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

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25 Oct 2017, 23:45
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45% (medium)

Question Stats:

63% (01:06) correct 37% (01:32) wrong based on 52 sessions

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[GMAT math practice question]

Is x>0?

1) x^3+x-1=0
2) x^3>1
[Reveal] Spoiler: OA

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Math Expert
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Re: Is x>0? 1) x^3+x-1=0 2) x^3>1 [#permalink]

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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
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6149 [0], given: 121

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4485

Kudos [?]: 3168 [0], given: 0

GPA: 3.82
Re: Is x>0? 1) x^3+x-1=0 2) x^3>1 [#permalink]

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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.

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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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