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Is sqrt.(x-3)^2 = 3-x? (1) x != 3 (2) -x|x| > 0 Looking

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Senior Manager
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Is sqrt.(x-3)^2 = 3-x? (1) x != 3 (2) -x|x| > 0 Looking [#permalink] New post 28 Jul 2007, 11:09
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Is sqrt.(x-3)^2 = 3-x?

(1) x != 3
(2) -x|x| > 0

Looking for explanations for both the statements here.

According to me statement 1 is sufficient as it yields NO
Director
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Re: DS: GMAT Prep 1 #28 [#permalink] New post 28 Jul 2007, 18:50
nupurgupt wrote:
Is sqrt.(x-3)^2 = 3-x?

(1) x != 3
(2) -x|x| > 0

Looking for explanations for both the statements here.

According to me statement 1 is sufficient as it yields NO


(1) for x=4 No; for x=-4 Yes INSUFF
(2) X has to be negative; sqrt.(x-3)^2 = 3-x holds true for all -ve X. SUFF
B ?
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 [#permalink] New post 28 Jul 2007, 20:05
OA is B!!!

Thanks Juaz, that was a nice explanation =)
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Re: DS: GMAT Prep 1 #28 [#permalink] New post 28 Jul 2007, 21:26
nupurgupt wrote:
Is sqrt.(x-3)^2 = 3-x?

(1) x != 3
(2) -x|x| > 0

Looking for explanations for both the statements here.

According to me statement 1 is sufficient as it yields NO


hmmm. skipped A b/c when i looked at it I wasn't sure so I went to B.

B tells me that x has to be a negative number |x| is always going to be positive. but if -x|x|>0 then x must be a negative number. lets say x=2
-(2)|2| >0??? no... so it must be negative x=-2: -(-2)|x|>0 x =4

now it can easily be seen that the answer (When using stmnt 2) is NO.

ex: (-2-3)^2=3-2... NO

Stmnt 1: now going back to this I understand it better. x!=3. This is not saying that x=3. So we have no idea and thus stmnt 1 is insuff.

Answer B
Re: DS: GMAT Prep 1 #28   [#permalink] 28 Jul 2007, 21:26
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