What is the value of x? (1) |x| = x (2) |x|^2 = x^2

Question

What is the value of x?

(1)  |x| = −x

(2)  |x|^2 = −x^2

Bunuel · Accepted Answer

What is the value of x?

(1) |x| = −x. This implies that x is less than or equal to zero. Not sufficient.

(2)  |x|^2= -x^2  -->  x^2=-x^2  -->  2x^2=0  -->  x=0 . Sufficient.

Answer: B.

GMATinsight · Answer

Question: x = ?

Statement 1 :  |x| = −x

i.e. x is non-positive
i.e.x may be be {0, -1, -2, -3...}

NOT SUFFICIENT

Statement 2 :  |x|^2 = −x^2

|x|^2 can NOT be Negative
−x^2 can NOT be Positive

i.e. for  |x|^2 = −x^2 , x must be zero 
i.e. x = 0

SUFFICIENT

Answer: Option B

JoeAl · Answer

Statement1: 
X <=0

Statement 2:
 x^2 + |x|^2 = 0

Only value that satisfies is 0
Hence B.

Posted from my mobile device

TarunKumar1234 · Answer

What is the value of x? Stat1: |x|=−x. so can be any value x= 0, -1, -2...So, Not sufficient. Stat2: |x|^2=−x^2, which is only possible at x = 0, Sufficient. So, I think B.

smmc29 · Answer

(1) |x| = -x

This states that x <= 0

Remember that for data sufficiency questions we must have ONE UNIQUE ANSWER

INSUFFICIENT

(2) (|x|)^2 = -x^2

The expression of an absolute value can never be less than 0. This expression only holds true when x=0

SUFFICIENT.

The answer is B

EgmatQuantExpert · Answer

Solution

Given  
In this question stem, we are given no information.

To find  
We need to determine
  The value of x

Approach and Working out

Statement 1:
  |x| = -x
  Since |x| ≥ 0, we have that -x ≥ 0
 Thus, x ≤ 0.
 But this gives us no value of x. 
 Statement 1 is insufficient alone.

Statement 2:
   |x|^2 = -x^2 
  Since  |x|^2 ≥ 0 , we have that  -x^2 ≥ 0 
 Thus,  x^2 ≤ 0 .
 This is only possible if x = 0. (since,  x^2 ≥ 0 )
 
 Statement 2 is sufficient alone.

Thus, option B is the correct answer.

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What is the value of x? (1) |x| = x (2) |x|^2 = x^2

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