Is x y? (1) x + a x - a (2) ax ay

Question

Is x > y?

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

BrentGMATPrepNow · Accepted Answer

Target question :    Is x > y?

Statement 1 : x + a > x - a   
This statement doesn't include any information about y, so there's no way to answer the  target question . 
Since we cannot answer the  target question  with certainty, 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. As it stands, we don't know whether a is positive or negative.

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 to get: x + 2a > x
Subtract x from both sides to get: 2a > 0
Divide both sides by 2 to get: a > 0. In other words,  a is POSITIVE

Statement 2 tells us that ax > ay
Now that we know that  a is POSITIVE , we can take ax > ay and safely divide both sides by a to get:  x > y  
PERFECT!
Since we can answer the  target question  with certainty, the combined statements are SUFFICIENT

Answer: C

RELATED VIDEO FROM OUR COURSE
 https://www.youtube.com/watch?v=Od98BOicIq4

MathRevolution · Answer

==> In the original condition, there are 2 variables (x, y) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), from con 1), you get a>-a, 2a>0, or a>0, and from con 2), you get ax>ay, and the inequality sign doesn’t change even if you divide both sides by a because since a>9, you get x>y, hence yes, it is always sufficient.

Therefore, the answer is C.
Answer: C

Therefore, the answer is C.
Answer: C

BalysLTU · Answer

Target question : Is x > y? Statement 1 : x + a > x - a a + a > x - x 2a > 0 a > 0 a is POSITIVE That's all this statement tells us. Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT. Statement 2 : ax > ay ax - ay > 0 a(x - y) > 0 Case a: a > 0 and (x - y) > 0, in which case x > y Case b: a < 0 and (x - y) < 0, 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 a is POSITIVE Statement 2 tells us that, if a > 0, x > y Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer: C

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is x > y? (1) x + a > x - a (2) ax > ay

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Is x > y? (1) x + a > x - a (2) ax > ay­