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Source: — Data Sufficiency |

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by [email protected] » Sun Dec 01, 2013 7:58 pm
Hi shibsriz,

This DS question is perfect for TESTing Values.

We're asked: Is |X| +|Y| = 0? This is a YES/NO question.

Fact 1: X + 2|Y| = 0

X = 0
Y = 0
The answer to the question is YES

X = -2
Y = -1
The answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: Y +2|X| = 0
**Notice this is essentially the same "math" as Fact 1? Similar logic will work here**

X = 0
Y = 0
The answer to the question is YES

X = -1
Y = -2
The answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we know that X and Y must both be 0. There are no other sets of values that will fit both equations (because of the "times 2" in each equation).
Together, SUFFICIENT

Final Answer: C

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by Matt@VeritasPrep » Sun Dec 01, 2013 10:27 pm
Start with the stem: |x| + |y| = 0 if and only if x = y = 0. So the question is really "Are x and y both equal to 0?"

Statement 1 gives us

2|y| = -x
or
|y| = -x/2

This seems to give us a contradiction, but if x is negative, -x is positive, so -x/2 can be literally anything nonnegative. NOT sufficient!

Statement 2 is pretty much the same thing.

Together, however, we have

x + 2|y| = 0, or x = -2|y|, which we can substitute into the second equation to obtain

y + 2|-2|y|| = 0, or y + 4|y| = 0, or y = -4|y|, or y = 0.

From here, substitute y = 0 into the first equation to find that x = 0, and you're done!
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by GMATGuruNY » Mon Dec 02, 2013 5:39 am
Is |x| + |y| = 0?

Statement 1: x + 2|y| = 0
x = -2|y|.

Case 1: x=0 and y=0.
In this case, |x| + |y| = 0.

Case 2: x=-2 and y=1.
In this case, |x| + |y| ≠ 0.
INSUFFICIENT.

Statement 2: y + 2|x| = 0
y = -2|x|.

Case 1: x=0 and y=0.
In this case, |x| + |y| = 0.

Case 3: x=1 and y=-2.
In this case, |x| + |y| ≠ 0.
INSUFFICIENT.

Statements combined:
Squaring x = -2|y|, we get:
x² = 4y².

Squaring y = -2|x|, we get:
y² = 4x².

Substituting y² = 4x² into x² = 4y², we get:
x² = 4(4x²)
x² = 16x²
0 = 15x²
0 = x²
0 = x.
Since x=0, we know that y=0, as indicated in Case 1 above.
Thus, |x| + |y| = 0.
SUFFICIENT.

The correct answer is C.
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