DS with absolute value

[susan.meng]

Is sqrt ((x-5)^2) = 5 - x?
1. -x*abs(x) > 0
2. 5-x>0

[mxs2009]

This question can be rephrased as: is 5-x > 0? Or, more specifically, is x<5 because the left side of the equation can never be negative (the square root of a number cannot be negative in GMAT math)

(1) -x*|x|>0
The absolute value must be positive so we have -x*(a positive number)>0
Thus, x must be negative. x<0. SUFFICIENT

(2) 5-x>0 (subtract each side by 5)
-x>-5 (divide by negative 1)
x<5 (don't forget to switch the signs)
SUFFICIENT

Answer is D

[RonPurewal]

this question is very similar to the following one, so take a look at it.

(in fact, the problem statement is EXACTLY the same; the only difference is that a "5" has been substituted for the "3")

is-sqrt-x-3-2-3-x-t7258.html