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If mn>0, is m^3n^4>0?

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If mn>0, is m^3n^4>0? [#permalink]

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New post 27 Oct 2017, 00:29
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

41% (00:23) correct 59% (00:41) wrong based on 46 sessions

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[GMAT math practice question]

If mn>0, is m^3n^4>0?

1) m>0
2) n>0
[Reveal] Spoiler: OA

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If mn>0, is m^3n^4>0? [#permalink]

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New post 27 Oct 2017, 01:08
MathRevolution wrote:
[GMAT math practice question]

If mn>0, is m^3n^4>0?

1) m>0
2) n>0


\(mn>0\) implies if \(m>0\) then \(n>0\) and if \(m<0\) then \(n<0\)

Statement 1: \(m>0\) so \(m^3>0\) and \(n^4\) is always positive. hence \(m^3n^4>0\). Sufficient

Statement 2: \(n>0\) implies \(m>0\) so \(m^3n^4>0\). Sufficient

Option D

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Re: If mn>0, is m^3n^4>0? [#permalink]

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New post 27 Oct 2017, 02:51
MathRevolution wrote:
[GMAT math practice question]

If mn>0, is m^3n^4>0?

1) m>0
2) n>0

mn>0
case 1: m>0 & n>0
case 2: m<0 & n<0

1) if m>0 then only case 1 holds..sufficient

2) if n>0 then only case 1 holds..sufficient

D
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Re: If mn>0, is m^3n^4>0? [#permalink]

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New post 27 Oct 2017, 03:42
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Question is m^3*n^4>0 or <0?
Because n^4 always >0 => more simple question is m>0 or m<0

From 1: m>0 => m^3*n^4 >0
From 2: n>0. We know mn>0 => m>0 => m^3*n^4>0

Answer D.

Please kudo if it's helpful. Thanks.

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Re: If mn>0, is m^3n^4>0? [#permalink]

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New post 29 Oct 2017, 17:03
=>

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 2 variables and 1 equation, D is most likely to be the answer.
In an inequality question, an inequality in the original condition is counted as an equation.

The question m^3n^4>0? is equivalent to m > 0?, after dividing both sides by m^2n^4. Since mn>0, m>0 is equivalent to n>0 too.

Condition 1)
m > 0 is same as the question.
This is sufficient.

Condition 2)
We have m > 0 from mn > 0 and n > 0. It is same as the question.
This is sufficient too.
By tip 1), D is the answer, due to 1) = 2).
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: If mn>0, is m^3n^4>0?   [#permalink] 29 Oct 2017, 17:03
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