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

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Math Revolution GMAT Instructor
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Is x^2+x>0? 1) 0<x<1 2) x^3-x<0 [#permalink]

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05 Sep 2017, 00:24
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Difficulty:

75% (hard)

Question Stats:

40% (01:29) correct 60% (01:33) wrong based on 55 sessions

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[GMAT math practice question]

Is $$x^2+x>0$$?

1) $$0<x<1$$
2) $$x^3-x<0$$
[Reveal] Spoiler: OA

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Is x^2+x>0? 1) 0<x<1 2) x^3-x<0 [#permalink]

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05 Sep 2017, 00:51
MathRevolution wrote:
[GMAT math practice question]

Is $$x^2+x>0$$?

1) $$0<x<1$$
2) $$x^3-x<0$$

$$x^2+x > 0 \iff x(x+1) > 0 \iff x<-1$$ or $$x>0$$

(1) $$0<x<1 \implies x(x+1) > 0$$. Sufficient.

(2) $$x^3-x < 0 \iff x(x^2-1) < 0 \iff x(x+1)(x-1) < 0 \implies x<-1$$ or $$0<x<1$$

$$x<-1 \implies x(x+1) > 0$$
$$0<x<1 \implies x(x+1) >0$$.

Sufficient.

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Is x^2+x>0? 1) 0<x<1 2) x^3-x<0 [#permalink]

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05 Sep 2017, 13:59
MathRevolution wrote:
[GMAT math practice question]

Is $$x^2+x>0$$?

1) $$0<x<1$$
2) $$x^3-x<0$$

$$x^2 + x>0$$ or $$x(x+1)>0$$. this can be represented in the number line as shown in the image (attachment -Question stem)
so any value within this range will satisfy the inequality
Also as $$x^2$$ is positive, so if $$x$$ is positive then the inequality $$x^2+x>0$$ will always be true

Statement 1: Directly provides the information that $$x$$ is positive, hence $$x^2+x>0$$ for all values of $$x$$. Sufficient

Statement 2: $$x^3-x<0$$ or $$x(x^2-1)<0$$ or $$x(x+1)(x-1)<0$$
this can be represented in number line as shown in the image (attachment - statement 2)
Hence $$-1>x$$ or $$0<x<1$$ and both these ranges of $$x$$ satisfy the question stem. Hence Sufficient

Option D
Attachments

File comment: Question Stem

inequality 1.jpg [ 37.2 KiB | Viewed 393 times ]

File comment: Statement 2

inequality 2.jpg [ 30.51 KiB | Viewed 393 times ]

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Math Revolution GMAT Instructor
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Is x^2+x>0? 1) 0<x<1 2) x^3-x<0 [#permalink]

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07 Sep 2017, 01:45
=>

Q: x^2+x>0 ⬄ x(x+1) > 0 ⬄ x < -1 or x > 0

1) 0<x<1
Since the range of the question includes the rage of the condition 1), it is sufficient.

2) x^3-x<0 ⬄ x(x^2-1) < 0 ⬄ x(x+1)(x-1) < 0 ⬄ x < -1 or 0 < x < 1
Since the range of the question includes the rage of the condition 2), it is sufficient too.

Ans: D
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Re: Is x^2+x>0? 1) 0<x<1 2) x^3-x<0 [#permalink]

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17 Sep 2017, 12:13
broall wrote:
MathRevolution wrote:
[GMAT math practice question]

Is $$x^2+x>0$$?

1) $$0<x<1$$
2) $$x^3-x<0$$

$$x^2+x > 0 \iff x(x+1) > 0 \iff x<-1$$ or $$x>0$$

(1) $$0<x<1 \implies x(x+1) > 0$$. Sufficient.

(2) $$x^3-x < 0 \iff x(x^2-1) < 0 \iff x(x+1)(x-1) < 0 \implies x<-1$$ or $$0<x<1$$

$$x<-1 \implies x(x+1) > 0$$
$$0<x<1 \implies x(x+1) >0$$.

Sufficient.

Hi, regarding the above, I have a question: if x(x+1)(x-1) < 0 wouldn't x be x = 1 or -1
Why only consider x = -1 ?
Thank you!

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Re: Is x^2+x>0? 1) 0<x<1 2) x^3-x<0   [#permalink] 17 Sep 2017, 12:13
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