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GMAT Prep: Root X Squared

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GMAT Prep: Root X Squared

by i_have_no_cool_username » Thu May 17, 2012 9:51 am
If x is not equal to 0, then [sq root (x)^2]/x =

a) -1
b) 0
c) 1
d) x
e) |x|/x

This looked so simple, and yet there's some concept here that I got wrong. Please enlighten me? (And I'm sure someone has asked this same question somewhere before, but I can't seem to find it - sorry for the repetition!) Thanks.
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by LalaB » Thu May 17, 2012 9:58 am
sq root (x)^2 =|x|

so ur answ is |x|/x

for more please read about modulus

hope it helps
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by Anurag@Gurome » Thu May 17, 2012 8:14 pm
i_have_no_cool_username wrote:If x is not equal to 0, then [sq root (x)^2]/x =

a) -1
b) 0
c) 1
d) x
e) |x|/x

This looked so simple, and yet there's some concept here that I got wrong. Please enlighten me? (And I'm sure someone has asked this same question somewhere before, but I can't seem to find it - sorry for the repetition!) Thanks.
√(x²) = |x| because the "√" symbol always gives a positive value.
So, √(x²)/x = |x|/x

The correct answer is E.
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by i_have_no_cool_username » Thu May 17, 2012 8:30 pm
Anurag@Gurome wrote:
i_have_no_cool_username wrote:If x is not equal to 0, then [sq root (x)^2]/x =

a) -1
b) 0
c) 1
d) x
e) |x|/x

This looked so simple, and yet there's some concept here that I got wrong. Please enlighten me? (And I'm sure someone has asked this same question somewhere before, but I can't seem to find it - sorry for the repetition!) Thanks.
√(x²) = |x| because the "√" symbol always gives a positive value.
So, √(x²)/x = |x|/x

The correct answer is E.
Ok, this was where I went wrong. I know that the sq root of a number is always positive - which was why I thought root x^2 = x, thus x/x = 1. What is the difference between x/x and |x|/x?

Does x/x imply possibilities of positive x/x OR negative x/x, which is why it is incorrect?
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by LalaB » Thu May 17, 2012 9:25 pm
|x|/x means

if x<0 then x/(-x)=-1

if x>0 then x/x=1

since two possibilities are here, u cant just write x/x=1
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