Here goes:
|x| > 0 no matter what x is
x < 0, therefore |x| = -x > 0
x < 0, therefore -x > 0
-x * |x| = (-x) * (-x) = x^2 > 0
sqrt( -x * |x| ) = sqrt( x^2 )
Note that in the GMAT, the square root of anything is always positive - this is the key to this question.
sqrt( x^2 ) = -x > 0
Answer = A
The quicker way I think about this (may be confusing to some):
The thing inside the sqrt is not going to be negative, since "undefined" is not an answer choice. Therefore, the two x's inside the sqrt will yield a positive number, x^2. (No need to work out the details of absolute value or negatives.) Therefore, square root of x^2 will be "x-like", ie, either x or -x. Since x<0, but sqrt(anything)>0, the answer is -x, which is greater than 0.
Hint: it's important to master this kinda question
