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

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Manager
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Joined: 10 Feb 2011
Posts: 116
Followers: 1

Kudos [?]: 40 [0], given: 10

If x 0, is |x| <1? (1) x^2<1 (2) |x| < 1/2 [#permalink] New post 26 Feb 2011, 15:23
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

86% (01:35) correct 14% (00:13) wrong based on 14 sessions
If x≠0, is |x| <1?
(1) x^2<1
(2) |x| < 1/2
[Reveal] Spoiler: OA
Director
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Joined: 04 Jan 2011
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Location: Kochi, India
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Kudos [?]: 130 [0], given: 66

Re: Modules & inequalities [#permalink] New post 27 Feb 2011, 00:18
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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Kudos [?]: 297 [0], given: 36

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Re: Modules & inequalities [#permalink] New post 27 Feb 2011, 04:05
Answer is D

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.

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Subhash
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Kudos [?]: 144 [0], given: 10

Re: Modules & inequalities [#permalink] New post 19 May 2011, 23:50
clean D.

regions -1<x<1 and -0.5 < x < 0.5
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Re: Modules & inequalities   [#permalink] 19 May 2011, 23:50
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If x 0, is |x| <1? (1) x^2<1 (2) |x| < 1/2

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