modular arithmetic

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ildude02: Master | Next Rank: 500 Posts; Posts: 320; Joined: Sun Jan 13, 2008 10:00 pm; Thanked: 10 times

by ildude02 » Wed Jun 25, 2008 8:31 am

Is |x| < 1?

1) x^2 < 1
2) |x| < 1/x.

Can someone explain how you breakdown statement 2 considering x can be < or < 0. Appreciate it

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Source: Beat The GMAT — Data Sufficiency | Wed Jun 25, 2008 8:31 am

atlantic: Master | Next Rank: 500 Posts; Posts: 132; Joined: Sun Apr 27, 2008 10:31 am; Location: Portugal; Thanked: 7 times

by atlantic » Wed Jun 25, 2008 10:13 am

Hi Ildude02,

(1) obviously SUFF

(2) x < 1/x or -x < 1/x

The first equation says that x^2<1 which the same as (1).

The second says that -x^2 < 1 <x> -1 which can be any value since x^2 is always greater than -1. So (2) alone is INSUFF

Answer A.

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lvincy: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Thu Jun 12, 2008 5:38 pm; Thanked: 2 times

by lvincy » Wed Jun 25, 2008 11:31 am

2) |x| <1> 1 then statement is false
IF x < 0 then also statement is false.

This will be true only for positive fraction numbers between 0 and 1.
So B is sufficient to say |x| < 1

Ans D.

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atlantic: Master | Next Rank: 500 Posts; Posts: 132; Joined: Sun Apr 27, 2008 10:31 am; Location: Portugal; Thanked: 7 times

by atlantic » Wed Jun 25, 2008 1:04 pm

Of course lvincy. My mistake.

B says that modX cannot less than 1, so in fact it answers tha question.

Answer is D.

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