Data Sufficiency

Hi semwal,

This question can be solved using Number Properties or by TESTING a value:

Since x < 0, we know that it's negative. Under the square root sign, we have:

(-1 times a negative)(absolute value of a negative) this becomes:

(positive)(positive)

So, we're taking the square root of a positive number, which will give us a positive value.

Since x is negative, but we need a positive answer, we can eliminate B, D and E

A bit of playing around will prove that the answer is A

What if x = -2 or - 3 or -4 or -5, etc? By plugging in ANY of those values, what would you end up with for an answer?

If x = -2 then

Root[(-1 x -2)(absolute value of -2)] =

Root[ 2 )( 2 ) = Root (4) = + 2

Answer A matches when you plug x = -2 into the answer choices.

GMAT assassins aren't born, they're made,
Rich

semwal wrote: If x < 0, then sqrt(-x |x|) =
a. -x
b. -1
c. 1
d. X
e. sqrt(x)

IMPORTANT RULE: sqrt(x^2) = |x|

Okay, here's another approach:
If x < 0, then x is negative
So, -x = the positive version of x
Likewise, |x| = the positive version of x

So, sqrt(-x |x|) = sqrt(the positive version of x times the positive version of x)
= sqrt(x^2)
= |x|
= the positive version of x
= -x
= A

Cheers,
Brent