Is |x| < 1 ? (1) x^4 - 1 > 0 (2) 1/(1 - |x|) > 0

Not a good question.

Is \(|x| < 1\)? --> is \(-1<x<1\)?

(1) \(x^4-1>0\) --> \(x^4>1\) --> \(x<-1\) or \(x>1\). So \(x\) is not in the range (-1,1). Sufficient.

(2) \(\frac{1}{1-|x|}>0\) --> nominator is positive thus denominator must also be positive for fraction to be positive --> \(1-|x|>0\) --> \(|x|<1\). Sufficient.

Answer: D.

But: From (1) we have that \(x\) is NOT in the range (-1,1) and from (2) that \(x\) is in the range (-1,1). Two statements contradict each other.

This will never occur on GMAT as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.


Consider the following question (I just made it up):

If \(y\) is an integer, is \(|y+1|<3\)?

\(|y+1|<3\) means is \(-4<y<2\) (-3, -2, -1, 0, 1)?

(1) \(-3<y^3<10\) --> \(y\) can be: -1, 0, 1, or 2. Not sufficient.

(2) \((y^2+4y)(y-1)=0\) --> \(y\) can be: -4, 0, or 1. Not sufficient.

(1)+(2) Intersection of the values from (1) and (2) are \(y=0\) and \(y=1\), both these values satisfy inequality \(|y+1|<3\). Sufficient.

Answer: C.

So if statement (1) gives one set of values for x and statement (2) gives another set of values for x, then when considering statements together we should take only the values which satisfy both statements.

Hope it helps.