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# Is x^3-x^2+x<0?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4908
GPA: 3.82

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14 Jan 2018, 23:27
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Difficulty:

45% (medium)

Question Stats:

76% (01:03) correct 24% (01:48) wrong based on 46 sessions

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[GMAT math practice question]

Is $$x^3-x^2+x<0?$$

1) $$x < 0$$
2) $$x^5+x<0$$
[Reveal] Spoiler: OA

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Intern
Joined: 15 Aug 2017
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Re: Is x^3-x^2+x<0? [#permalink]

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15 Jan 2018, 01:20
Both 1 and 2 can independently answer whether Is x^3-x^2+x<0?.
So D.
Math Revolution GMAT Instructor
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Re: Is x^3-x^2+x<0? [#permalink]

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17 Jan 2018, 00:02
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

Modifying the question:
$$x^3-x^2+x<0$$
$$⇔ x(x^2-x+1)<0$$
$$⇔ x<0$$ since $$x^2-x+1>0$$ always.

So, the question becomes, ‘is x<0?’.

Condition 1) is certainly sufficient.

Condition 2), $$x^5+x<0$$, is equivalent to $$x(x^4+1)<0$$ or $$x < 0$$, since $$x^4+1 > 0$$ is always true. So, condition 2) is also sufficient.

Therefore, D is the answer.
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Re: Is x^3-x^2+x<0?   [#permalink] 17 Jan 2018, 00:02
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# Is x^3-x^2+x<0?

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