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Updated on: 06 Jan 2014, 03:12
Originally posted by gmatgambler on 05 Jan 2014, 21:28.
Last edited by Bunuel on 06 Jan 2014, 03:12, edited 1 time in total.
Last edited by Bunuel on 06 Jan 2014, 03:12, edited 1 time in total.
Edited the question.
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
63% (01:46) correct
38%
(02:20)
wrong
based on 88
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Is |x| < 1 ?
(1) \(x^4-1> 0\)
(2) \(\frac{1}{1-|x|}> 0\)
How to solve this algebraically ?
(1) \(x^4-1> 0\)
(2) \(\frac{1}{1-|x|}> 0\)
How to solve this algebraically ?
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06 Jan 2014, 03:18
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Is |x| < 1 ?
(1) \(x^4-1> 0\) --> \(x^4>1\) --> since both side are non-negative we can take the fourth root from both: \(|x|>1\), Sufficient.
(2) \(\frac{1}{1-|x|}> 0\) --> since the numerator is positive, then the fraction to be positive denominator must also be positive: \(1-|x|>0\) --> \(|x|<1\). Sufficient.
Technically answer should be D, as EACH statement ALONE is sufficient to answer the question.
But even though formal answer to the question is D (EACH statement ALONE is sufficient), this is not a realistic GMAT question, as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. But the statements above contradict each other:
From (1) we have that \(|x|>1\) and from (2) we have that \(|x|<1\). The statements clearly contradict each other.
So, the question is flawed. You won't see such a question on the test.
(1) \(x^4-1> 0\) --> \(x^4>1\) --> since both side are non-negative we can take the fourth root from both: \(|x|>1\), Sufficient.
(2) \(\frac{1}{1-|x|}> 0\) --> since the numerator is positive, then the fraction to be positive denominator must also be positive: \(1-|x|>0\) --> \(|x|<1\). Sufficient.
Technically answer should be D, as EACH statement ALONE is sufficient to answer the question.
But even though formal answer to the question is D (EACH statement ALONE is sufficient), this is not a realistic GMAT question, as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. But the statements above contradict each other:
From (1) we have that \(|x|>1\) and from (2) we have that \(|x|<1\). The statements clearly contradict each other.
So, the question is flawed. You won't see such a question on the test.
General Discussion
06 Jan 2014, 00:51
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gmatgambler
There are two possible cases here: Either x is between 1 and -1 in which case |X|<1 or X is less than -1 or greater than 1 in which case |X|>1
Statement I is sufficient:
If X^4>1 then we are sure that X cannot be between -1 and 1. It has to be greater than 1 or less than -1. Hence this statement is sufficient
Statement II is sufficient
If x is between 0 and 1 then (1/(1 - |X|) will be greater than zero.
If x is greater than 1 or -1 then this statement will not hold true as the denominator will become negative.
Note: the question should have a disclaimer that x is not equal to 1 or -1 as 1/(1 - 1) becomes undefined.
