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# Is |x|<1?

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Intern
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Is |x|<1? [#permalink]  23 Sep 2009, 16:26
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1) x^4-1>0
2) 1/(1-|x|)>0

I thought the answer was E because in 1) x>1 which is sufficient. In 2) |x| is less than 1. Then answer is D. So my question is if 1 and 2 have separate answers that are sufficient it has to be D right? Or am I seeing this wrong?
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Re: Is |x|<1? [#permalink]  23 Sep 2009, 16:51
mosquitojoyride wrote:
1) x^4-1>0
2) 1/(1-|x|)>0

I thought the answer was E because in 1) x>1 which is sufficient. In 2) |x| is less than 1. Then answer is D. So my question is if 1 and 2 have separate answers that are sufficient it has to be D right? Or am I seeing this wrong?

Hi mosquitojoyride,
Pretty question.

[EDITED]
Here we go:
Question:
is |X|<1? --> is -1 < X < 1?

(1)
Xˆ4 -1 > 0
Xˆ4>1
Xˆ2 > +-1
X > +-1

|X|>1
(sufficient, because he proved the countrary)

(2)
1 / (1-|X|) > 0

Either:
1 and (1-|X|) are <0 (no)
or
1 and (1-|X|) are > 0 (yes!)

then:
1-|X| > 0

- |X|> -1
|X|<1
(sufficient)

Since (1) and (2) are independently sufficient, the answer is D

Is that the correct answer?

Last edited by diogoguitarrista on 24 Sep 2009, 01:58, edited 1 time in total.
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Re: Is |x|<1? [#permalink]  23 Sep 2009, 20:35
This is a weird question. According to Kaplan:

"The Statements will never contradict each other. True, they won't always be sufficient, but they'll never be mutually exclusive."

However it's probably obvious that Statement 1 requires |X| > 1, and Statement 2 requires |X| < 1.

Where did you get this question from?
Intern
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Re: Is |x|<1? [#permalink]  24 Sep 2009, 04:08
D is the answer. I got this from Research and Association Education GMAT 4th ed. I really don't like this book and am about to junk it.
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Re: Is |x|<1? [#permalink]  24 Sep 2009, 06:02
For me, it's a normal question. Because with the question "is |x| <1",
from (1) the answer is definitively NO because x^4 > 1 <=> |x| > 1 => suff
from (2) the answer is definitively YES because 1 - |x| > 0 <=> |x| < 1 => suff

Ans: D

AKProdigy87 wrote:
This is a weird question. According to Kaplan:

"The Statements will never contradict each other. True, they won't always be sufficient, but they'll never be mutually exclusive."

However it's probably obvious that Statement 1 requires |X| > 1, and Statement 2 requires |X| < 1.

Where did you get this question from?
Manager
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Posts: 115
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Re: Is |x|<1? [#permalink]  07 Oct 2009, 16:08
AKProdigy87 wrote:
This is a weird question. According to Kaplan:

"The Statements will never contradict each other. True, they won't always be sufficient, but they'll never be mutually exclusive."

However it's probably obvious that Statement 1 requires |X| > 1, and Statement 2 requires |X| < 1.

Where did you get this question from?

Yeah... that may not be an official question...

At least in OG I have never seen the statement contradicting with each other.
Kaplan GMAT Instructor
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Re: Is |x|<1? [#permalink]  08 Oct 2009, 21:46
Expert's post
diogoguitarrista wrote:
Yeah... that may not be an official question...

At least in OG I have never seen the statement contradicting with each other.
Let me confirm--as our book says, they never will. If you see a problem with two conflicting statements, either you've made a mistake or the source has.
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Re: Is |x|<1?   [#permalink] 08 Oct 2009, 21:46
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