Is x y ? (1) (x - y)(x - y) 0 (2) y 0

Question

Is x > y ?

(1) (x - y)(x - y) > 0
(2) y > 0

Bunuel · Answer

Is x > y ?

(1) (x - y)(x - y) > 0 -->  (x-y)^2>0  --> the only thing we can deduce from this is that  x
eq{y} . (square of a number is always more than or equal to zero. Square of a number equals to zero when the number itself is a zero. Now, as we are given that the square of a number is strictly more than zero thus this number doesn't equal to zero). Not sufficient.

(2) y > 0. Clearly not sufficient.

(1)+(2) All we know is that  x
eq{y}  and  y>0  --> insufficient to say whether  x>y . Not sufficient.

Answer: E.

sang5650 · Answer

Hi,

My questions is cant we simplify the eq as:

(x-y)^2 > 0 
=> (x-y) > 0
=> x > y

Is this method wrong?

Bunuel · Answer

No we cannot simplify like this.

(x-y)^2  is never negative, as x-y is squared, hence  (x-y)^2>0  is true in both cases when x>y and x<y.

When you are writing  x-y>0  after  (x-y)^2>0 , what you are actually doing is reducing (dividing) the inequality by x-y but we can not do that as we don't know whether x-y>0 or not (actually we are asked to determine this).

msand · Answer

just thinking , if we could change the option 1 to (x-y)(x+y) >0. what will the new answer be ?

Bunuel · Answer

Answer would be the same: E.  x^2-y^2>0  and  y>0  does not help us to determine whether  x>y : consider following pairs of (x,y): (-5,3) - answer NO or (5,3) - answer YES.

eragotte · Answer

For these types of questions I find it easier to just check extreme solutions

if x = -100, y = 1 both expressions are true 
if x = 4, y = 3 both expressions are true

In one example x > y in the other y > x therefore e

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 - y)(x - y) > 0 (2) y > 0

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