Is x > 0 ?

(1) xy + y = y

(2) xy + x = x

OA E

## Kaplan: Is x > 0 ?

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- conquistador
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Last edited by conquistador on Tue Dec 15, 2015 9:21 am, edited 1 time in total.

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- Brent@GMATPrepNow
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Mechmeera wrote:Is x > 0 ?

(1) xy + y = y

(2) xy + x = x

**Target question:**

**Is x > 0 ?**

**Statement 1: xy + y = y**

Subtract y from both sides to get xy = 0

There are several values of x and y that satisfy this. Here are two:

Case a: x = 1 and y = 0, x > 0

Case b: x = -1 and y = 0, x < 0

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

**Statement 2: xy + x = x**

Subtract x from both sides to get xy = 0

IMPORTANT: This is the SAME INFORMATION we got from statement 1.

When both statements provide the same information, the correct answer is either D or E.

Since statement 1 is NOT SUFFICIENT, we can conclude that the correct answer must be E

Cheers,

Brent

- conquistador
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why cant we say thatBrent@GMATPrepNow wrote:Mechmeera wrote:Is x > 0 ?

(1) xy + y = y

(2) xy + x = xTarget question:Is x > 0 ?

Statement 1: xy + y = y

Subtract y from both sides to get xy = 0

There are several values of x and y that satisfy this. Here are two:

Case a: x = 1 and y = 0, x > 0

Case b: x = -1 and y = 0, x < 0

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: xy + x = x

Subtract x from both sides to get xy = 0

IMPORTANT: This is the SAME INFORMATION we got from statement 1.

When both statements provide the same information, the correct answer is either D or E.

Since statement 1 is NOT SUFFICIENT, we can conclude that the correct answer must be E

Cheers,

Brent

(1) xy+y=y

(x+1)y=y

cancel y on both sides

x+1=1

x=0

so x is not greater than zero

whats wrong in this approach?

- DavidG@VeritasPrep
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When you divided both of sides of (x+1)y=y by 'y' you assumed that 'y' did not equal zero. We can't assume that.why cant we say that

(1) xy+y=y

(x+1)y=y

cancel y on both sides

x+1=1

### GMAT/MBA Expert

- Brent@GMATPrepNow
- GMAT Instructor
**Posts:**16207**Joined:**Mon Dec 08, 2008 6:26 pm**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1268 members**GMAT Score:**770

Good question.Mechmeera wrote: why cant we say that

(1) xy+y=y

(x+1)y=y

cancel y on both sides

x+1=1

x=0

so x is not greater than zero

whats wrong in this approach?

The answer lies in what you mean when you say "cancel y on both sides"

You aren't really "canceling;" you're dividing both sides by y.

This is fine in many situations.

For example, if 5x = 5y, we can divide both sides by 5 to get x = y

However, what if we have 0x = 0y? Can we divide both sides by 0 to get x = y?

No.

We can't divide both sides by 0 and make any conclusions.

So, when you divide by y (to cancel the y's), you must eliminate the possibility that y = 0.

In this case, it's quite possible that y = 0, in which case we can't conclude that x + 1 = 1

Cheers,

Brent