GMAT PREP 1 QUESTION

[semwalsanjay423]

Dear all,
could the solution to following question be explained?

162) x < 0, then √-x |x| (root of the whole expression)
a. -x
b. -1
c. 1
d. X
e. √x


OA is (a)

Thanks

[jlucero]

The trick here is to recognize that you need a positive number inside the square root and then a positive number that comes out of the square root. Since the question starts by saying that x is a negative number, you need to recognize that -x will be a positive number. So we take the equation:

√(-x |x|)

since both -x and |x| are positive, we can multiply these together to get:

-x * |x| = (-x)^2

So we are going to take the square root of a number that is squared. This is the same as the absolute value of a number. So what comes out of the root is the positive value of x. But this is where the trick is in this question... remember that we will get the positive value of x out of this root, and since x is negative, we need to remember that the answer is the opposite of a negative number, or -x.

Another way: plug in x = -3

√(-x |x|)
√(-(-3) |-3|)
√(9)
3
and since x = -3, the value of √(-x |x|) is equal to -x = - (-3)