I still dont understand..

isnt |x| just the positive value of the number x?

let say -x=y (y is positive)

sqrt (-x |x|) = sqrt (y|-y|) = sqrt (y^2) = y or -y

when y +ve --> answer =y = -x
wnen y -ve --> answer = -y=x

here y is +ve so answer =-x

E
_________________

Your attitude determines your altitude
Smiling wins more friends than frowning

Thanks Ian for the explanation and for posting the question in mathematical format.

+2

+1 to you.

Thanks for the explanation. When I saw this problem, I had a feeling there was something I was missing.

But why ?? is this a standard formula ?

I think the answer is 4. X


Coz: given that x<0 , -(-x) is positive and module x is also positive so we get x^2 , and end result is x

If you do not think so please correct me

I guess the best way to solve this question is to plug in values and see how the result features.

Before we do the same, explanation by HongHu is perfect. (Cant post the link to his reply as I am new to the club )

i.e Square root of any positive number is a positive number

Now getting back to the actual question:

If x<0, then \sqrt{-x*|x|} equals:
1. -x
2. -1
3. 1
4. x
5. \sqrt{x}

Approach:
Since x <0, let use plug in a negative integer as x, for e.g.

Let x = -2 ---- [1]

Hence \sqrt{-x*|x|}= \sqrt{-(-2)*|-2|} = \sqrt{2*2} = \sqrt{4} ---- [2]

Now as per the discussion going on, the point of disagreement is that \sqrt{4} = 2 or -2. But as stated by HongHu, we would consider \sqrt{4} = 2 only! The reason for this conclusion is that the radical sign used in sqrt{x} is used to show the positive square root of a number x.

Therefore \sqrt{4} = 2 ---- [3]

Now as per Equation [1] marked above, x = -2 which can also be written as -x = 2 ---- [4]

Hence if we subsitute the values of \sqrt{4} from equation 2 ( i.e. \sqrt{-x*|x|} ) and value of 2 from equation [4] ( i.e. -x )... in equation [3], we get the following result:

\sqrt{-x*|x|} = -x and hence the correct answer is 1

This approach can be verified by another question which featured in the GMAT prep exams...

If x \neq 0, then \frac{\sqrt{x^2}}{x} equals:
1. -1
2. 0
3. 1
4. x
5. \frac{|x|}{x}

Approach:
In this question, we don't know whether x is negative or positive. Hence \sqrt{x^2} is always equal to |x|. Reason for the same is: x is a variable here and we dont know the exact value. The absolute value sign is needed when we are taking the square root of a square of a variable, which may be positive or negative

Therefore in this situation, the answer would be 5

Hope this helps!

Cheers!
JT
_________________

Cheers!
JT...........
If u like my post..... payback in Kudos!!

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice|
|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|


~~Better Burn Out... Than Fade Away~~