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x-y

by muzali » Sun Dec 07, 2008 7:17 pm
If x is not equal to -y, is [(x-y)/(x+y)]>1?

1. x>0
2. y<0

I tried the following approach:
[(x-y)/(x+y)]>1
so, x-y>x+y or, 2y<0, or y<0.

Alternatively, [(x-y)/(x+y)]>1, or [(x-y)/(x+y)]-1>0, or [-2y/(x+y)]>0, or -2y>0, or y<0

Thus I chose B, but the correct choice is E. Now knowing the answer, I tried substituting values for x and y and found E to be correct. What was incorrect in my previous approach(es) which led me to B?

Thanks.

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by cramya » Sun Dec 07, 2008 7:18 pm
Dont know if x+y is negative. This would reverse the inequality!

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by Stuart@KaplanGMAT » Mon Dec 08, 2008 3:13 am
cramya wrote:Dont know if x+y is negative. This would reverse the inequality!
Correct!

Whenever you see an inequality, especially in data sufficiency, you need to remember a cardinal rule of manipluation: if you ever multiple or divide both sides by a negative, you must flip the inequality.

So, when we have a variable in the denominator, we have to be very careful about cross-multiplying, since if the denominator is negative, we'll end up flipping.

If the denominator could be positive or negative, then you'll have two different cases, each of which needs to be explored.
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