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sqrt((x-3)^2) = 3 - x?

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Source: — Data Sufficiency |
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by ajith » Sun Feb 14, 2010 2:34 am
gmatmachoman wrote:Is sqrt((x-3)^2) = 3 - x?

1) x is not equal to 3
2) -x|x| > 0


OA: b
sqrt() function refers to the positive square root
sqrt((x-3)^2) = x-3 when x-3>0
sqrt((x-3)^2) = 3-x when 3-x >0

1.) x is not equal to 3 is not sufficient to answer Is sqrt((x-3)^2) = 3 - x
2) -x|x| > 0 => -x > 0 => x< 0
sufficient to prove that 3-x>0
and hence sqrt((x-3)^2) = 3-x

Sufficient

Hence B
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by shashank.ism » Sun Feb 21, 2010 7:37 pm
gmatmachoman wrote:Is sqrt((x-3)^2) = 3 - x?

1) x is not equal to 3
2) -x|x| > 0


OA: b
sqrt((x-3)^2) = |x-3|
Now ((x-3)^2) = 3 - x ---> |x-3| =3-x --> x-3<0 --> x<3(we require this condition to be satisfied)

St.1) x=/= 3 not sufficient
St.2) -x|x| > 0 --> x|x| < 0 --> x<0 (as |x| > 0) which satisfies x<3 hence sufficient .....Ans B
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