Is x > y?

1) x + a > x - a

Subtract x from both sides: a > -a
Add a to both sides: 2a > 0
Divide both sides by 2: a > 0

This tells us nothing about x or y. Insufficient.

2) ax > ay

Here, we cannot divide both sides by a, since we don't know the sign. If a were positive, then dividing by a would yield x > y. If a were negative, though, we'd get x < y.
Insufficient.

(1) & (2) together:
Since statement (1) tells us that a is positive, we can divide both sides of ax > ay by a, and we get: x > y. Sufficient.

The answer is C.

Here are some other examples of problems that deal with multiplying or dividing a variable across an inequality:
https://www.beatthegmat.com/inequalities ... tml#540464
https://www.beatthegmat.com/if-x-0-is-y- ... tml#784623
https://www.beatthegmat.com/is-xy-x-2-y- ... tml#788145

Please also POST YOUR SOURCE. It's a copyright violation to post a question without citing the source.

Vincen wrote:Is x > y?

1) x + a > x - a
2) ax > ay

Target question: Is x > y ?

Statement 1: x + a > x - a
Since there's no information about y, it's IMPOSSIBLE to answer the target question with certainty
As such, statement 1 is NOT SUFFICIENT

Statement 2: ax > ay
Some students will divide both sides by a and incorrectly conclude that x > y.
However, before we divide by a variable, we must ensure that the variable is EITHER positive OR negative, because if we divide by a negative value, we must reverse the direction of the inequality, and if we divide by a positive value, the direction of the inequality stays the same.
To see what I mean, consider these values of a, x and y that satisfy the given condition:
Case a: a = 1, x = 3 and y = 2, in which case x > y
Case b: a = -1, x = 2 and y = 3, in which case x < y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x + a > x - a
Add a to both sides of the inequality to get: x + 2a > x
Subtract x from both sides to get: 2a > 0
Divide both sides by 2 to get: a > 0
So, a is POSITIVE

Statement 2 tells us that ax > ay
Since we now know that a is POSITIVE, we can safely take ax > ay and divide both sides by a
When we do so, we get: x > y. PERFECT, this is exactly what the target question is asking us.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

RELATED VIDEO (inequalities): https://www.gmatprepnow.com/module/gmat ... /video/979

Cheers,
Brent