BTGModeratorVI wrote: ↑

Fri May 29, 2020 6:32 am

If x > y, is cx > cy ?

(1) c > 0
(2) xy > 0

Answer: A
Source: GMAT prep

Given: x > y
If we subtract y from both sides of the inequality, we get x - y > 0
In other words, x - y is positive

Target question: Is cx > cy ?
This is a good candidate for rephrasing the target question.
Take: Is cx > cy ?
Subtract cy from both sides to get: Is cx - cy > 0 ?
Factor to get: Is c(x - y) > 0 ?
Since we already know that x - y is positive, we get: Is c(some positive number) > 0 ?
In order for c(some positive number) to be positive, c must be positive
So the target question is really asking us whether c is positive
REPHRASED target question: Is c > 0 ?

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

Statement 1: c > 0
Perfect!!
The answer to the REPHRASED target question is YES, c is positive
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: xy > 0
Since statement 2 provides no information how about the value of c, there's no way to answer the REPHRASED target question with certainty
Statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent