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# Is sqrt( (x-3)^2 ) = 3 -x ? 1. x not equal to 3. 2. -x|x|

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Joined: 20 Sep 2005
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Is sqrt( (x-3)^2 ) = 3 -x ? 1. x not equal to 3. 2. -x|x| [#permalink]  22 Mar 2006, 22:29
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Is sqrt( (x-3)^2 ) = 3 -x ?

1. x not equal to 3.
2. -x|x| > 0
Director
Joined: 13 Nov 2003
Posts: 793
Location: BULGARIA
Followers: 1

Kudos [?]: 27 [0], given: 0

Think it is B)
When x<0 then the sqrt(x-3)^2=3-x
Manager
Joined: 09 Feb 2006
Posts: 91
Location: Prague, CZ
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Kudos [?]: 15 [0], given: 0

I would say it's B

Statement 1
Let's say x=-2 ..... 5=5
Let's say x=4 ...... 1=-1
INSUFFICIENT

Statement 2
This statement says that x<0
Let's say x=-2 .... 5=5
Let's say x=-4 .... 7=7
SUFFICIENT
SVP
Joined: 24 Sep 2005
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Re: DS [#permalink]  23 Mar 2006, 03:04
lhotseface wrote:
Is sqrt( (x-3)^2 ) = 3 -x ?

1. x not equal to 3.
2. -x|x| > 0

we have: sqrt( (x-3)^2 ) = | x-3|
In order to make the squareroot = 3- x , | x-3| must = 3-x . This happens only when x<= 3

1. Doesn't provide anything about the comparison between x and 3 --> insuff
2. -x|x| >0 ---> -x> 0 ---> x< 0 --> x< 3 ---> this is what we need!--> suff

B it is.
Re: DS   [#permalink] 23 Mar 2006, 03:04
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