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# Is x>0? 1) x^3+x-1=0 2) x^3>1

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6985
GMAT 1: 760 Q51 V42
GPA: 3.82
Is x>0? 1) x^3+x-1=0 2) x^3>1  [#permalink]

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25 Oct 2017, 23:45
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:36) correct 42% (02:02) wrong based on 61 sessions

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[GMAT math practice question]

Is x>0?

1) x^3+x-1=0
2) x^3>1

_________________

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" Math Expert Joined: 02 Aug 2009 Posts: 7335 Re: Is x>0? 1) x^3+x-1=0 2) x^3>1 [#permalink] ### Show Tags 26 Oct 2017, 01:46 MathRevolution wrote: [GMAT math practice question] Is x>0? 1) x^3+x-1=0 2) x^3>1 lets see the statements.. 1) $$x^3+x-1=0$$.. $$x^3+x-1=0......x(x^2+1)=1$$ clearly $$x^2+1$$ has to be POSITIVE, AND therefore x will have to be POSITIVE, otherwise $$x(x^2+1)$$ will become NEGATIVE so x>0 suff 2) x^3>1 so x>1 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 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html GMAT Expert Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6985 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x>0? 1) x^3+x-1=0 2) x^3>1 [#permalink] ### Show Tags 29 Oct 2017, 17:02 => Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution. Since we have 1 variable and 0 equation, D is most likely to be the answer. Condition 1) x^3+x-1=0 x^3+x = 1 x(x^2+1) = 1 x = 1/(x^2+1) > 0. This is sufficient. Condition 2) x^3 > 1 x^3 – 1 > 0 ( x – 1 )( x^2 + x + 1 ) > 0 x – 1 > 0, since x^2 + x + 1 > 0. x > 1 > 0. This is sufficient. Therefore, D is the answer as expected. For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both con 1) and con 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Thus, D is most likely to be the answer using con 1) and con 2) separately according to DS definition. Obviously, 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$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
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Re: Is x>0? 1) x^3+x-1=0 2) x^3>1   [#permalink] 29 Oct 2017, 17:02
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