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Is |x| < 1 ? (1) x^4 - 1 > 0 (2) 1/(1 - |x|) > 0
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06 Oct 2021, 01:00
06 Oct 2021, 01:00
1
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Expert Reply
Show timer
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A
B
C
D
E
Difficulty:
35%
(medium)
Question Stats:
72% (01:34) correct
28%
(02:17)
wrong
based on 105
sessions
Is |x| < 1 ?
(1) \(x^4 - 1 < 0\)
(2) \(\frac{1}{1-|x|}> 0\)
M36-02
(1) \(x^4 - 1 < 0\)
(2) \(\frac{1}{1-|x|}> 0\)
M36-02
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Re: Is |x| < 1 ? (1) x^4 - 1 > 0 (2) 1/(1 - |x|) > 0
[#permalink]
09 Oct 2021, 08:30
09 Oct 2021, 08:30
1
Kudos
Expert Reply
Official Solution:
Is \(|x| < 1\) ?
(1) \(x^4 - 1 < 0\):
\(x^4 < 1\).
Take the fourth root: \(|x| < 1 \). Sufficient.
(2) \(\frac{1}{1-|x|} > 0\):
The numerator is positive, so for the fraction to be positive the denominator must also be positive: \(1 - |x| > 0 \). So, \(|x| < 1 \). Sufficient.
Answer: D
Is \(|x| < 1\) ?
(1) \(x^4 - 1 < 0\):
\(x^4 < 1\).
Take the fourth root: \(|x| < 1 \). Sufficient.
(2) \(\frac{1}{1-|x|} > 0\):
The numerator is positive, so for the fraction to be positive the denominator must also be positive: \(1 - |x| > 0 \). So, \(|x| < 1 \). Sufficient.
Answer: D
General Discussion
Re: Is |x| < 1 ? (1) x^4 - 1 > 0 (2) 1/(1 - |x|) > 0
[#permalink]
06 Oct 2021, 06:00
06 Oct 2021, 06:00
Expert Reply
Is |x| < 1 ?
(1) \(x^4 - 1 < 0………..(x^2-1)(x^2+1)<0\)
\(x^2+1\) is always positive, so \(x^2-1<0\) or \frac{x^2<1[}{fraction], that is |x|<1.
Sufficient
(2) \([fraction]1/1-|x|}> 0\)
Since 1>0, 1-|x|>0 or |x|<1.
Sufficient
D
(1) \(x^4 - 1 < 0………..(x^2-1)(x^2+1)<0\)
\(x^2+1\) is always positive, so \(x^2-1<0\) or \frac{x^2<1[}{fraction], that is |x|<1.
Sufficient
(2) \([fraction]1/1-|x|}> 0\)
Since 1>0, 1-|x|>0 or |x|<1.
Sufficient
D
