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Number Properties Gmat Prep question confusing...

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Number Properties Gmat Prep question confusing...

by mustbeatgmat » Mon Nov 15, 2010 10:11 pm
Is X>0?

1) XY>0

2) X+Y>0


I picked E. However the OA is C...

I know that from statement 1, X and Y either have to be both (-) or both (+), and statement 2 tells us that X>Y...but couldnt X still be negative and larger than Y? Ex: X is -2, Y is -4, AND X can be (+) and still bigger than Y...what am i missing?

thank yoU!
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by Rahul@gurome » Mon Nov 15, 2010 10:21 pm
mustbeatgmat wrote:Is X>0?

1) XY>0

2) X+Y>0


I picked E. However the OA is C...

I know that from statement 1, X and Y either have to be both (-) or both (+), and statement 2 tells us that X>Y...but couldnt X still be negative and larger than Y? Ex: X is -2, Y is -4, AND X can be (+) and still bigger than Y...what am i missing?

thank yoU!
Statement 2 is (X + Y) > 0. Which tells us X > -Y not X > Y
If X = -2 and Y = -4, statement doesn't satisfies.

The solution is as follows:

Statement 1: xy > 0
Implies,
  • (1) x > 0 and y > 0
    (2) x < 0 and y < 0
Not sufficient.

Statement 2: x + y > 0
Implies,
  • (1) x > 0 and y > 0
    (2) x > 0 and y < 0 and |x| > |y|
    (3) x < 0 and y > 0 and |x| < |y|
Not sufficient.

1 & 2 together: Only possibility is x > 0 and y > 0.

Sufficient.

The correct answer is C.
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by Rezinka » Mon Nov 15, 2010 11:44 pm
Taking Statement I and II together :
When :

1)
X and Y both are positive :
XY > 0................... Possible
X + Y > 0............... Possible

2)
X and Y both are negative :
XY > 0................... Possible
X + Y > 0............... Not Possible
The sum of 2 negative numbers cannot be a positive number.

Hence we only have 1 option.
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