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If n and mare positive integers, is n^m+2n divisible by 3?
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Updated on: 14 Oct 2016, 05:45
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If n and mare positive integers, is \(n^m\)+2n divisible by 3? 1)m=3 2)n=1
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Originally posted by MathRevolution on 11 Oct 2016, 04:57.
Last edited by abhimahna on 14 Oct 2016, 05:45, edited 1 time in total.
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Re: If n and mare positive integers, is n^m+2n divisible by 3?
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11 Oct 2016, 06:46
MathRevolution wrote: If n and mare positive integers, is n^m+2n divisible by 3?
1)m=3 2)n=1 Answer D. We are given whether [m]n^m+2n [\m] is divisible by 3. Statement 1 : m = 3. or I can say [m]n^3+2n [\m] = [m]n(n^2+2) [\m]. This will always be divisible by 3 for any positive integral value of n. Hence, sufficient. Statement 2 : n =1 or I can say [m]1^m+2 [\m]. Now [m]1^m[\m] will always be equal to 1. So, 1 + 2 = 3. Divisible by 3. Hence , Sufficient.
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Re: If n and mare positive integers, is n^m+2n divisible by 3?
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Updated on: 14 Oct 2016, 05:44
abhimahna wrote: MathRevolution wrote: If n and mare positive integers, is n^m+2n divisible by 3?
1)m=3 2)n=1 Answer D. We are given whether [m]n^m+2n [\m] is divisible by 3. Statement 1 : m = 3. or I can say [m]n^3+2n [\m] = [m]n(n^2+2) [\m]. This will always be divisible by 3 for any positive integral value of n. Hence, sufficient. Statement 2 : n =1 or I can say [m]1^m+2 [\m]. Now [m]1^m[\m] will always be equal to 1. So, 1 + 2 = 3. Divisible by 3. Hence , Sufficient. Can someone clarify what is the question? Is it (n^m) + 2n or n^(m+2n)??
Originally posted by mechky on 13 Oct 2016, 07:10.
Last edited by abhimahna on 14 Oct 2016, 05:44, edited 1 time in total.
Corrected the Quote



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Re: If n and mare positive integers, is n^m+2n divisible by 3?
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13 Oct 2016, 07:28
==>In the original condition, there are 2 variables, and C is the answer. However, 1) and 2) each becomes yes, so D is the answer, a common CMT 4(B). Especially in the case of 1), if you substitute m=3, you get n^3+2n=n^3n+3n=(n1)n(n+1)+3n. Here, (n1)n(n+1) is the multiple of three consecutive integers, and you always get the multiples of 6, hence yes each time. Answer: D
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Re: If n and mare positive integers, is n^m+2n divisible by 3?
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14 Oct 2016, 05:46
mechky wrote: abhimahna wrote: MathRevolution wrote: If n and mare positive integers, is n^m+2n divisible by 3?
1)m=3 2)n=1 Answer D. We are given whether [m]n^m+2n [\m] is divisible by 3. Statement 1 : m = 3. or I can say [m]n^3+2n [\m] = [m]n(n^2+2) [\m]. This will always be divisible by 3 for any positive integral value of n. Hence, sufficient. Statement 2 : n =1 or I can say [m]1^m+2 [\m]. Now [m]1^m[\m] will always be equal to 1. So, 1 + 2 = 3. Divisible by 3. Hence , Sufficient. Can someone clarify what is the question? Is it (n^m) + 2n or n^(m+2n)?? Corrected the format. Please check now.
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Re: If n and mare positive integers, is n^m+2n divisible by 3?
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11 Apr 2017, 10:17
MathRevolution wrote: If n and mare positive integers, is \(n^m\)+2n divisible by 3?
1)m=3 2)n=1 1. we can rewrite: n(n^2 +2)/3 let's try few values. if n=1, then it is divisible if n=2, then it is divisible if n=5, it is divisible if n=7, it is divisible so works all the times...sufficient. 2. sufficient alone. answer is D.




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