Data Sufficiency

lionsshare wrote:What is the value of |x| ?

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

OA: B

Please help, Experts, what's the best approach to solving this problem. Thanks!

Statement 1: x = -|x|

Since |x| is positive, we can deduce that x is a negative number; however, the value of x, thus |x| is interminable. Insufficient.

Statement 2: x^2 = 4

=> x = ±2

=> |x| = |±2| = 2. Sufficient.

The correct answer: B

Hope this helps!

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lionsshare wrote:What is the value of |x| ?

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

We need to determine the absolute value of x.

Statement One Alone:

x = -|x|

If x = -|x|, then x must be negative or 0. For example, if x = -3, -3 = -|-3|. However, since we do not have an exact value for x, statement one is not sufficient. We can eliminate answer choices A and D.

Statement Two Alone:

x^2 = 4

We can simplify by taking the square root of both sides of the equation:

√x^2 = √4

|x| = 2

Since we have 2 as the value for |x|, this answers the question.

Answer: B