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

Question

Is x > k?

(1)  2^x * 2^k = 4

(2)  9^x * 3^k = 81

Bunuel · Accepted Answer

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.

jlgdr · Answer

From Statement 1 we get that x+k=2.

From Statement 2 we get that 2x+k=4. This is also insufficient.

From both statements we get that x=2, and k=0.

Therefore C is the correct answer

Please ask if anything remains unclear
Cheers
J :-D

I'm back and not stopping until I hit 760+

I'm back and not stopping until I hit 760+

pacifist85 · Answer

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

From   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  , as 1 in whichever power is 1, and because in   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?

pacifist85 · Answer

Or perhaps you cannot do that due to the order of calculations? So, we would need to resolve the powers first, and then take the common factor out..

law258 · Answer

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

GMATwithAK · Answer

Can you take the common factor 3 out like this?

No. Because it is a multiplication. Had the expression been 9^x+3^k, you can take out 3 as a common factor.

nottheusual · Answer

For Option C, can someone please explain why x cannot be = 0?

x + k = 4
2x + k = 4
where x = 0, k =4?

Bunuel · Answer

We have x + k = 2, not x + k = 4.

bumpbot · Answer

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Is x > k? (1) 2^x * 2^k = 4 (2) 9^x * 3^k = 81

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