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# If x is not equal to 0, is less than 1? 1. x/ <x 2. >

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If x is not equal to 0, is less than 1? 1. x/ <x 2. > [#permalink]  11 Feb 2007, 00:59
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If x is not equal to 0, is [x] less than 1?

1. x/[x] <x

2. [x] > x

Last edited by bz9 on 11 Feb 2007, 15:53, edited 1 time in total.
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[#permalink]  11 Feb 2007, 04:01
disable HTML FROM PROFILE , SO THAT WE CAN SEE THE QUESTION IN FULL . THANKS
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Re: MGMAT DS [#permalink]  12 Feb 2007, 10:17
bz9 wrote:
If x is not equal to 0, is [x] less than 1?

1. x/[x] <x

2. [x] > x

Question: x not= 0, |x| < 1?

From question: x = (-1, 1). Our job is to find whether choice (1) and (2) is fit in this range.

(1) x/|x| < x
x - x/|x| > 0
x|x| - x > 0

Case 1: x >= 0
x^ - x > 0
x(x-1) >0
x = (1, oo)

Case 2: x < 0
-x^2 - x > 0
x^2 + x < 0
x(x + 1) < 0
x = (-1, 0)

Therefore; x = (-1, 0) U (1, 00)
The range is larger than the question. INSUFF.

(2) |x| > x
Case 1: x >= 0
x > x Impossible x = ∅
Case 2: -x > x
-2x > 0
x < 0

Therefore; x = (-oo, 0)
The range is larger than the question. INSUFF.

(1) + (2)

Intersecting the answer from (1) and (2) we get
x = (-1,0)

This range fit in the range required from the question x = (-1,1). SUFF

C is the answer.
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[#permalink]  12 Feb 2007, 13:20
Nothing to add :D

Perhaps just that I'm not the devil :p

Other explanations here : http://www.gmatclub.com/phpbb/viewtopic.php?t=39804
[#permalink] 12 Feb 2007, 13:20
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