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If n is positive integer, is (3^n)+(n^2) not divisible by 3?

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If n is positive integer, is (3^n)+(n^2) not divisible by 3?

by Max@Math Revolution » Sat Mar 19, 2016 10:09 pm
If n is positive integer, is (3^n)+(n^2)+1 not divisible by 3?

1) n is not multiple of 2
2) n is not multiple of 3


* A solution will be posted in two days.
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Source: — Data Sufficiency |
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by Max@Math Revolution » Tue Mar 22, 2016 4:54 pm
If n is positive integer, is (3^n)+(n^2)+1 not divisible by 3?

1) n is not multiple of 2
2) n is not multiple of 3


In the original condition, 3^n can be divided by 3 and the question is if (n^2)+1 can be divided by 3. There is 1 variable(n), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), n=1,3,5,7,.., which is always yes and sufficient.
For 2), n=1,2,4,5,7.., which is always yes and sufficient.
Therefore, the answer is D.
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