since the square root of a negative number is impossible on the GMAT, the expression under square root sign has to be positive

-x|x| will be positive only if x is negative. because negative x will take care of the minus sign under square roots.

let x=-2

-(-2)|-2| = 2*2 = 4 and squre root of 4 = 2 = -(-2) = -(x)

hope this helps.

aaaahhhh such a subtle trick...

I am also confused by this quesiton and the square root function in GMAT general.

Obviously here the number is squrt (4) but that can be +2 or -2 right, or is the square root in the gmat always positive?

mehravikas wrote:Please explain why is the answer -x. Completely stumped by this one.

Hi vikas,

given x < 0,

and we know that |x| = -x when x < 0 and |x| = x when x > 0

so the eqn becomes
sqrt(-x(-x)) which is equal to -x. hence the choice is A.

Hope it helps!!

hi Jimmy,

I still don't quite understand - according to the question sqrt-x¦x¦, shouldn't it really be sqrt(-(-x)(-x)), ie you have sqrt(x(-x))? I still don't get why the answer should be -x.. please help.

test numbers. take x = -6

so the term becomes

sqrt(-(-6) * 6)
sqrt(36)
=6

x = -6
-(x) = 6 = Answer.

Ok, read the question carefully!
It clearly says X<0; Let's assume x =-6
so though sqrt(36) = +6 or -6; X has to be -ve per the question. Hence since x<0, -X is the Answer