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# PS: SQRT

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SVP
Joined: 29 Aug 2007
Posts: 2426

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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.

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Manager
Joined: 04 Jan 2009
Posts: 229

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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.

sqrt is either (x-3) or (3-x) whichever is positive.
So, mod (3-x).
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tusharvk

Intern
Joined: 31 Jan 2009
Posts: 10
Schools: UTA, Fuqua, UNC, Yale, Colombia

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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.
SVP
Joined: 07 Nov 2007
Posts: 1738
Location: New York

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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.

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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Manager
Joined: 04 Jan 2009
Posts: 229

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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.

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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tusharvk

Current Student
Joined: 28 Dec 2004
Posts: 3292
Location: New York City
Schools: Wharton'11 HBS'12

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06 Feb 2009, 12:53
i agree this is |3-x| ..c it is.
Intern
Joined: 31 Jan 2009
Posts: 10
Schools: UTA, Fuqua, UNC, Yale, Colombia

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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?
SVP
Joined: 07 Nov 2007
Posts: 1738
Location: New York

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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

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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Smiling wins more friends than frowning

Intern
Joined: 31 Jan 2009
Posts: 10
Schools: UTA, Fuqua, UNC, Yale, Colombia

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06 Feb 2009, 13:46
That clears it up. Thanks.
Director
Joined: 29 Aug 2005
Posts: 819

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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?
Manager
Joined: 04 Jan 2009
Posts: 229

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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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tusharvk

SVP
Joined: 29 Aug 2007
Posts: 2426

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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,
= $$l3-xl$$

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

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