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Kaplan: Is x > 0 ?

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue Dec 15, 2015 7:35 am
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
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by conquistador » Tue Dec 15, 2015 7:42 am
Brent@GMATPrepNow wrote:
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
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?
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by DavidG@VeritasPrep » Tue Dec 15, 2015 7:50 am
why cant we say that
(1) xy+y=y
(x+1)y=y
cancel y on both sides
x+1=1
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.
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by Brent@GMATPrepNow » Tue Dec 15, 2015 7:53 am
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?
Good question.
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
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