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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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New post 25 Oct 2017, 23:45
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D
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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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Re: Is x>0? 1) x^3+x-1=0 2) x^3>1 [#permalink]

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New post 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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Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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

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New post 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
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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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