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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6826
GMAT 1: 760 Q51 V42
GPA: 3.82

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14 Jan 2018, 23:27
00:00

Difficulty:

35% (medium)

Question Stats:

75% (01:15) correct 25% (01:34) wrong based on 111 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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 15 Aug 2017 Posts: 14 Re: Is x^3-x^2+x<0? [#permalink] ### Show Tags 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 Joined: 16 Aug 2015 Posts: 6826 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x^3-x^2+x<0? [#permalink] ### Show Tags 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. Answer: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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06 Dec 2018, 05:18
MathRevolution wrote:
[GMAT math practice question]

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

1) $$x < 0$$
2) $$x^5+x<0$$

Question : $$x^3-x^2+x<0?$$
$$x(x^2-x+1) <0$$
$$x[(x-1/2)^2+3/4] <0$$
$$x<0?$$

Statement 1 : $$x < 0$$
SUFFICIENT

Statement 2: $$x^5+x<0$$
$$x(x^4+1)<0$$
$$x<0 as x^4+1 is always positive.$$
SUFFICIENT

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Is x^3-x^2+x<0? &nbs [#permalink] 06 Dec 2018, 05:18
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