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# If x is an integer, is |x| \gt 1 ? 1. (1 - 2x)(1 + x) < 0

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Manager
Joined: 22 May 2007
Posts: 218
If x is an integer, is |x| \gt 1 ? 1. (1 - 2x)(1 + x) < 0 [#permalink]

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26 Jul 2008, 19:24
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If x is an integer, is $$|x| \gt 1$$ ?

1. (1 - 2x)(1 + x) < 0
2. (1 - x)(1 + 2x) < 0
Director
Joined: 23 Sep 2007
Posts: 782

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26 Jul 2008, 20:32
aaron22197 wrote:
If x is an integer, is $$|x| \gt 1$$ ?

1. (1 - 2x)(1 + x) < 0
2. (1 - x)(1 + 2x) < 0

C

statement 1: 1 < $$2x^2 + x$$ --> x = -1 does not work, but x = 1 works
statement 2: 1 < $$2x^2 - x$$ --> x = 1 does not work, but x = -1 works

also, x can't be 0 according to each statements

together x can't be -1, 0, or 1, so it must be the other integers
Senior Manager
Joined: 06 Apr 2008
Posts: 428

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26 Jul 2008, 21:38
aaron22197 wrote:
If x is an integer, is $$|x| \gt 1$$ ?

1. (1 - 2x)(1 + x) < 0
2. (1 - x)(1 + 2x) < 0

For statement 1) if x= 0 then statement 1) is false and if x=1 then statement 1 is true

For statement 2) if x= 0 then statement 2) is false and if x=-1 then statement 2 is true

Combining both statement 1) and 2) x is not equal to -1 or 1.

For x>1 or x<-1 both statements are true

Re: DS   [#permalink] 26 Jul 2008, 21:38
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