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Gmat prep tough question!

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Gmat prep tough question! [#permalink] New post 07 Mar 2007, 03:30
Could u help me out with this question?? The OA is the one circled in blue (while the other is the one i picked =( )

Please provide extensive explanation to the solution, cause i really don't know how to get it!!

Thanks

Riccardo

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 [#permalink] New post 07 Mar 2007, 04:13
U should focus on the definition of the function sqrt(). This function is returning always a positive value or 0.

That said, since x < 0, u must have sqrt() = something positive. So, it can be only -x or 1.

In a direct solve, we have : -x*|x| = x^2.
Thus, sqrt(x^2) = |x| = -x as x < 0

Note : sqrt(x) is impossible as the content of sqrt() must always be positive or equal to 0.
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 [#permalink] New post 07 Mar 2007, 04:54
We can write

sqrt((-1)(x)|x|)
=sqrt(x|x|), as x<0, so -x is +ve
=sqrt(x^2)
= +/-x

Still not sure why the answer is -x. May be as x is -ve.
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 [#permalink] New post 07 Mar 2007, 05:04
just pick number x=-4 and compute...
sqrt(-x|x|) = sqrt(16) = 4
now check the answer choices...
it is certainly not 1 or -1, it is not x (which is -4 and the answer is 4) and certainly not sqrt(x) which is undefined.
it is, however exactly -x. so the answer is A

also, if you are attentive enough to details, you should notice that
sqrt(something) is always positive, and x is negative (given in the stem) hence answer cannot be x (neither can it be -1 for the same reason).
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 [#permalink] New post 07 Mar 2007, 05:11
it is a tricky one. but not so complex.

the main point is when x<0 then |x| = -x. because |x| must be > 0.

Let's assume x = -1. |-1|=1 = -(-1).

So we got sqrt ( -x*|x| ) = sqrt (-x * -x) = sqrt (x^2) = x.

that's it. -)
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 [#permalink] New post 08 Mar 2007, 21:33
My answer is (A) -x

If x<0, then Sqrt(-x|x|) = ?

x<0 so let's say x = -2

Sqrt(-x|x|) = Sqrt(-(-2)|-2|) = Sqrt(2*2) = Sqrt(4) = 2

2 = -(-2) = -(x) because x = -2

So the answer is -x

Is it correct?
  [#permalink] 08 Mar 2007, 21:33
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