If xyz ≠ 0, what is the value of

AbeNeedsAnswers wrote:If xyz ≠ 0, what is the value of (x^4)(z^2) / (z^2)(y^2)?

(1) y^2 = x^4
(2) x = 2 and y = 4

D

Source: Official Guide 2020

Target question: What is the value of (x�z²)/(z²y²)?
This is a good candidate for rephrasing the target question.
Since z ≠ 0, we know that z² ≠ 0
So, we can safely take (x�z²)/(z²y²) and divide top and bottom by z² to get: x�/y²
REPHRASED target question: What is the value of x�/y²?

Aside: Here’s a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: y² = x�
Take: x�/y² and replace y² with x� to get: x�/x�, which equals 1
So, the answer to the REPHRASED target question is x�/y² = 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x = 2 and y = 4
So, x�/y² = 2�/4² = 16/16 = 1
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

Hi All,

We're told that If (X)(Y)(Z) ≠ 0. We're asked for the value of (X^4)(Z^2) / (Z^2)(Y^2). This question can be approached in a number of different ways, including Algebra and TESTing VALUES.

To start, it's worth noting that none of the given variables can equal 0 and the term (Z^2) appears in both the numerator and denominator (meaning that it essentially 'cancels out' - and we're ultimately asked for the value of (X^4)/(Y^2).

1) Y^2 = X^4

The information in Fact 1 matches the two 'terms' that we need to have values for to answer the given question. Since these two items are equal, the question can be rewritten as "What is the value of (X^4)/(X^4)?" Since the numerator is divided by itself, the answer to the question is clearly "1." You can also use TEST IT to prove that the answer is always 1...

IF...
X=2 and Y=4, then the question becomes "What is the value of 16/16?" That fraction simplifies to 1 - and it will always simplify to 1 as long as you choose values that fit the given information.
Fact 1 is SUFFICIENT

(2) X = 2 and Y = 4

We can 'plug in' the values from Fact 2 - which would give us 16/16 = 1. Even if we didn't cancel out the Z^2 terms, we would have 16(Z^2)/16(Z^2), which is still 1.
Fact 2 is SUFFICIENT

Final Answer: D

GMAT assassins aren't born, they're made,
Rich