Is x^2 > y^2?

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Is x^2 > y^2?

by Vincen » Fri Sep 22, 2017 11:07 am
Is x^2 > y^2?

(1) x + y = 2
(2) x > y

The OA is C.

Why statement (2) is not sufficient? What is wrong with it?

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by Brent@GMATPrepNow » Fri Sep 22, 2017 1:50 pm
Vincen wrote:Is xÂ² > yÂ²?

(1) x + y = 2
(2) x > y
Target question: Is xÂ² > yÂ²?
When I SCAN ahead, I see that statement 1 has the expression x+y on one side of the equation.
This is a nice hint telling me that this could be a good candidate for rephrasing the target question.

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

Take xÂ² > yÂ² and subtract yÂ² from both sides to get: xÂ² - yÂ² > 0
Factor to get: (x + y)(x - y) > 0

REPHRASED target question: Is (x + y)(x - y) positive?

Statement 1: x + y = 2
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 2 and y = 0, in which case (x + y)(x - y) = (2 + 0)(2 - 0) = 4. So, (x + y)(x - y) IS positive
Case b: x = 0 and y = 2, in which case (x + y)(x - y) = (0 + 2)(0 - 2) = -4. So, (x + y)(x - y) is NOT positive
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x > y
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 2 and y = 0, in which case (x + y)(x - y) = (2 + 0)(2 - 0) = 4. So, (x + y)(x - y) IS positive
Case b: x = -1 and y = -2, in which case (x + y)(x - y) = (-1 + -2)(-1 - -2) = -3. So, (x + y)(x - y) is NOT positive
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x + y = 2, which means (x + y) is POSITIVE
Statement 2 tells us that x > y
If we take x > y and subtract y from both sides, we get x - y > 0
In other words (x - y) is POSITIVE

So, (x + y)(x - y) = (POSITIVE)(POSITIVE) = POSITIVE
In other words, (x + y)(x - y) IS positive
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT