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

Cheers,
Brent