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

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Math Revolution GMAT Instructor
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Is x < 0? 1) x^5+x^3+1<0 [#permalink]

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14 Nov 2017, 00:12
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Question Stats:

86% (00:38) correct 14% (01:32) wrong based on 44 sessions

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[GMAT math practice question]

Is $$x < 0$$?

1) $$x^5+x^3+1<0$$
2) $$x^3+1 < 0$$
[Reveal] Spoiler: OA

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Re: Is x < 0? 1) x^5+x^3+1<0 [#permalink]

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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
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Re: Is x < 0? 1) x^5+x^3+1<0 [#permalink]

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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
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Re: Is x < 0? 1) x^5+x^3+1<0 [#permalink]

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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.
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Re: Is x < 0? 1) x^5+x^3+1<0   [#permalink] 16 Nov 2017, 00:15
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