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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6400
GMAT 1: 760 Q51 V42
GPA: 3.82

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27 Oct 2017, 01:29
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Difficulty:

45% (medium)

Question Stats:

49% (00:45) correct 51% (00:55) wrong based on 60 sessions

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[GMAT math practice question]

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

1) m>0
2) n>0

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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 $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" PS Forum Moderator Joined: 25 Feb 2013 Posts: 1216 Location: India GPA: 3.82 If mn>0, is m^3n^4>0? [#permalink] Show Tags 27 Oct 2017, 02:08 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 Director Joined: 18 Aug 2016 Posts: 625 Concentration: Strategy, Technology GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38 Re: If mn>0, is m^3n^4>0? [#permalink] Show Tags 27 Oct 2017, 03:51 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 _________________ We must try to achieve the best within us Thanks Luckisnoexcuse Intern Joined: 25 Jul 2017 Posts: 38 Re: If mn>0, is m^3n^4>0? [#permalink] Show Tags 27 Oct 2017, 04:42 1 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. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6400 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If mn>0, is m^3n^4>0? [#permalink] Show Tags 29 Oct 2017, 18:03 => 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 _________________ 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$99 for 3 month Online Course"
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Re: If mn>0, is m^3n^4>0? &nbs [#permalink] 29 Oct 2017, 18:03
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