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# Is x < 0? 1) x^5+x^3+1<0

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6621
GMAT 1: 760 Q51 V42
GPA: 3.82
Is x < 0? 1) x^5+x^3+1<0  [#permalink]

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14 Nov 2017, 00:12
00:00

Difficulty:

15% (low)

Question Stats:

86% (01:00) correct 14% (01:50) wrong based on 57 sessions

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[GMAT math practice question]

Is $$x < 0$$?

1) $$x^5+x^3+1<0$$
2) $$x^3+1 < 0$$

_________________

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 $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7102 Re: Is x < 0? 1) x^5+x^3+1<0 [#permalink] ### Show Tags 14 Nov 2017, 01:11 MathRevolution wrote: [GMAT math practice question] Is $$x < 0$$? 1) $$x^5+x^3+1<0$$ 2) $$x^3+1 < 0$$ 1) $$x^5+x^3+1<0$$.. $$x^5+x^3+1<0......x^3(x^2+1)+1<0.......x^3(x^2+1)<-1$$ $$x^2+1$$ is POSITIVE, so $$x^3$$ has to be NEGATIVE suff 2) $$x^3+1 < 0$$.. $$x^3+1 < 0......x^3<-1.....x<-1$$, so x<0 suff D _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Manager Joined: 11 Oct 2016 Posts: 73 Location: India GMAT 1: 610 Q47 V28 Re: Is x < 0? 1) x^5+x^3+1<0 [#permalink] ### Show Tags 14 Nov 2017, 19:32 IMO B X^3 (X^2+1) < -1 X should be less than -1 X^3 < -1 X should be less than -1 _________________ Hit kudos if you like my post Today's preparation determines tomorrow's achievement. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6621 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x < 0? 1) x^5+x^3+1<0 [#permalink] ### Show Tags 16 Nov 2017, 00:15 => 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. Since the question includes 1 variable (x) and 0 equations, D is most likely to be the answer. Condition 1) $$x^5+x^3+1<0$$ implies that $$x^3(x^2+1)< -1$$. Since $$x^2+1>0$$ always, $$x^3< \frac{-1}{x^2+1}<0$$. Therefore, $$x<0.$$ This is sufficient. Condition 2) $$x^3+1 < 0$$ is equivalent to $$(x+1)(x^2-x+1)<0$$. Since $$x^2-x+1>0$$ always, it follows that $$x+1<0$$. This is sufficient, too. Therefore, the answer is D, as expected. 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. 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$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
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Re: Is x < 0? 1) x^5+x^3+1<0 &nbs [#permalink] 16 Nov 2017, 00:15
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