If \(|x| < x^2,\) which of the following must be true?

[Vincen]

If \(|x| < x^2,\) which of the following must be true?

A. \(x > 0\)
B. \(x < 0\)
C. \(x > 1\)
D. \(-1 < x < 1\)
E. \(x^2 > 1\)

Answer: E

Source: GMAT Prep

[Brent@GMATPrepNow]

If \(|x| < x^2,\) which of the following must be true?

A. \(x > 0\)
B. \(x < 0\)
C. \(x > 1\)
D. \(-1 < x < 1\)
E. \(x^2 > 1\)

Answer: E

Source: GMAT Prep

I find that these questions can be solved quickly (and accurately) by testing values.

For example, if |x| < x², then x could equal 2 (since |2| < 2²)
This means we can eliminate choices B and D since they state that x cannot equal 2.

Similarly, if |x| < x², then x could equal -2 (since |-2| < (-2)²)
This means we can eliminate choices A and C since they state that x cannot equal -2.

By the process of elimination, the correct answer is E