## If $$|x| < x^2,$$ which of the following must be true?

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### If $$|x| < x^2,$$ which of the following must be true?

by Vincen » Fri May 28, 2021 6:53 am

00:00

A

B

C

D

E

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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. $$x^2 > 1$$

Source: GMAT Prep

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### Re: If $$|x| < x^2,$$ which of the following must be true?

by [email protected] » Sat Nov 27, 2021 7:18 am
Vincen wrote:
Fri May 28, 2021 6:53 am
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. $$x^2 > 1$$

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
Brent Hanneson - Creator of GMATPrepNow.com

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