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# Is |x-1|<1 for all integers x ?

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Intern
Joined: 05 Feb 2013
Posts: 1

Kudos [?]: 3 [0], given: 3

Is |x-1|<1 for all integers x ? [#permalink]

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05 Feb 2013, 14:14
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Difficulty:

45% (medium)

Question Stats:

61% (01:01) correct 39% (01:01) wrong based on 74 sessions

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Is |x-1|<1 for all integers x ?

(1) (x-1)^2 >1
(2) x<0
[Reveal] Spoiler: OA

Last edited by Bunuel on 06 Feb 2013, 01:08, edited 1 time in total.
Renamed the topic, edited the question and moved to DS forum.

Kudos [?]: 3 [0], given: 3

Math Expert
Joined: 02 Sep 2009
Posts: 41889

Kudos [?]: 129205 [0], given: 12196

Re: Is |x-1|<1 for all integers x ? [#permalink]

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06 Feb 2013, 01:15
Is |x-1|<1 for all integers x ?

Is |x-1|<1? --> is 0<x<2?

(1) (x-1)^2>1. Since both sides of the inequality are non-negative, then we can safely take the square root to get |x-1|>1. So, the answer to the question is NO. Sufficient.

(2) x<0. Sufficient.

_________________

Kudos [?]: 129205 [0], given: 12196

Re: Is |x-1|<1 for all integers x ?   [#permalink] 06 Feb 2013, 01:15
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