$432 = (2)(2)(2)(2)(3)(3)(3) = (2^4)(3^3)$

Since $2^4 = 4^2$, we can write: $432 = (4^2)(3^3)$

So, one way to express the relationship is as follows: $3^xy^2=(3^3)(4^2)$
In this case, $x=3$ and $y=4$
We get:
QUANTITY A: $3^x=3^3=27$
QUANTITY B: $y^2=4^2=16$
In this case, Quantity A is greater


HOWEVER, we can also rewrite $432$ a different way
Take: $432 = (2)(2)(2)(2)(3)(3)(3)$
Rewrite as follows: $432 = [(2)(2)(3)(2)(2)(3)](3)$
In other words: $432 = [(2)(2)(3)]^2(3)$
In other words: $432 = (12^2)(3^1)$
So we can express is our relationship as: $3^xy^2=(12^2)(3^1)$
In this case, $x=1$ and $y=12$
We get:
QUANTITY A: $3^x=3^1=3$
QUANTITY B: $y^2=12^2=144$
In this case, Quantity B is greater

Answer: D

Cheers,
Brent

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.