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# If X is not equal to -Y, is

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Director
Joined: 03 Sep 2006
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If X is not equal to -Y, is [#permalink]  14 Apr 2008, 22:45
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If X is not equal to -Y, is $$(X-Y)/(X+Y)>1?$$

( i ) $$X>0$$

( ii ) $$Y<0$$
Director
Joined: 10 Sep 2007
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Re: DS [#permalink]  15 Apr 2008, 03:41
Statement 1:
Tells us x is positive. But nothing about Y. If y is also positive then expression will be smaller than 1, if y is -ve and |x|>|y|, then expression is bigger than 1, if y is -ve and |x|<|y|, then expression is less than 1, and finally if y = 0, then expression is equal to 1. So this statement alone is not sufficient.

Statement 2:
Tells us y is negative. But nothing about x. If x is positive then expression will be greater than 1, if x is -ve then expression is less than 1, and finally if x = 0, then expression is equal to -1. So this statement alone is not sufficient.

Combining both the statements:
x is +ve and y is -ve.
Say y = x - k (Where k is some -ve constant)
So x-y = x - x + k = k
x+y = x+x-k = 2x - k

If 2x - k > k, then answer is +ve
2x > 2k,
x > k

However if 2x - k < k then answer is -ve.

So even after combining we cannot have the answer.

CEO
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Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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Re: DS [#permalink]  15 Apr 2008, 22:13
Expert's post
Some manipulations with the inequality:

$$\frac{X-Y}{X+Y}>1$$ --> $$\frac{X+Y-2Y}{X+Y}>1$$ ---> $$1-\frac{2Y}{X+Y}>1$$ --> $$\frac{2Y}{X+Y}<0$$ --> $$\frac{Y}{X+Y}<0$$

Now, construct examples:

x=10, y=-1 --> the expression is lesser than 0
x=10, y=-11 --> the expression is greater than 0

E
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Re: DS   [#permalink] 15 Apr 2008, 22:13
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