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

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.