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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. _________________

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. _________________

Explanation: Statement (1) is insufficient. If \(x < x^3\), x could be negative: \(x^2\) will always be positive, so for any negative value of x, \(x^2\) will be greater. x could also be positive and greater than 1: for any such value, \(x^2\) will be larger. If x is positive and less than 1, \(x^2\) is smaller. Long story short: according to (1), x must be negative or greater than 1. That isn’t enough information.

Statement (2) is also insufficient. x must be between –1 and 0, or greater than 1. If x is a negative fraction, \(x^3\) is a larger number: a negative fraction closer to zero. If x is a positive number greater than 1, \(x^3\) is greater still.

Taken together, it’s still not enough information to determine whether x is positive. x could be between –1 and 0, or it could be greater than 1. The correct choice is (E).

Explanation: Statement (1) is insufficient. If \(x < x^3\), x could be negative: \(x^2\) will always be positive, so for any negative value of x, \(x^2\) will be greater. x could also be positive and greater than 1: for any such value, \(x^2\) will be larger. If x is positive and less than 1, \(x^2\) is smaller. Long story short: according to (1), x must be negative or greater than 1. That isn’t enough information.

Statement (2) is also insufficient. x must be between –1 and 0, or greater than 1. If x is a negative fraction, \(x^3\) is a larger number: a negative fraction closer to zero. If x is a positive number greater than 1, \(x^3\) is greater still.

Taken together, it’s still not enough information to determine whether x is positive. x could be between –1 and 0, or it could be greater than 1. The correct choice is (E).

Question asks if x>0 ?

Per statement 1, x^2>x --> x^2-x>0 ---> x(x-1)>0 ---> either x<0 or x>1. Not sufficient to answer the question asked.

Per statement 2, x^3>x ---> x^3-x>0 ---> x(x+1)(x-1)>0 ---> either -1<x<0 or x> 1. Again, not sufficient to answer the question asked.

Combining the 2 statements, you get the ranges for x as -1<x<0 or x>1. Again, still not a definitive answer to the question asked.

Explanation: Statement (1) is insufficient. If \(x < x^3\), x could be negative: \(x^2\) will always be positive, so for any negative value of x, \(x^2\) will be greater. x could also be positive and greater than 1: for any such value, \(x^2\) will be larger. If x is positive and less than 1, \(x^2\) is smaller. Long story short: according to (1), x must be negative or greater than 1. That isn’t enough information.

Statement (2) is also insufficient. x must be between –1 and 0, or greater than 1. If x is a negative fraction, \(x^3\) is a larger number: a negative fraction closer to zero. If x is a positive number greater than 1, \(x^3\) is greater still.

Taken together, it’s still not enough information to determine whether x is positive. x could be between –1 and 0, or it could be greater than 1. The correct choice is (E).

Merging topics.

Please refer to the discussion on previous 2 pages. _________________

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