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If n and m are positive integers, what is the remainder when

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If n and m are positive integers, what is the remainder when [#permalink] New post 12 Nov 2006, 14:38
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If n and m are positive integers, what is the remainder when 3^(4n+2) + m is divided by 10?

(1) n=2
(2) m=1

OA is B
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 [#permalink] New post 12 Nov 2006, 15:17
Given that n and m are positive integers, knowing n is useless because the expression (4n+2) will always give an answer which is 4 units apart. What we need to know is what m is for it will determine the remainder of the expression when divided by 10.
Notice that for any exponent of 3, the unit digit is repeating in cycles of 4:
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
____________________________
3^5 = 243
3^6 = 729
3^7 = 2187
3^8 = 6561
____________________________
Notice the cycle: 3-9-7-1
Hence, knowing that m is 1, we know that the whole expression (4n+2)+m will give an exponent of 7, 11, 15, etc.
This ensures that the remainder will ALWAYS be 7 and B is sufficient.

:btw do not provide the answer before it is answered, nobody may attempt it. Give it a maximum of 2 days and provide the answer thereafter.
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Best Regards,

Paul

  [#permalink] 12 Nov 2006, 15:17
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