If x is not equal to 0, is |x| less than 1? x > x/|x| |x| : DS Archive
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# If x is not equal to 0, is |x| less than 1? x > x/|x| |x|

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Director
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If x is not equal to 0, is |x| less than 1? x > x/|x| |x| [#permalink]

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04 Nov 2007, 05:33
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If x is not equal to 0, is |x| less than 1?

x > x/|x|
|x| > x

Statement I :

x > x/|x| so this hold true when x > 1
2 > 2/2 -- true
x = -2
-2 > -2/2 = -2 > -1 not true therefore x > 1

Statement II :

(2) |x| > x states that x <0> -1 but still doesn't tell whether |x| < 1 .

I + II : 0 <x> 2

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Senior Manager
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Re: Absolute less - DS [#permalink]

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04 Nov 2007, 06:24
If x is not equal to 0, is |x| less than 1?

x > x/|x|
|x| > x

Statement I :
x > x/|x| so this hold true when x > 1
2 > 2/2 -- true
x = -2
-2 > -2/2 = -2 > -1 not true therefore x > 1

Your method is correct, but your conclusion is wrong. If you know for sure that |x| > 1 then the data is SUFFICIENT.

Statement II :
(2) |x| > x states that x <0> -1 but still doesn't tell whether |x| < 1 .
I + II : 0 <x> 2

Statement 2 is insufficient like you proved. Hence the answer is A.
Director
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04 Nov 2007, 06:42
please move this to the math forum
SVP
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04 Nov 2007, 12:21
04 Nov 2007, 12:21
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