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

Author Message
Senior Manager
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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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

Manager
Joined: 23 Aug 2008
Posts: 63

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

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05 Nov 2008, 08:11
1
KUDOS
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
Joined: 21 Aug 2008
Posts: 24

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

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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
Joined: 27 May 2008
Posts: 200

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

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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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