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PS: SQRT

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PS: SQRT [#permalink]

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New post 06 Feb 2009, 09:58
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Which of the following is always equal to sqrt (9+x^2-6x)?

a) x - 3
b) 3 + x
c) |3 - x|
d) |3 + x|
e) 3 - x


This is from this forum and could be debatable. :oops:
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Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html
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Re: PS: SQRT [#permalink]

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New post 06 Feb 2009, 10:05
GMAT TIGER wrote:
Which of the following is always equal to sqrt (9+x^2-6x)?

a) x - 3
b) 3 + x
c) |3 - x|
d) |3 + x|
e) 3 - x


This is from this forum and could be debatable. :oops:

sqrt is either (x-3) or (3-x) whichever is positive.
So, mod (3-x).
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Re: PS: SQRT [#permalink]

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New post 06 Feb 2009, 10:08
I guess the answer is either A or E. 9+x^2-6x = (3-x)^2 or (x-3)^2.

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Re: PS: SQRT [#permalink]

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New post 06 Feb 2009, 11:16
GMAT TIGER wrote:
Which of the following is always equal to sqrt (9+x^2-6x)?

a) x - 3
b) 3 + x
c) |3 - x|
d) |3 + x|
e) 3 - x


This is from this forum and could be debatable. :oops:


As per my knowledge..

GMAT considers only postive values under sqrt..

sqrt (+ve) --> valid for GMAT
sqrt (-ve) --> unreal value not valid for GMAT


y=sqrt (9+x^2-6x) --> SQRT ((3-x)^2) = |3-x|
y= |3-x|
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Re: PS: SQRT [#permalink]

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New post 06 Feb 2009, 11:28
further if b=a^2
sqrt(b) = a and not (-a).
x2suresh wrote:
GMAT TIGER wrote:
Which of the following is always equal to sqrt (9+x^2-6x)?

a) x - 3
b) 3 + x
c) |3 - x|
d) |3 + x|
e) 3 - x


This is from this forum and could be debatable. :oops:


As per my knowledge..

GMAT considers only postive values under sqrt..

sqrt (+ve) --> valid for GMAT
sqrt (-ve) --> unreal value not valid for GMAT


y=sqrt (9+x^2-6x) --> SQRT ((3-x)^2) = |3-x|
y= |3-x|

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Re: PS: SQRT [#permalink]

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New post 06 Feb 2009, 12:53
i agree this is |3-x| ..c it is.

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Re: PS: SQRT [#permalink]

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New post 06 Feb 2009, 13:30
Sorry to harp on this, but 9+x^2-6x = x^2-6x+9. Simple, right? And you can factor that for (x-3)^2. Why is the answer 3-x when logically I can solve it for x-3?

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Re: PS: SQRT [#permalink]

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New post 06 Feb 2009, 13:38
djveed wrote:
Sorry to harp on this, but 9+x^2-6x = x^2-6x+9. Simple, right? And you can factor that for (x-3)^2. Why is the answer 3-x when logically I can solve it for x-3?


(x-3)^2 = (3-x)^2
no doubt about that..

also |x-3| = |3-x|
this is same as

Distance between New York and DC = say 500 miles
=Distance between DC and New York = say 500 miles ( don't say -500 miles)
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Re: PS: SQRT [#permalink]

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New post 06 Feb 2009, 13:46
That clears it up. Thanks.

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New post 06 Feb 2009, 14:11
I don't think on GMAT you will be specifically tested on whether sqr(x^2)=x or sqr(x^2)=/x/
What is the source of this question?

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Re: PS: SQRT [#permalink]

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New post 06 Feb 2009, 14:36
djveed wrote:
That clears it up. Thanks.

when taking a sqrt, we always want a positive number.
Since, the value of x is unknown, we ensure (x-3) is positive by using mod.
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Re: PS: SQRT [#permalink]

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New post 07 Feb 2009, 15:25
GMAT TIGER wrote:
Which of the following is always equal to sqrt (9+x^2-6x)?

a) x - 3
b) 3 + x
c) |3 - x|
d) |3 + x|
e) 3 - x


Thats D.

= \(sqrt (9 + x^2 - 6x)\)
= \(sqrt (3-x)^2\) or \(sqrt (x-3)^2\)
= \((3-x)\) or \((x-3)\) whichever is +ve,
= \(l3-xl\)
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Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html
Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html


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Re: PS: SQRT   [#permalink] 07 Feb 2009, 15:25
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