If x < 0, then sqrt (-x |x|) is
a. -x
b. -1
c. 1
d. x
e. sqrt x
OA is A.
Can someone please explain how to get the answer?
[spoiler]My logic was the following: x = -1. Thus -(-1) = 1, and the absolute value of -1 is 1. So the sqrt (1) is 1, thus x, OA D.
FUrthermore, how can it be - isn't the square root of a negative impossible?[spoiler]
[/spoiler]
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Gmat Prep Question - please help
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dumb.doofus
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Well, if you were to put numbers it will be immediately clear to you..
Let's say x = -2
so for x < 0, |x| = -x
therefore root(-x|x|) = root(-(-2)(-(-2)) = root(4) = 2
So root(-x|x|) = 2
but x = -2, so therefore root(-x|x|) = 2 = -x and that's the answer..
Let's say x = -2
so for x < 0, |x| = -x
therefore root(-x|x|) = root(-(-2)(-(-2)) = root(4) = 2
So root(-x|x|) = 2
but x = -2, so therefore root(-x|x|) = 2 = -x and that's the answer..
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El Cucu wrote:I thought another posibility while driving back home yesterday...Baldini wrote:If x < 0, then sqrt (-x |x|) is
a. -x
b. -1
c. 1
d. x
e. sqrt x
Hi Baldini, I agree with you.
Answer can not be negative! I would choose D also.
Pls. some guru who can help, tks!
May be x*|x|=|x|^2 so the square root of |x|^2 would have 2 results one negative and one positive. As we already know that x is negative, so the only result should be negative. Also this reasoning avoids having a negative value inside the square root
Does this sound to anyone?
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bluementor
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well, the point to note here is that the sqrt() function will only return a non-negative value. there are no two ways about this.
for eg., sqrt(4) = 2, and not -2.
this is slightly different from the following:
if x^2 = 4, then x can be either of the these two values:
(i) x = + sqrt(4) = +2, or
(ii) x = - sqrt(4) = -2
so in the gmatprep question above, if x<0, then -x is positive. therefore, -x|x| = x^2, which is a positive value. and since the sqrt() function must return a positive (or strictly speaking, a non-negative value) value, sqrt(-x|x|) must equal to -x.
choose A.
-BM-
for eg., sqrt(4) = 2, and not -2.
this is slightly different from the following:
if x^2 = 4, then x can be either of the these two values:
(i) x = + sqrt(4) = +2, or
(ii) x = - sqrt(4) = -2
so in the gmatprep question above, if x<0, then -x is positive. therefore, -x|x| = x^2, which is a positive value. and since the sqrt() function must return a positive (or strictly speaking, a non-negative value) value, sqrt(-x|x|) must equal to -x.
choose A.
-BM-
