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# Is sqrt (x-3)^2= 3-x 1) x is not equal to 3 2) -x|x|>0

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Is sqrt (x-3)^2= 3-x 1) x is not equal to 3 2) -x|x|>0 [#permalink]

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27 Mar 2009, 11:23
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Is sqrt (x-3)^2= 3-x

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

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Senior Manager
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Re: DS GMAT Prep - Inequalities [#permalink]

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27 Mar 2009, 16:35
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IMO D.

The question stem is asking "Is sqrt((x-3)^2)= 3-x" which can be phrased as "Is x-3 = 3 -x" This is possible only when x = 3. Now coming to statements.

From stmt1 : - x <> 3. We can say ans the question "Is x -3 = 3 -x" as No. Hence sufficient.

From stmt2 : - it is given -x|x| > 0. This is true only when x< 0. Again from this we can say answer the question "Is x -3 = 3 -x" as No. Hence sufficient.

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Re: DS GMAT Prep - Inequalities [#permalink]

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27 Mar 2009, 18:20
OA is B. Please try again.

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Re: DS GMAT Prep - Inequalities [#permalink]

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27 Mar 2009, 18:22
Please note that (x-3)^2 is under sqroot.

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Re: DS GMAT Prep - Inequalities [#permalink]

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28 Mar 2009, 00:02
IMO B.

when x-3 < 0 (or x<3 )=> we get sqrt (x-3)^2= 3-x.
1)
x is not equal to 3. Insuff.
2)
|x| is always +ve, so x is -ve in this case.
x<0 => x < 3, hence Suff.

Accountant wrote:
Is sqrt (x-3)^2= 3-x

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

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Re: DS GMAT Prep - Inequalities [#permalink]

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28 Mar 2009, 01:09
Ok I am a bit confused. It's agreed that statement 2 is sufficient. But I am not clear why statement 1 is not sufficient. I was thinking it was D.

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Re: DS GMAT Prep - Inequalities [#permalink]

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28 Mar 2009, 04:40
I think the trick here is to recognize that x has to be less than 3 for the given statement to be true. Statement 1 only says that x is not equal to three, meaning that it can be 4, 5 etc. If you put in a value of 5 in given statement it wont hold true while value of less than 3 will hold true. Therefore statment 1 is not sufficient.

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Re: DS GMAT Prep - Inequalities [#permalink]

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28 Mar 2009, 07:31
Oh yeah - thanks for the clarification - I completely missed that out. Got it now.

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Re: DS GMAT Prep - Inequalities [#permalink]

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11 Jul 2011, 16:44
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sqrt((x-3)^2) = |x-3|

So the original equation become: |x-3|=3-x
If you graph this equation it is easy to recognize that the solution is x<=3

Statement 1: x is not equal to 3 ==> INSUFF.
Statement 2: -x|x|>0 --> x < 0 ==> SUFF.

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Re: DS GMAT Prep - Inequalities [#permalink]

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16 Jul 2011, 11:41
mrsmarthi wrote:
IMO D.

The question stem is asking "Is sqrt((x-3)^2)= 3-x" which can be phrased as "Is x-3 = 3 -x" This is possible only when x = 3. Now coming to statements.

From stmt1 : - x <> 3. We can say ans the question "Is x -3 = 3 -x" as No. Hence sufficient.

From stmt2 : - it is given -x|x| > 0. This is true only when x< 0. Again from this we can say answer the question "Is x -3 = 3 -x" as No. Hence sufficient.

We need to keep in mind

"sqrt((x-3)^2)= 3-x" which can NOT be phrased as "Is x-3 = 3 -x"

It can only be rephrased as "|x-3| = 3 -x"
that means we need to see if we can prove that "sqrt((x-3)^2)<> -(3-x)"

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Re: Is sqrt (x-3)^2= 3-x 1) x is not equal to 3 2) -x|x|>0 [#permalink]

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18 Sep 2016, 00:05
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Re: Is sqrt (x-3)^2= 3-x 1) x is not equal to 3 2) -x|x|>0   [#permalink] 18 Sep 2016, 00:05
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