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# If x 0, is |x| <1? (1) x^2<1 (2) |x| < 1/2

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Manager
Joined: 10 Feb 2011
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If x 0, is |x| <1? (1) x^2<1 (2) |x| < 1/2 [#permalink]

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26 Feb 2011, 16:23
3
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Difficulty:

25% (medium)

Question Stats:

69% (01:53) correct 31% (00:47) wrong based on 121 sessions

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If x≠0, is |x| <1?
(1) x^2<1
(2) |x| < 1/2
[Reveal] Spoiler: OA
Director
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Kudos [?]: 222 [0], given: 78

Re: Modules & inequalities [#permalink]

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27 Feb 2011, 01:18
1
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is |x| < 1?

We know that x can be any value less that 1 unit away from zero.

Therefore, what we really wanna know is if -1 < x < 1

Statement 1:
x^2 < 1

Sq. rt. (x^2) < sq. rt. (1)

=> |x| < 1

Sufficient!

Statement 2:
x < 1/2

Therefore, -1/2 < x < 1/2
=> x is between -1 and 1!

Sufficient!

Ans: 'D'
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Re: Modules & inequalities [#permalink]

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27 Feb 2011, 05:05

From 1, it is clear that :

x^2 < 1 => (x-1)(x+1) < 0, so x is between -1 and 1 (not inclusive)

From 2, it is evident as well.

Regards,
Subhash
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Re: Modules & inequalities [#permalink]

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20 May 2011, 00:50
clean D.

regions -1<x<1 and -0.5 < x < 0.5
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Re: If x 0, is |x| <1? (1) x^2<1 (2) |x| < 1/2 [#permalink]

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17 Sep 2016, 13:28
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x 0, is |x| <1? (1) x^2<1 (2) |x| < 1/2   [#permalink] 17 Sep 2016, 13:28
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# If x 0, is |x| <1? (1) x^2<1 (2) |x| < 1/2

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