Practice Quant problem

myspecialtie wrote:I'm having difficulty figuring out the solution to this problem from one of the GMAT practice exams:

If xy=1, what is the value of {2^[(x+y)^2]}/{2^[(x-y)^2]}?

A. 2
B. 4
C. 8
D. 16
E. 32

Any help/advice would be much appreciated!

We have {2^[(x+y)^2]}/{2^[(x-y)^2]}

{2^[(x+y)^2]}/{2^[(x-y)^2]} = 2^[{(x+y)^2} – {(x-y)^2}] = 2^[{x^2 + y^2 + 2xy} – {x^2 + y^2 – 2xy}] = 2^(4xy) = 2^(4*1) = 2^4 = 16

The correct answer: D

Alternate approach:

Since we can choose any value for x or y given that xy = 1, say x = y = 1

Thus, (x + y)^2 = (1 + 1)^2 = 2^2 = 4 and (x – y)^2 = (1 – 1)^2 = 0^2 = 0

{2^[(x+y)^2]}/{2^[(x-y)^2]} = {2^4}/{2^0} = 16/1 = 16 -- Correct answer is D.

Hope this helps!

-Jay
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