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# is ((x-3)^2)^1/2 =3-x? a)x not = 3(is not equal to )

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Current Student
Joined: 11 May 2008
Posts: 553
is ((x-3)^2)^1/2 =3-x? a)x not = 3(is not equal to ) [#permalink]

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24 Aug 2008, 00:17
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

is ((x-3)^2)^1/2 =3-x?

a)x not = 3(is not equal to )
b)-x|x|>0

i THOUGHT d IS THE ans.. what is wrong?
Director
Joined: 12 Jul 2008
Posts: 514
Schools: Wharton
Re: GMAT PREP [#permalink]

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24 Aug 2008, 08:26
arjtryarjtry wrote:
is ((x-3)^2)^1/2 =3-x?

a)x not = 3(is not equal to )
b)-x|x|>0

i THOUGHT d IS THE ans.. what is wrong?

B

Rephrase: |x-3| = 3-x

This occurs when x-3 < 0, i.e., |x-3| = -(x-3)
This means x < 3

(1) Insufficient

For example
((5-3)^2)^(1/2) = 2; 3-x = -2
((0-3)^2)^(1/2) = 3; 3-0 = 3

(2) Sufficient
-x|x| > 0 implies -x > 0 and/or x < 0 (since we know |x|>0)

Last edited by zonk on 24 Aug 2008, 09:02, edited 1 time in total.
Intern
Joined: 10 Aug 2008
Posts: 22
Schools: Emory Goizueta (Class of 2013)
WE 1: Management consultant
WE 2: Marketing consultant
Re: GMAT PREP [#permalink]

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24 Aug 2008, 08:47
zoinnk wrote:
arjtryarjtry wrote:
is ((x-3)^2)^1/2 =3-x?

a)x not = 3(is not equal to )
b)-x|x|>0

i THOUGHT d IS THE ans.. what is wrong?

B

Rephrase: |x-3| = 3-x

This occurs when x-3 < 0, i.e., |x-3| = -(x-3)
This means x < 3

(1) Insufficient

For example
((5-3)^2)^(1/2) = 2; 3-x = -2
((0-3)^2)^(1/2) = 3; 3-0 = 3

(2) Sufficient
-x|x| > 0 implies -x > 0 and/or x < 0 (since we know |x|>0)

What about the case x=3? Is 0^(1/2) defined?
Director
Joined: 12 Jul 2008
Posts: 514
Schools: Wharton
Re: GMAT PREP [#permalink]

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24 Aug 2008, 09:01
winnie wrote:
zoinnk wrote:
arjtryarjtry wrote:
is ((x-3)^2)^1/2 =3-x?

a)x not = 3(is not equal to )
b)-x|x|>0

i THOUGHT d IS THE ans.. what is wrong?

B

Rephrase: |x-3| = 3-x

This occurs when x-3 < 0, i.e., |x-3| = -(x-3)
This means x < 3

(1) Insufficient

For example
((5-3)^2)^(1/2) = 2; 3-x = -2
((0-3)^2)^(1/2) = 3; 3-0 = 3

(2) Sufficient
-x|x| > 0 implies -x > 0 and/or x < 0 (since we know |x|>0)

What about the case x=3? Is 0^(1/2) defined?

In this problem, x = 3 case is irrelevant, because (2) tells you x < 0. I have fixed my original analysis of the stem, though.
Manager
Joined: 22 Jul 2008
Posts: 146
Re: GMAT PREP [#permalink]

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24 Aug 2008, 09:41
Statement 1: Let x > 3, say, 4.
(4-3) is not equal to 3-4.
Let x < 3, say, 2; {(2-3)^2}^1/2 = {(-1)^2}^1/2 = 1= 3-2 (True)
Now, let x = 0; {(0-3)^2}^1/2 = (9)^1/2 = +/-3
+3 = 3-0, but -3 is not so.
Therefore St1 is not sufficient.

Statement 2: -x|x| >0 implies that x<0
Let x + -2; {(-2-3)^2}^1/2 = (25)^1/2 = +/-5
Again, +5 = 3-(-2) but -5 is not so.
Therefore, St2 is also not sufficient.
Therefore Answer should be E
Manager
Joined: 14 Jun 2007
Posts: 166
Location: Vienna, Austria
Re: GMAT PREP [#permalink]

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25 Aug 2008, 00:18
have never seen this on gmatprep - still, very good Q! Can someone pls confirm the OA?
Intern
Joined: 10 Aug 2008
Posts: 22
Schools: Emory Goizueta (Class of 2013)
WE 1: Management consultant
WE 2: Marketing consultant
Re: GMAT PREP [#permalink]

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26 Aug 2008, 06:32
In this problem, x = 3 case is irrelevant, because (2) tells you x < 0. I have fixed my original analysis of the stem, though.

I totally agree with your answer. I just wanna ask a/0 is undefined, Is O^a undefined?
Director
Joined: 12 Jul 2008
Posts: 514
Schools: Wharton
Re: GMAT PREP [#permalink]

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26 Aug 2008, 08:09
winnie wrote:
In this problem, x = 3 case is irrelevant, because (2) tells you x < 0. I have fixed my original analysis of the stem, though.

I totally agree with your answer. I just wanna ask a/0 is undefined, Is O^a undefined?

nope, 0^a is just 0.
Re: GMAT PREP   [#permalink] 26 Aug 2008, 08:09
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# is ((x-3)^2)^1/2 =3-x? a)x not = 3(is not equal to )

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