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

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Is sqrt( (x-3)^2 ) = 3 -x ? 1. x not equal to 3. 2. -x|x| [#permalink] New post 22 Mar 2006, 23:29
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Is sqrt( (x-3)^2 ) = 3 -x ?

1. x not equal to 3.
2. -x|x| > 0
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 [#permalink] New post 23 Mar 2006, 02:35
Think it is B)
When x<0 then the sqrt(x-3)^2=3-x
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 [#permalink] New post 23 Mar 2006, 03:08
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
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Re: DS [#permalink] New post 23 Mar 2006, 04:04
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, 04:04
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