Is |x| < 1 ?

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.