GMAT Prep: Root X Squared

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i_have_no_cool_username: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Sat Oct 22, 2011 9:01 am

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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Source: Beat The GMAT — Problem Solving | Thu May 17, 2012 9:51 am

LalaB: Master | Next Rank: 500 Posts; Posts: 425; Joined: Wed Dec 08, 2010 9:00 amFollowed by: 7 members; Thanked: 56 times; GMAT Score:690

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

Happy are those who dream dreams and are ready to pay the price to make them come true.(c)

In order to succeed, your desire for success should be greater than your fear of failure.(c)

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

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.

âˆš(xÂ²) = |x| because the "âˆš" symbol always gives a positive value.
So, âˆš(xÂ²)/x = |x|/x

The correct answer is E.

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i_have_no_cool_username: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Sat Oct 22, 2011 9:01 am

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.
âˆš(xÂ²) = |x| because the "âˆš" symbol always gives a positive value.
So, âˆš(xÂ²)/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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LalaB: Master | Next Rank: 500 Posts; Posts: 425; Joined: Wed Dec 08, 2010 9:00 amFollowed by: 7 members; Thanked: 56 times; GMAT Score:690

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

Happy are those who dream dreams and are ready to pay the price to make them come true.(c)

In order to succeed, your desire for success should be greater than your fear of failure.(c)

Like this post

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