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

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Math Revolution GMAT Instructor
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D
Joined: 16 Aug 2015
Posts: 5585
GMAT 1: 800 Q59 V59
GPA: 3.82
Is x^3-x^2+x<0? [#permalink]

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New post 15 Jan 2018, 00:27
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A
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C
D
E

Difficulty:

  45% (medium)

Question Stats:

74% (01:07) correct 26% (01:38) wrong based on 54 sessions

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[GMAT math practice question]

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

1) \(x < 0\)
2) \(x^5+x<0\)

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Re: Is x^3-x^2+x<0? [#permalink]

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New post 15 Jan 2018, 02:20
Both 1 and 2 can independently answer whether Is x^3-x^2+x<0?.
So D.
Expert Post
Math Revolution GMAT Instructor
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D
Joined: 16 Aug 2015
Posts: 5585
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: Is x^3-x^2+x<0? [#permalink]

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New post 17 Jan 2018, 01:02
=>

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.
Answer: D
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Re: Is x^3-x^2+x<0?   [#permalink] 17 Jan 2018, 01:02
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