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# Gmat prep tough question!

Author Message
Intern
Joined: 21 Jan 2007
Posts: 23

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07 Mar 2007, 04:30
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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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SVP
Joined: 01 May 2006
Posts: 1796

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07 Mar 2007, 05:13
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.
Manager
Joined: 09 Jan 2007
Posts: 240

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07 Mar 2007, 05:54
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.
Senior Manager
Joined: 23 Jun 2006
Posts: 387

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07 Mar 2007, 06:04
just pick number x=-4 and compute...
sqrt(-x|x|) = sqrt(16) = 4
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).
Manager
Joined: 20 Jun 2005
Posts: 145

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07 Mar 2007, 06:11
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. -)
Senior Manager
Joined: 20 Feb 2007
Posts: 256

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08 Mar 2007, 22:33

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

Is it correct?
08 Mar 2007, 22:33
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