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# GMATPrep: Algebra. Take a shot!

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Director
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GMATPrep: Algebra. Take a shot! [#permalink]  29 Dec 2007, 10:26
CEO
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[#permalink]  29 Dec 2007, 10:40
Expert's post
E

√x²/x can change sign for positive and negative x. So, |x|/x
Senior Manager
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[#permalink]  29 Dec 2007, 10:41
root x^2 == +/-X o |X|

so answer = |X|/X
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[#permalink]  29 Dec 2007, 10:45
Correct answer, but I'm not understanding. I understand that the sqroot of x^2 will give me a positive or negative x. But I don't see how that translates into absolute value of x. Can you elaborate?

I said it was 1. I squared the entire thing. got rid of the sqroot on the top. so I had x^2/x^2. Which equals 1.
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[#permalink]  29 Dec 2007, 11:11
Expert's post
|x|=√x² for any x. it is definition.

so, √x²/x=|x|/x always

|x|/x=1 for positive x.
|x|/x=-1 for negative x.
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[#permalink]  29 Dec 2007, 12:36
The value in the numerator is independent of the sign since it is sq(X) and X!=0. Hence |x|

And the denomination can be either positive or negative. Hence just X.
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[#permalink]  29 Dec 2007, 15:10
well, we know that square root always gives a negative and positive value, so the answer to this question cannot be -1 or +1 by itself.

the only logical answer is E, as the absolute value sign takes care of both situations
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[#permalink]  29 Dec 2007, 20:18
Expert's post
pmenon wrote:
well, we know that square root always gives a negative and positive value...

√x² is always positive.
x gives us a negative and positive value
[#permalink] 29 Dec 2007, 20:18
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# GMATPrep: Algebra. Take a shot!

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