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Guest
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Post subject: If x < 0, then sqrt(-x|x|) is  Posted: Sat Aug 11, 2007 4:39 pm |
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Please refer to the attached image.
The answer is -x.
a) how is the answer to a sqrt negative?
b) isn't the sqrt of (-x) * (-x) = sqrt of x^2 = x.
What am I missing?
Thank you.
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StaceyKoprince
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Post subject: Posted: Sun Aug 12, 2007 3:16 pm |
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Location: San Francisco
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Really confusing. The question begins by telling us that x is negative. The second term, [x] (those are supposed to be absolute value signs) actually becomes -x. Think about it - absolute value means the number becomes positive. x by itself indicates a negative number. So to indicate the positive version of the negative number, I have to put another negative sign in front of it, to cancel out the negatives.
That leaves me with SQRT(-x*-x). The square root of that is -x, which is not actually a negative number - it's a positive number. (Remember, again, that x is negative.)
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Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT
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Guest
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Post subject: Got it Posted: Sun Aug 12, 2007 3:49 pm |
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mrohekar
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Post subject: Posted: Mon Aug 20, 2007 5:48 am |
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Another tip : Square root of a negative number will have an 'i' (imaginary number) in its answer
eg. square root of -16 = 4i.
Hence if the answer choices have a -ve number without an 'i' they can be straight away ruled out. Additionally I dont think GMAT test imaginary numbers.
Hence if you get a negative number under the square root sign check to see if the answer choices have an 'i' or you have made a mistake.
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Harish Dorai
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Post subject: Posted: Mon Aug 20, 2007 9:03 am |
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Given X is negative.
So (-X) is positive.
|X| is always positive.
So (-X) multiplied by |X| is also positive which is also equal to Square of X. Its square root can be -X or +X
Since they have given the Radical sign and there is no negative sign before the radical sign the resultant expression should be Positive. For that it has to be (-X) (Because X is negative from the first statement).
Hope it helps
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Guest
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Post subject: What does ve stand for? Posted: Mon Aug 20, 2007 2:53 pm |
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"have a -ve number"
Don't understand the lingo, what does "ve" or "-ve" stand for?
thanks.
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Guest
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Post subject: Re: What does ve stand for? Posted: Mon Aug 20, 2007 8:02 pm |
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Guest wrote: "have a -ve number"
Don't understand the lingo, what does "ve" or "-ve" stand for?
thanks.
-ve : negative number
ve : positive number
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StaceyKoprince
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Post subject: Posted: Tue Aug 21, 2007 6:41 pm |
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The GMAT doesn't test imaginary numbers. You'll never see an i indicating an imaginary number on the test.
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Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT
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vinversa
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Post subject: Re: If x < 0, then sqrt(-x|x|) is Posted: Wed Jul 14, 2010 1:09 pm |
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IF x<0, then SQRT(-x.|x|) is
|x| = -x if x<0 (GMAT given rule)
Then we get SQRT(-x.-x)
SQRT(x^2)
+/-x
But since x<0 (given)
We pick –x as answer
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sudaif
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Post subject: Re: If x < 0, then sqrt(-x|x|) is Posted: Wed Jul 14, 2010 4:46 pm |
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i like vinesa's method the best
very often, i've made the mistake of cancelling out the the square with the overhanging square root sign without considering the positive negative sign that results.
also, another way to quickly solve such a tricky question would be to pick numbers.
if you take x=-1, you get answer =1
if you take x=-2, you get answer =2
the result in itself is the negative of x...and results in a positive number.
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debmalya.dutta
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Post subject: Re: If x < 0, then sqrt(-x|x|) is Posted: Thu Jul 15, 2010 5:58 pm |
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sqrt(-x|x|) = sqrt(-x*-x) because |x| = -x when x<0
= sqrt(+x^2)
= +x or -x
But question stem says x<0..hence sqrt(-x|x|)=-x
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RonPurewal
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Post subject: Re: If x < 0, then sqrt(-x|x|) is Posted: Thu Aug 05, 2010 6:31 am |
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by far the easiest way to solve this problem is to pick your own number for x.
the prompt implies that this will work for all values of x < 0, so it's guaranteed that you'll be able to pick any such value.
let's say x = -4.
then the prompt becomes √(-(-4)(4)), or √16 = 4.
(a) 4
(b) -1
(c) 1
(d) -4
(e) impossible
done. answer (a).
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gmataker
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Post subject: My approach. Posted: Wed Sep 29, 2010 3:45 am |
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[*]|x| -> Absolute value of x
[*]Given, x<0
So, after substituting x = -x, the equation √-x|x| can be re-written as
√-(-x)|-x|
= √x.x (because |-x| = x) (DONT stop here)
=√x²
= +x or -x
But because x<0 (given) , we choose the answer as -x. I guess the mistake most people make is to ignore the given condition of x being negative and assume √x.x = x
Is this a correct approach?
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gokul_nair1984
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Post subject: Re: If x < 0, then sqrt(-x|x|) is Posted: Wed Sep 29, 2010 6:11 am |
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gmataker wrote: [*]|x| -> Absolute value of x
[*]Given, x<0
So, after substituting x = -x, the equation √-x|x| can be re-written as
√-(-x)|-x|
= √x.x (because |-x| = x) (DONT stop here)
=√x²
= +x or -x
But because x<0 (given) , we choose the answer as -x. I guess the mistake most people make is to ignore the given condition of x being negative and assume √x.x = x
Is this a correct approach? Correct :)
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tim
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Post subject: Re: If x < 0, then sqrt(-x|x|) is Posted: Fri Oct 08, 2010 1:37 am |
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Location: Southwest Airlines, seat 21C
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you don't want to substitute x=-x. that is an incorrect statement. the better way to do this is to say x = -|x|. now the negatives cancel out and you have root(|x||x|). well, |x||x| = x^2 so it is root(x^2), which you should memorize is equal to |x|. since x<0, |x| is a positive number, in other words -x..
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Tim Sanders
Manhattan GMAT Instructor
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