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Please clarify Official Guide DS Prob 1

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Please clarify Official Guide DS Prob 1

by utkalnayak » Sun Jan 04, 2015 5:00 pm
"What is the value of |X| ?

(1) X = - |X|
(2) X^2 = 4

The explanation says with option 1, it can be derived that the value of |X| is positive or 0. I did not understand how it can be any positive number. I think it should be always 0. Can anybody explain ? TIA
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by Brent@GMATPrepNow » Sun Jan 04, 2015 5:22 pm
utkalnayak wrote:What is the value of |x| ?

(1) x = -|x|
(2) x² = 4
Target question: What is the value of |x|?

NOTE: the question is not asking for the value of x. We want the value of |x|

Statement 1: x = -|x|
There are several values of x that satisfy this condition. Here are two:
Case a: x = 0, since 0 = -|0|. In this case |x| = |0| = 0
Case b: x = -1, since -1 = -|-1|. In this case |x| = |-1| = 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x² = 4
This means that x = 2 OR x = -2
Don't make the mistake of concluding that statement 2 is not sufficient. We are not asked to find the value of x. We want the value of |x|
If x = 2, then |x| = |2| = 2
If x = -2, then |x| = |-2| = 2
In both cases, we get the same answer to the target question: |x| = 2
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

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Brent
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by Matt@VeritasPrep » Mon Jan 05, 2015 11:16 am
As an addendum to this, x = -|x| is just a confusing way of saying that x ≤ 0. (The GMAT is quite fond of this equation, as it says something simple in the most painful way imaginable. :D)
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