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# Is sqrt((x-3)^2) = 3-x? (1) x ? 3 (2) x | x | > 0

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Joined: 06 Aug 2005
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Is sqrt((x-3)^2) = 3-x? (1) x ? 3 (2) x | x | > 0 [#permalink]  08 Nov 2005, 18:20
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Is sqrt((x-3)^2) = 3-x?
(1) x ≠ 3
(2) â€“ x | x | > 0

ans is : C .
Why?
Intern
Joined: 01 Jun 2005
Posts: 40
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Re: help!! DS question [#permalink]  08 Nov 2005, 19:53
as13 wrote:
Is sqrt((x-3)^2) = 3-x?
(1) x ≠ 3
(2) â€“ x | x | > 0

ans is : C .
Why?

Note: in GMAT sqrt(x^2) = lxl

therefore the question is just: is lx-3l = -(x-3)? i.e. is (x-3) negative?
From 1: x ≠3. this eliminates the possibility of x-3 = 0; but it doesn't tell us if (x-3)<0

From 2: -xlxl > 0 => x<0. If x <0 than (x-3) <0. therefore sufficient.
The statement -xlxl > 0 already precludes x from being = 3. Hence, i don't understand why 1 is necessary.
I would go with B
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Joined: 24 Sep 2005
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Re: help!! DS question [#permalink]  08 Nov 2005, 19:58
as13 wrote:
Is sqrt((x-3)^2) = 3-x?
(1) x ≠ 3
(2) â€“ x | x | > 0

ans is : C .
Why?

Huh, weird...it shouldn't be C ...coz from 2, -x|x|>0 ---> x <0 ...of coz x<3 ...so (1) doesn't elaborate anything to (2) . From this point, C is already not the correct answer.
SVP
Joined: 24 Sep 2005
Posts: 1893
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agree with tank's point of view. It must be B!
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