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x != y, Is x-y/x+y > 1?

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zchampz
 Post subject: x != y, Is x-y/x+y > 1?
 Post Posted: Mon Jan 18, 2010 8:23 pm 
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Course Students


Posts: 21
x != y

Is x-y/x+y > 1?

1) x > 0
2) y < 0

If we plug-in the number it is clear that the answer is E. But is there any conceptual approach to solve this. I tried to do the following which results in the solution as B (which is incorrect)

x-y/x+y > 1?

If we simplify...
=> x-y > x+y
=> x-x > y+y
=> 0>2y
=> y < 0
So, can we rephrase the question as "is y < 0?"

Thanks,
Champ
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esledge
 Post subject: Re: x != y, Is x-y/x+y > 1?
 Post Posted: Wed Jan 20, 2010 3:33 pm 
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ManhattanGMAT Staff


Posts: 903
Location: St. Louis, MO
zchampz wrote:
x != y

Can you clarify your notation? I'm reading this as x! = x factorial = y. That would imply y is positive, so (2) conflicts and I know this is the wrong interpretation.

Do you mean "x does not equal y"? Or was it originally "x does not equal -y"? (so the denominator of the expression can't be zero)?

zchampz wrote:
x-y/x+y > 1?

If we simplify...
=> x-y > x+y
=> x-x > y+y
=> 0>2y
=> y < 0
So, can we rephrase the question as "is y < 0?"

In any case, your error occured here. You assumed that (x+y) was positive, so when you multiplied both sides of the inequality by that denominator, you didn't have to flip the sign.

If (x+y) were negative, the rephrase would be:
x-y/x+y > 1?
=> x-y < x+y? FLIPPED SIGN HERE
=> x-x < y+y?
=> 0<2y?
=> y > 0?

So without info on x and y, we don't even know whether to ask "Is y > 0?" or "Is y < 0?"

The answer is E because x > 0 and y < 0 means that x+y = pos + neg, which could be either pos or neg depending on the (unknown) relative size of x and y.

_________________
Emily Sledge
Instructor
ManhattanGMAT
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zchampz
 Post subject: Re: x != y, Is x-y/x+y > 1?
 Post Posted: Thu Jan 21, 2010 2:38 am 
Offline
Course Students


Posts: 21
I meant x is not equal to y (x != y )...

Thanks...as you said I assumed x+y as positive.
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mschwrtz
 Post subject: Re: x != y, Is x-y/x+y > 1?
 Post Posted: Fri Apr 16, 2010 4:26 pm 
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ManhattanGMAT Staff


Posts: 506
We're glad that Emily was able to help.
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gurvindersingh2004
 Post subject: Re: x != y, Is x-y/x+y > 1?
 Post Posted: Mon Nov 07, 2011 4:01 pm 
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Students


Posts: 24
If we combine 1 and 2
and plug in numbers x=5
y=-3
then x-y=8
x+y = 2
x-y/x+y = 4 . Therefore C why E ?

I got it thanks
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RonPurewal
 Post subject: Re: x != y, Is x-y/x+y > 1?
 Post Posted: Wed Nov 09, 2011 6:58 am 
Offline
ManhattanGMAT Staff


Posts: 6765
gurvindersingh2004 wrote:
If we combine 1 and 2
and plug in numbers x=5
y=-3
then x-y=8
x+y = 2
x-y/x+y = 4 . Therefore C why E ?

that's "yes" to the question.
now try plugging in x = 3 and y = -5. you'll get a "no" to the question. so, (e).
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