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# Is x^3-x>0？

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42
GPA: 3.82

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02 Oct 2018, 01:39
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Difficulty:

25% (medium)

Question Stats:

77% (00:50) correct 23% (00:58) wrong based on 51 sessions

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[Math Revolution GMAT math practice question]

Is $$x^3-x>0$$？

$$1) x>1$$
$$2) x>0$$

_________________
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 $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 20 Feb 2015 Posts: 737 Concentration: Strategy, General Management Re: Is x^3-x>0？ [#permalink] ### Show Tags 02 Oct 2018, 01:53 MathRevolution wrote: [Math Revolution GMAT math practice question] Is $$x^3-x>0$$？ $$1) x>1$$ $$2) x>0$$ x(x+1)(x-1) > 0 1. $$1) x>1$$ substitute the value sufficient 2. $$2) x>0$$ substitute x = 1 x(x+1)(x-1) = 0 substitute x = 2 x(x+1)(x-1) > 0 not sufficient A GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 935 Re: Is x^3-x>0？ [#permalink] ### Show Tags 02 Oct 2018, 13:33 MathRevolution wrote: [Math Revolution GMAT math practice question] Is $$x^3-x>0$$？ $$1) x>1$$ $$2) x>0$$ $${x^3} - x\,\,\mathop > \limits^? \,\,0\,\,\,\,\, \Leftrightarrow \,\,\,\,\boxed{\,x\left( {{x^2} - 1} \right)\,\,\mathop > \limits^? \,\,0\,}\,$$ $$\left( 1 \right)\,\,x > 1\,\,\,\, \Rightarrow \,\,\,\left\{ \matrix{ x > 0 \hfill \cr {x^2} > 1\,\,\,\, \Rightarrow \,\,\,{x^2} - 1 > 0 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle$$ $$\left( 2 \right)\,\,\,x > 0\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,x = 1\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,x = 2\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8261 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x^3-x>0？ [#permalink] ### Show Tags 04 Oct 2018, 00:54 => 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. We then recheck the question. The question $$x^3-x>0$$ is equivalent to $$-1<x<0$$ or $$x > 1$$ as shown below: $$x^3-x>0$$ $$=> x(x^2-1)>0$$ $$=> x(x+1)(x-1) > 0$$ $$=> -1<x<0$$ or $$x > 1$$ Attachment: 10.4.png [ 6.75 KiB | Viewed 307 times ] Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first. In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient. Condition 1) Since the solution set of the question includes that of condition 1), condition 1) is sufficient. Condition 2) Since the solution set of the question does not include that of condition 2), condition 2) is not sufficient. Therefore, A is the answer. Answer: A If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E. _________________ 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$79 for 1 month Online Course"
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Re: Is x^3-x>0？   [#permalink] 04 Oct 2018, 00:54
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