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# If x is not equal to 0, is |x| less than 1?

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Manager
Joined: 05 May 2005
Posts: 78
If x is not equal to 0, is |x| less than 1? [#permalink]

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18 May 2007, 17:31
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How would you solve?

If x is not equal to 0, is |x| less than 1?

1) x/|x| is less than x

2) |x| is greater than x
Director
Joined: 26 Feb 2006
Posts: 899
Re: Absolute Value - DS [#permalink]

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18 May 2007, 19:48
above720 wrote:
How would you solve?

If x is not equal to 0, is |x| less than 1?

1) x/|x| is less than x
2) |x| is greater than x

ween from i, x/lxl < x refers to x as -ve and but grater than -1. so its sufficient to say that lxl is <1> x only implies that x is ve. nsf.

A.
Manager
Joined: 02 May 2007
Posts: 152
Re: Absolute Value - DS [#permalink]

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18 May 2007, 20:47
Himalayan wrote:
above720 wrote:
How would you solve?

If x is not equal to 0, is |x| less than 1?

1) x/|x| is less than x
2) |x| is greater than x

ween from i, x/lxl < x refers to x as -ve and but grater than -1. so its sufficient to say that lxl is <1> x only implies that x is ve. nsf.

A.

(1) (A) is also insuff because if x/|x| <x

then -1 < x <0> 1

(2) |x| > x => x must be -ve => insuff

(1) & (2) => suff

Hence, (C)
Current Student
Joined: 22 Apr 2007
Posts: 1097

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18 May 2007, 21:27
C

is |x| < 1?

(1)
If x is +ve => 1/x < 1 => 1 < x
If x is -ve => x/|x| < x => |x|/|x| > |x| => 1 > |x|

Since (a) and (b) don't give same result for x, this is insufficient

(2) |x| > x means x is -ve, thus < 1. Insufficient

Combined, if x is -ve and (1) is true, we know from (1) that |x| is greater than 1 for sure.
Director
Joined: 26 Feb 2006
Posts: 899
Re: Absolute Value - DS [#permalink]

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18 May 2007, 21:39
Himalayan wrote:
above720 wrote:
How would you solve?

If x is not equal to 0, is |x| less than 1?

1) x/|x| is less than x
2) |x| is greater than x

ween from i, x/lxl < x refers to x as -ve and but grater than -1. so its sufficient to say that lxl is <1> x only implies that x is ve. nsf.

A.

agree with C.
Re: Absolute Value - DS   [#permalink] 18 May 2007, 21:39
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# If x is not equal to 0, is |x| less than 1?

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