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?

## Is x^2 > y^2?

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- Brent@GMATPrepNow
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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

Answer: C

Cheers,

Brent