|x| + |y| = 0 is possible only when x =y =0

(1) x + 2|y| = 0
both x and y could be 0
or x= -2|y|, so say y =1 , x = -1
insuff

(2) y + 2|x| = 0
SAME as statement I above
insuff

combined..
x+y+2|x|+2|y|=0
x=-2|y| not possible as then y cannot equal -2|x|
so x=y=0..
ans is YES for "is |x|+|y|=0?"
suff
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Is |x| + |y| = 0 ?
First, think of possible scenarios where this is true. Due to Modulus, the only possibility is if x=0 and y=0. Remember this when approaching Statement 1 and 2.

(1) x + 2|y| = 0
If x=0 and y=0, then our answer is Yes.
If we make x=-2 and y=1, then this statement will satisfy the equation, however our answer to the question will now be No.
Yes+No=NF

(2) y + 2|x| = 0
If x=0 and y=0, then our answer is Yes.
If we make y=-2 and x=1, this this statement satisfies the equation, however our answer to the question will now be No.
Yes+No=NF

(1)+(2) x+y+2|x|+2|y|=0
If x=0 and y=0, then our answer is Yes.
There is not a possible scenario where you can use negative numbers for x or y and satisfy the equation.
Therefore, the only possible answer here is x=0 y=0. Yes. Sufficient

Answer: C
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