joinn wrote:Is X > K ?

1) 2x * 2k = 4
2) 9x * 3k = 81

Please anyone explain in detail ...

I think the question is not correct as the two statements are contradicting each other. From statement 1 we get xk = 1 and from statement 2 we get xk = 3. But in GMAT DS question, the statements never contradict each other.

I guess the question is as below:

Is x > k ?

1) 2^x * 2^k = 4
2) 9^x * 3^k = 81

(1) 2^x * 2^k = 4 implies 2^(x + k) = 2^2 implies x + k = 2; NOT sufficient.

(2) 9^x * 3^k = 81 implies 3^(2x + k) = 3^4 implies 2x + k = 4; NOT sufficient.

Combining (1) and (2), x + k = 2 and 2x + k = 4
Solving we get, x = 2 and k = 0, which implies x > k; SUFFICIENT.

The correct answer is C.