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(1) x^3-x>0 --> x(x^2-1)>0: Two cases: A.x>0, x^2-1>0 --> x>0 and x>1x<-1--> x>1 B. x<0, x^2-1<0 --> x<0 and -1<x<1 --> -1<x<0

Two ranges x>1 or -1<x<0, not sufficient.

(2) x>0, x^2>x --> x^2-x>0--> x(x-1)>0 --> as x>0, x-1>0 --> x>1. One range x>1. Sufficient.

Answer: B.

Hi Bunuel!

I have seen already your answers in which you mention the ranges both in inequalities & in modules questions. Can you kindly explain how does it work or refer to some good resource to understand the raging concept. _________________

(1) x^3-x>0 --> x(x^2-1)>0: Two cases: A.x>0, x^2-1>0 --> x>0 and x>1x<-1--> x>1 B. x<0, x^2-1<0 --> x<0 and -1<x<1 --> -1<x<0

Two ranges x>1 or -1<x<0, not sufficient.

(2) x>0, x^2>x --> x^2-x>0--> x(x-1)>0 --> as x>0, x-1>0 --> x>1. One range x>1. Sufficient.

Answer: B.

Hi Bunuel!

I have seen already your answers in which you mention the ranges both in inequalities & in modules questions. Can you kindly explain how does it work or refer to some good resource to understand the raging concept.

Unfortunately I can not refer to any resources as I studied this staff in school. But I'll try to explain the basics of it if you specify the issue or post question(s). _________________

x>0, x^2>x --> x^2-x>0--> x(x-1)>0 --> as x>0, x-1>0 --> x>1. One range x>1. Sufficient.

you haven't considered the second half i guess..

x(x-1)>0 --->x<0, x<1--->x<1..

if x = -2 then -2(-2-1)>0..

I think its E..correct me if am wrong..

Not so.

Statement 2 states: x^2>x>0

When we split we get x^2>x AND x>0, so there is no second part. x can not be less than zero, so the only chance x(x-1)>0 to be true is when x and x-1 is BOTH more than zero. _________________

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________