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Is x^2 + x > 0 ? (1) 0 < x < 1 (2) x^3 - x < 0

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Bunuel
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Is x^2 + x > 0 ? (1) 0 < x < 1 (2) x^3 - x < 0 [#permalink] New post   30 Dec 2022, 13:38
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75% (hard)

Question Stats:

50% (02:01) correct 50% (01:49) wrong based on 113 sessions
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Is \(x^2+x>0\)?

(1) \(0<x<1\)
(2) \(x^3-x<0\)
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D
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gmatophobia
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Re: Is x^2 + x > 0 ? (1) 0 < x < 1 (2) x^3 - x < 0 [#permalink] New post   30 Dec 2022, 23:01
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Bunuel wrote:
Is \(x^2+x>0\)?

(1) \(0<x<1\)
(2) \(x^3-x<0\)


\(x^2+x>0\)

\(x(x+1)>0\)

Using wavy curve approach we can determine that the inequality holds true under the following conditions -

  • x > 0
  • x < -1

Statement 1

\(0<x<1\)

As x > 0, the inequality , \(x^2+x>0\), holds true for the given range of x.

Sufficient.

Statement 2

\(x^3-x<0\)

\(x(x^2-1)<0\)

\(x(x-1)(x+1)<0\)

The inequality \(x^3-x<0\) hold true in under the following range of x

  • 0 < x < 1
  • x < -1

In both the above ranges, \(x^2+x>0\)

Sufficient.

Option D
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Vibhatu
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Re: Is x^2 + x > 0 ? (1) 0 < x < 1 (2) x^3 - x < 0 [#permalink] New post   26 Jan 2023, 05:23
Bunuel post the official answer
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Chanovski
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Re: Is x^2 + x > 0 ? (1) 0 < x < 1 (2) x^3 - x < 0 [#permalink] New post   18 May 2023, 14:34
gmatophobia wrote:
Bunuel wrote:
Is \(x^2+x>0\)?

(1) \(0<x<1\)
(2) \(x^3-x<0\)


\(x^2+x>0\)

\(x(x+1)>0\)

Using wavy curve approach we can determine that the inequality holds true under the following conditions -

  • x > 0
  • x < -1

Statement 1

\(0<x<1\)

As x > 0, the inequality , \(x^2+x>0\), holds true for the given range of x.

Sufficient.

Statement 2

\(x^3-x<0\)

\(x(x^2-1)<0\)

\(x(x-1)(x+1)<0\)

The inequality \(x^3-x<0\) hold true in under the following range of x

  • 0 < x < 1
  • x < -1

In both the above ranges, \(x^2+x>0\)

Sufficient.

Option D



thanks for the explanation. I do not understand why (2) is sufficient.

Question stem asks if X>0; x<-1

(2) gives us three breakpoints 1, 0, -1
Can someone share a sketch with OA?
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gmatclubot
Re: Is x^2 + x > 0 ? (1) 0 < x < 1 (2) x^3 - x < 0 [#permalink]
18 May 2023, 14:34
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Bunuel
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