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Modulus problem

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by surajgarg » Fri Jul 23, 2010 6:07 am
If |x|+|y| = -x-y and xy does not equal 0, which of the following must be true?

A. x+y>0
B. x+y<0
C. x-y>0
D. x-y<0
E. x^2-y^2>0

Pls tell me how to approach this problem.

Also need some tips on problems involving modulus and inequalities.
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by kvcpk » Fri Jul 23, 2010 6:13 am
If |x|+|y| = -x-y and xy does not equal 0, which of the following must be true?

A. x+y>0
B. x+y<0
C. x-y>0
D. x-y<0
E. x^2-y^2>0

xy is not 0. Hence x or y cannot be 0

|x|+|y| = -x-y

Let x>0, y>0
x+y = -x-y
Possible only when x+y = 0
But x>0,y>0 Hence NOT POssible.

Let x>0, y<0
x-y=-x-y
x=0
But x>0 hence not possible

Let x<0,y>0
-x+y=-x-y
y=0
but y>0 hence not possible

Let x<0,y<0
-x-y = -x-y
Possible for all x, y

Hence x<0, y<0
x+y will be negative.

pick B

When dealing with modulus questions, Important point is to exhaust all the possible scenarios.
I follow only this approach, though its a bit time consuming. But its effective and less prone to errors.

Hope this helps!!
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