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If n and mare positive integers, is n^m+2n divisible by 3?

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MathRevolution
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If n and mare positive integers, is n^m+2n divisible by 3? [#permalink] New post  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.
Corrected the format
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abhimahna
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Re: If n and mare positive integers, is n^m+2n divisible by 3? [#permalink] New post  11 Oct 2016, 06:46
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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? [#permalink] New post  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.
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Re: If n and mare positive integers, is n^m+2n divisible by 3? [#permalink] New post  13 Oct 2016, 07:28
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==>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^3-n+3n=(n-1)n(n+1)+3n. Here, (n-1)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? [#permalink] New post  14 Oct 2016, 05:46
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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? [#permalink] New post  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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