In its current form statement (1) xk=1 and statement (2) xk=3 clearly contradict each other and we know that on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

So I think the question should be:

Is x > k?
(1) 2^x * 2^k = 4 --> \(2^{x+k}=2^2\) --> \(x+k=2\) --> not sufficient to determine which one is greater.
(2) 9^x * 3^k = 81 --> \(3^{2x+k}=3^4\) --> \(2x+k=4\) --> not sufficient to determine which one is greater.

(1)+(2) \(x+k=2\) and \(2x+k=4\) --> subtract 1 from 2: \(x=2\) --> \(k=0\) --> so, \(x>k\). Sufficient.

Answer: C.
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Hello,

I ended up in the same but in a more complicated way perhaps. I don't know why, as I always use this proposed way by bunuel. But, this is a good oportunity to ask something.

So, from [1] I ended up that x=1, k=1 or that x=2 and k=0 (or the opposite). So, NS.

From [2] I concluded that k should be zero, so x will be greater than k, like this:
9^x*3^k=81
3*(3^x*1^k)=3^4
3*3^x=3^4, so again not sufficient.

From [1 and 2], as 1 in whichever power is 1, and because in [2] we have 1^k, I accepted that k=0 and x=2.

Anyway, this could be wrong, but would like to ask about the part in red. Can you take the common factor 3 out like this?

C is correct. Here's why:

(1) (2^x)(2^k) = 4 --> Rewrite as (2^x)(2^k) = 2^2

x+k = 2

NOT SUFFICIENT - x and k could be any values for all we know at this point

(2) (9^x)(3^k) =81 --> Rewrite as (3^2x)(3^k) = 3^4

2x+k = 4

NOT SUFFICIENT - same as (1)

A,B,D eliminated

Together - (1) + (2) --> Plug equation from (1) (i.e. x = 2-k) into equation from (2) (i.e. 2x+k = 4)

2(2-k)+k = 4
4-2k+k = 4
4-k = 4
k = 0 --> x = 2

SUFFICIENT