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# If m and n are non-negative integers, mn=?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7343
GMAT 1: 760 Q51 V42
GPA: 3.82
If m and n are non-negative integers, mn=?  [#permalink]

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01 Aug 2017, 00:59
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Difficulty:

45% (medium)

Question Stats:

63% (01:15) correct 37% (01:40) wrong based on 58 sessions

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If m and n are non-negative integers, mn=?

1) $$9^n=3^m$$
2) $$2^n=5^m$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"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" Senior PS Moderator Joined: 26 Feb 2016 Posts: 3386 Location: India GPA: 3.12 Re: If m and n are non-negative integers, mn=? [#permalink] ### Show Tags 01 Aug 2017, 01:31 1 1. $$9^n=3^m$$ This is possible when the values of n and m are as follows: a) n=1,m=2 nm=2 b) n=2,m=4, nm=8 We are not able to come up with an unique value for the expression mn(Insufficient) 2. $$2^n=5^m$$ This is possible if and only if n=m=0. The value of nm=0 (Sufficient)(Option B) _________________ You've got what it takes, but it will take everything you've got Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7343 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If m and n are non-negative integers, mn=? [#permalink] ### Show Tags 03 Aug 2017, 01:25 ==> In the original condition, there are 2 variables (m,n) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), from con 1), you get $$9^n=(3^2)^n=3^{2n}=3^m$$, which becomes $$2n=m$$. In order for con 2) to satisfy as well, you only get m=n=0, hence it is unique and sufficient. The answer is C. However, this is an integer question, one of the key questions, so you apply CMT 4 (A: if you get C too easily, consider A or B). For con 1), the way to satisfy $$9^n=(3^2)^n=3^{2n}=3^m$$ to $$2n=m$$ is not unique and not sufficient. For con 2), from $$2^n=5^m$$, you get $$2^n=even$$ and $$5^m=odd$$, so even≠odd. Only m=n=0 satisfies this, hence it is unique and sufficient. Therefore, the answer is B, not C. Answer: B _________________ 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"
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Re: If m and n are non-negative integers, mn=?   [#permalink] 03 Aug 2017, 01:25
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