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# Is x > 0? (1) x = |x| (2) x^3 > x

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Is x > 0? (1) x = |x| (2) x^3 > x  [#permalink]

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22 Mar 2020, 01:53
1
00:00

Difficulty:

65% (hard)

Question Stats:

38% (01:08) correct 62% (01:03) wrong based on 38 sessions

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Is x > 0?

(1) x = |x|
(2) x^3 > x

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Re: Is x > 0? (1) x = |x| (2) x^3 > x  [#permalink]

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22 Mar 2020, 02:30
GMATinsight wrote:
Is x > 0?

(1) x = |x|
(2) x^3 > x

(1) x = |x|
—> x ≥ 0
—> Insufficient

(2) x^3 > x
—> x^3 - x > 0
—> x(x^2 - 1) > 0
Case 1: x > 0 & x^2 - 1 > 0
—> x > 0 & x^2 > 1
—> x > 1
Case 2: x < 0 & x^2 - 1 < 0
—> x < 0 & x^2 < 1
—> -1 < x < 0
Combine solution is -1 < x < 0 or x > 1
—> Insufficient

Combining (1) & (2),
Common solution is x > 1
So, x > 0 always
—> Sufficient

Option C

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Re: Is x > 0? (1) x = |x| (2) x^3 > x  [#permalink]

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22 Mar 2020, 05:57
#1
x = |x|
x=√x^2
x-√x^2=0
x=0 or x=1
insufficient
#2
x^3 > x
x(x^2-1)>0
x>0 or x=+/-1
insufficient
from 1 &2
x=1 sufficient
IMO C

GMATinsight wrote:
Is x > 0?

(1) x = |x|
(2) x^3 > x

Re: Is x > 0? (1) x = |x| (2) x^3 > x   [#permalink] 22 Mar 2020, 05:57