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

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Veritas Prep GMAT Instructor
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Re: If |x| < x^2, which of the following must be true ?  [#permalink]

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New post 11 Nov 2019, 22:26
1
Skywalker18 wrote:
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


Whenever you are stuck with an equation with an absolute sign, you know you can get rid of the sign by taking positive and negative values of x.

If x >= 0
x < x^2
x^2 - x > 0
x(x - 1) > 0
So x > 1 or x < 0. But x must be positive so x > 1 only.

If x < 0
-x < x^2
x^2 + x > 0
x(x + 1) > 0
So x > 0 or x < -1. But x must be negative so x < -1 only.

We see that x is either > 1 or < -1. This is the same range as option (E).
x^2 - 1 > 0
(x + 1)(x - 1) > 0
x > 1 or x < -1

Answer (E)
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Re: If |x| < x^2, which of the following must be true ?  [#permalink]

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New post 12 Nov 2019, 00:18
Thank you VeritasKarishma. I understand it better now.

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

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New post 24 Nov 2019, 05:18
@banuel Sir, Can you please quote an example to prove C is not always true?

Thanks in advance
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Re: If |x| < x^2, which of the following must be true ?  [#permalink]

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New post 24 Nov 2019, 05:21
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If |x| < x^2, which of the following must be true ?  [#permalink]

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New post 24 Nov 2019, 06:15
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For lxl < x^2 question the first thing that comes to my mind is the anomaly zone: [-1,1]. GMAT plays around this zone to test the number skills. (Trap 1)

By trial and error we can easily find out that x can be any real number (R) outside [-1,1] zone.
x is R - [-1,1]

Option c is very tempting as it's true but only if x>1. (Trap 2)
For a given value x<-1, say x=(-2) option C doesn't hold.

Hence, option E i.e. (x^2 > 1)
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If |x| < x^2, which of the following must be true ?   [#permalink] 24 Nov 2019, 06:15

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