If xy = 1, What is the Value of 2^(x + y)^2/2^(x-y)^2? GMAT Problem Solving

Question: If xy = 1, what is the value of \(\frac{2^{(x + y)^2}}{2^{(x-y)^2}}\)?

1. 2
2. 4
3. 8
4. 16
5. 32

Correct Answer: D

Approach Solution (1):

\(\frac{2^{(x + y)^2}}{2^{(x-y)^2}}=2^{(x + y)^2-(x-y)^2}=2^{(x+y+x+y)(x+y-x+y)}=2^{(2x)(2y)}=2^{4xy}=2^4=16\)

Approach Solution (2):

\(\frac{2^{(x + y)^2}}{2^{(x-y)^2}}\)

\(=\frac{2^{x^2+y^2+2xy}}{2^{x^2+y^2-2xy}}\)

\(=2^{(x^2+y^2+2xy)-(x^2+y^2-2xy)}\)

\(=2^{x^2+y^2+2xy-x^2-y^2+2xy}\)

\(=2^{4xy}=2^4=16\)

“If xy = 1, what is the value of \(\frac{2^{(x + y)^2}}{2^{(x-y)^2}}\)?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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