITIVE INTEGERS. We're asked if A^K is a factor of B^M. This is a YES/NO question.

Fact 1: A is a factor of B.

Let's TEST Values...
A = 1
B = 1
From here, the values of K and M are irrelevant (since we know that they're positive integers). 1^K IS a factor of 1^M and the answer to the question is YES.

A = 2
B = 2
K = 2
M = 1
2^2 is NOT a factor of 2^1, so the answer to the question is NO.
Fact 1 is INSUFFICIENT

Fact 2: K <= M

Without any information about the two base numbers (A and B), you should realize that there's not enough information to answer the question. You can quickly prove it though:

A = 1
B = 1
K = 1
M = 1
1^1 IS a factor of 1^1, so the answer to the question is YES.

A = 2
B = 1
K = 1
M = 1
2^1 is NOT a factor of 1^1, so the answer to the question is NO.
Fact 2 is INSUFFICIENT.

Combined, we know...
A is a factor of B
K <= M

Here we can use a Number Property rule about factors/multiples:
Since A is a factor of B, A divides evenly into B. For A^K to divide evenly into B^M, then M must be greater than or equal to K, which it is (info from Fact 2). So the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich