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Gmat Prep Question - please help

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by Baldini » Tue May 19, 2009 12:01 pm
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]
Last edited by Baldini on Tue May 19, 2009 9:51 pm, edited 1 time in total.
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Re: Gmat Prep Question - please help

by El Cucu » Tue May 19, 2009 2:06 pm
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!
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by dumb.doofus » Tue May 19, 2009 3:06 pm
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..
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Re: Gmat Prep Question - please help

by El Cucu » Wed May 20, 2009 6:27 am
El Cucu wrote:
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!
I thought another posibility while driving back home yesterday...
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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by bluementor » Thu May 21, 2009 1:11 am
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-
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