Is |x|

Question

Is |x| < 1 ?

(1)  x^4-1> 0

(2)  \frac{1}{1-|x|}> 0

How to solve this algebraically ?

PerfectScores · Answer

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.

bhatiamanu05 · Answer

Hi, To solve algebrically you first must understand the question Is |x| < 1 ? rewriting question statement as Is -1 0 (x^2+1)(x^2-1)>0 (x^2+1)(x+1)(x-1)>0 x^2+1 will always be greater than 1.(As x can be anything but square of anything +1 will always be greater than 1.) So there are two points +1 and -1. (x+1)(x-1) >0 will be solved only if x <-1 and x>1 so No. hence Sufficient. Using statement 2: \frac{1}{(1-|x|)}>0 1-|x| > 0 (if denominator is +ve than only this expression can be greater than zero.) |x|<1 so -1

Bunuel · Answer

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.

GMattest2016 · Answer

Is |x| < 1 ?

(1) x^4 – 1 > 0
 
(2)  \frac{1}{(1- |x|)} > 0

Could anyone please help with the solution.
Thanks in Advance!

Bunuel · Answer

Merging topics. Please refer to the discussion above. Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you.

Is |x| < 1 ?

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