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Gmatprep problem involving square-root

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jayhawk2001 Community Manager
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Gmatprep problem involving square-root

Sat Apr 14, 2007 2:29 pm
Another one from gmatprep.

1 - doesn't tell us much

2 - just tells us that x is negative

sqrt ((x-3)^2) can yield either x-3 or 3-x. So, I chose E which clearly was
wrong.

I'll post the OA after seeing a few replies.
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leo Senior | Next Rank: 100 Posts
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Mon Apr 16, 2007 6:33 pm
I go for D. Whats the Answer?

jayhawk2001 Community Manager
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Mon Apr 16, 2007 9:14 pm
OA is B

ajith Legendary Member
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Sat Apr 14, 2007 7:29 pm
sqrt refers to the positive root
sqrt ((x-3)^2) can yield either x-3 or 3-x,whichever one is positive

2 tells us that x is negative
3-x is positive and thus the root.

So 2 is clearly sufficient

1 is not sufficient

B is the answer for me!

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RAGS Senior | Next Rank: 100 Posts
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Sun Apr 15, 2007 7:41 am
The Q stem can be simplefied to say x-3 = 3-x ie 2x=6 or is x=3

1 is sufficient

2 says x is negative so cannot be equal to 3 hence sufficient

so ans is D

ajith Legendary Member
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Sun Apr 15, 2007 8:10 am
RAGS wrote:
The Q stem can be simplefied to say x-3 = 3-x ie 2x=6 or is x=3
wrong!

sqrt(x-3)^2 is x-3 when x>3 and 3-x when x<3

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jayhawk2001 Community Manager
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Sun Apr 15, 2007 8:28 am
ajith wrote:
sqrt(x-3)^2 is x-3 when x>3 and 3-x when x<3
Ok, this is the part I don't understand.

Take x = -1, (-1-3)^2 = 16 and root-16 can be +4 or -4 right ?

Why should the root operation yield only the positive root ?

ajith Legendary Member
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Sun Apr 15, 2007 9:53 am
jayhawk2001 wrote:
ajith wrote:
sqrt(x-3)^2 is x-3 when x>3 and 3-x when x<3
Ok, this is the part I don't understand.

Take x = -1, (-1-3)^2 = 16 and root-16 can be +4 or -4 right ?

Why should the root operation yield only the positive root ?
A square root, also called a radical or surd, of x is a number r such that r^2==x. The function sqrt(x) is therefore the inverse function of f(x)==x^2 for x>=0.
Source :http://mathworld.wolfram.com/SquareRoot.html

Please refer the attached image
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jayhawk2001 Community Manager
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Sun Apr 15, 2007 11:31 am
ajith wrote:
A square root, also called a radical or surd, of x is a number r such that r^2==x. The function sqrt(x) is therefore the inverse function of f(x)==x^2 for x>=0.
Source :http://mathworld.wolfram.com/SquareRoot.html
Ah, ok. Official Guide Quantitative Review (Green book) page 24,
section 7, also says the following --

"Ever positive number n has two square roots, one positive and the
other negative, but root-n denotes the positive number whose square
is n".

Darn, missed this.

Just to summarize, x^2 = 9 implies x can be +3 or -3 but
root-9 is always 3.

RAGS Senior | Next Rank: 100 Posts
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Tue Apr 17, 2007 9:16 am
thanks for correcting me

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