IMO : -X
pick a number say x=-5
then,root(-x|x| ) = -(-5)|-5| = 5 = -x.

How is it -X, the answer is 5 and not -5. Btw -x is the OA

we took x as -5.The answer we got after substitution is 5 which is -(-5) = -(x).

the definition for |x| goes as
|x|=-x when x<0
=x when x>0
This is the reason for the modulus of negative number to be positive.
Now -x|x|= -x*-x and this is (-x)2(square)
and sqrt((-x)2)=-x

Thanks a lot Sanjana and Venky, but I am still not able to comprehend the concept.

-x where x = -5 will be -(-5) = 5

|x| where x = -5 = |-5| = 5

root(5*5) = 5. I stop here, maybe I am missing a step or a concept.

Please let me know.

Thanks again,

Vineet

vineetbatra wrote:Thanks a lot Sanjana and Venky, but I am still not able to comprehend the concept.

-x where x = -5 will be -(-5) = 5

|x| where x = -5 = |-5| = 5

root(5*5) = 5. I stop here, maybe I am missing a step or a concept.

Please let me know.

Thanks again,

Vineet

Everything you've done so far is fine, you just stopped before answering the question.

You chose x = -5.

You calculated the value of root(-x|x|) as + 5.

Now you need to actually think about how +5 relates to your chosen value of x; remember, when we pick numbers the last step is to plug the number we've chosen into the choices.

So, we plug x=-5 into the choices and see which one matches our result of +5:

-x ; -(-5) = +5... a match!

-1 ; not +5... eliminate.

1 ; not +5... eliminate.

x ; -5... not the same as +5... eliminate.

root(x) ; root(-5)... imaginary number, these don't show up on the GMAT (and certainly not the same as +5)... eliminate.

Only choice (A) gives us the answer "+5", therefore (A) is correct.

Stuart,

Now I finally got it, I have to read the other side of the equation.

Thanks a lot.

Vineet