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# Is \sqrt{(x-5)^2 } = 5 - x ? 1. -x|x| > 0 2. 5 -x

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Is \sqrt{(x-5)^2 } = 5 - x ? 1. -x|x| > 0 2. 5 -x [#permalink]  28 Jan 2009, 09:16
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Is

\sqrt{(x-5)^2 } = 5 - x ?

1. -x|x| > 0
2. 5 -x > 0
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Re: DS - Number Properties, sq root [#permalink]  28 Jan 2009, 09:34
IMO D.

From Question stem, is sqrt((x-5) ^2) = (5 - x) ==> gets boiled down to trying to answer IS x-5 X 5 - x.(Reason being in GMAT, it is always true that sqrt(x^2) is always x.) which inturn boils down to answering the question = IS X = 5?

From Stmt 1, -x|x| > 0 ==> this is possible only when x < 0. For any value of X that is less than 0, x-5 <> 5 - x. This is sufficient to ans the question stem as NO. Hence it is sufficient.

From stmt 2, 5 - x > 0 ==> X < 5. For any value of X that is less than 5, x-5 <> 5 - x. This is sufficient to ans the question stem as NO. Hence it is sufficient.
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Re: DS - Number Properties, sq root [#permalink]  28 Jan 2009, 23:41
mrsmarthi wrote:
IMO D.

From Question stem, is sqrt((x-5) ^2) = (5 - x) ==> gets boiled down to trying to answer IS x-5 X 5 - x.(Reason being in GMAT, it is always true that sqrt(x^2) is always x.) which inturn boils down to answering the question = IS X = 5?

From Stmt 1, -x|x| > 0 ==> this is possible only when x < 0. For any value of X that is less than 0, x-5 <> 5 - x. This is sufficient to ans the question stem as NO. Hence it is sufficient.

From stmt 2, 5 - x > 0 ==> X < 5. For any value of X that is less than 5, x-5 <> 5 - x. This is sufficient to ans the question stem as NO. Hence it is sufficient.

Great explanation. I also came up with D.
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Re: DS - Number Properties, sq root [#permalink]  29 Jan 2009, 03:25
sqrt([x-5]^2) = |x-5|

Now, if x-5 > 0 then |x-5| = x-5
But, if x-5 < 0 then |x-5| = 5-x.

Thus, in order for the euality in the question to be true, x-5 has to be less than 0 or x < 5.

From stmt1: The inequality is possible only when x < 0. That means, x is already less than 5. Hence, sufficient to answer the question.

From stmt2: x-5 < 0. Again, sufficient to answer the question.

Hence, D.
Re: DS - Number Properties, sq root   [#permalink] 29 Jan 2009, 03:25
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