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Is |x - 1| < 1 ? 1. (x - 1)^2 <= 1 2. x^2 - 1

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Senior Manager
Senior Manager
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Joined: 05 Oct 2008
Posts: 270

Kudos [?]: 538 [0], given: 22

Is |x - 1| < 1 ? 1. (x - 1)^2 <= 1 2. x^2 - 1 [#permalink]

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New post 05 Nov 2008, 07:29
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Is \(|x - 1| < 1\) ?

1. \((x - 1)^2 <= 1\)
2. \(x^2 - 1 > 0\)

Kudos [?]: 538 [0], given: 22

1 KUDOS received
Manager
Manager
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Joined: 23 Aug 2008
Posts: 63

Kudos [?]: 54 [1], given: 0

Re: No. Properties [#permalink]

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New post 05 Nov 2008, 08:11
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study wrote:
Is \(|x - 1| < 1\) ?

1. \((x - 1)^2 <= 1\)
2. \(x^2 - 1 > 0\)

I'm getting E:

Restating the stem without the absolute values:
\(-1 < x-1 < 1\)
therefore for stem to be true, x must fall between these values: \(0<x<2\)

Using statement (1):
Expanding gives \(x^2+1-2x \leq 1\)
\(x^2-2x \leq 0\)
\(x(x-2) \leq 0\)
therefore \(0 \leq x \leq 2\)
Does not satisfy the stem (almost does though), so (1) insufficient

Using statement (2)
\(x^2-1>0\)
\(x^2>1\)
therefore \(x < -1, or x > 1\)
This also does not satisfy the stem, so (2) is insufficient

Combining (1) and (2):
\(1 < x \leq 2\)
also does not satisfy the stem, hence answer E

Kudos [?]: 54 [1], given: 0

Intern
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Joined: 21 Aug 2008
Posts: 24

Kudos [?]: 19 [0], given: 0

Re: No. Properties [#permalink]

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New post 05 Nov 2008, 08:39
study wrote:
Is \(|x - 1| < 1\) ?

1. \((x - 1)^2 <= 1\)
2. \(x^2 - 1 > 0\)


I'm going to say E

both 1.5 and 2 can be plugged into both and you'll get a different answer for the question.

Kudos [?]: 19 [0], given: 0

Manager
Manager
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Joined: 27 May 2008
Posts: 200

Kudos [?]: 45 [0], given: 0

Re: No. Properties [#permalink]

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New post 05 Nov 2008, 11:05
going for E

rephrasing Q as 0<x<2

Since 1) says 0<=x<=2.. so in number line it cannot satisfy -- INSUFF

2) -1> X > 1 so in number line it cannot satisfy -- INSUFF

Kudos [?]: 45 [0], given: 0

Re: No. Properties   [#permalink] 05 Nov 2008, 11:05
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Is |x - 1| < 1 ? 1. (x - 1)^2 <= 1 2. x^2 - 1

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