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# Inequality confusion

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Manager
Joined: 09 Jul 2008
Posts: 110
Location: Dallas, TX
Schools: McCombs 2011

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09 Feb 2009, 22:04
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

This one seems simple enough, But I don't seem to get this. How can I rephrase the stimulus ?

Is $$sqrt(x-5)^2 = 5-x$$?

1) $$-x|x| > 0$$
2) $$5-x > 0$$
SVP
Joined: 07 Nov 2007
Posts: 1765
Location: New York

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09 Feb 2009, 22:32
kman wrote:
This one seems simple enough, But I don't seem to get this. How can I rephrase the stimulus ?

Is $$sqrt(x-5)^2 = 5-x$$?

1) $$-x|x| > 0$$
2) $$5-x > 0$$

Is $$sqrt(x-5)^2 = 5-x$$?

sqrt(x-5)^2 --> should result positve value..
questions can be rephrased 5-x>0

1) $$-x|x| > 0$$
--> x>0
not sufficient..
5-x>0 or 5-x<0 possible

2) clearly sufficient

B
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VP
Joined: 18 May 2008
Posts: 1207

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10 Feb 2009, 02:17
Suresh, I dnt think $$sqrt(x-5)^2$$ will always yield positive value. For example square root of x has two values : +x and -x
Another thing:u said $$-x|x| > 0$$ --> x>0
Onthe contrary, this should imply x<0 bcos |x| is positive, so above equation can be >0 only if x is negative

x2suresh wrote:
kman wrote:
This one seems simple enough, But I don't seem to get this. How can I rephrase the stimulus ?

Is $$sqrt(x-5)^2 = 5-x$$?

1) $$-x|x| > 0$$
2) $$5-x > 0$$

Is $$sqrt(x-5)^2 = 5-x$$?

sqrt(x-5)^2 --> should result positve value..
questions can be rephrased 5-x>0

1) $$-x|x| > 0$$
--> x>0
not sufficient..
5-x>0 or 5-x<0 possible

2) clearly sufficient

B
VP
Joined: 18 May 2008
Posts: 1207

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10 Feb 2009, 02:26
Now coming back to the question, I think the given stem is true only if x=5
(1) as stated in my above post, x <0. This implies $$x =/ 5$$ Hence Sufficient
(2)5-x>0
x<5. Sufficient

Ans shld be D
Manager
Joined: 09 Jul 2008
Posts: 110
Location: Dallas, TX
Schools: McCombs 2011

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10 Feb 2009, 10:36
Thanks guys. This is the type of confusion I go through when I see these question types.
It is clear now, the question is asking whether x=5 ?
Director
Joined: 25 Oct 2006
Posts: 610

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10 Feb 2009, 12:04
No I think question is asking whether x<5.
because, x-5 = -(5-x) while the x-5 is negative or less than 0.
so x-5<0 means x<5

1 says x is negative hence less than 5....suffice
2 says x <5 ...suffice

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SVP
Joined: 07 Nov 2007
Posts: 1765
Location: New York

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10 Feb 2009, 12:47
ritula wrote:
Suresh, I dnt think $$sqrt(x-5)^2$$ will always yield positive value. For example square root of x has two values : +x and -x
Another thing:u said $$-x|x| > 0$$ --> x>0
Onthe contrary, this should imply x<0 bcos |x| is positive, so above equation can be >0 only if x is negative

x2suresh wrote:
kman wrote:
This one seems simple enough, But I don't seem to get this. How can I rephrase the stimulus ?

Is $$sqrt(x-5)^2 = 5-x$$?

1) $$-x|x| > 0$$
2) $$5-x > 0$$

Is $$sqrt(x-5)^2 = 5-x$$?

sqrt(x-5)^2 --> should result positve value..
questions can be rephrased 5-x>0

1) $$-x|x| > 0$$
--> x>0not sufficient..
5-x>0 or 5-x<0 possible

2) clearly sufficient

B

Ritual.. I don't think there is problem in my logic. rephrasing orignal question 5-x >0 or x<5

Only mitake I did was.. x|x| > 0 --> x<0 not x>0
in this definitely 5-x>0 when x is negative.

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Smiling wins more friends than frowning

Re: Inequality confusion   [#permalink] 10 Feb 2009, 12:47
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# Inequality confusion

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