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by mike22629 » Sat Apr 18, 2009 4:14 pm
Missing something simple here

If n and m are positive integers, what is the remainder of 3^(4n+2) + m divided by 10.

1) n =2
2) m =1

I assume that it is looking for patterns in the 3 powers (ie 3,9,1,3,9,1)
But do not understand how they get the answer they do.

OA after few responses.
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Source: — Data Sufficiency |
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by mike22629 » Sat Apr 18, 2009 4:16 pm
Ha I was just thinking about it and I believe it came to me. The pattern is 3,9,7,1 which makes perfect sense now.
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by m&m » Sat Apr 18, 2009 9:24 pm
is OA B?
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by mike22629 » Sun Apr 19, 2009 4:10 am
yes OA B.
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by PAB2706 » Wed Apr 29, 2009 11:09 am
:lol: just in case ppl dnt understand wht is happening here ( since both the post above are abstract ) i am posting the solution.

3^(4n+2) = 3^4n * 3^2
= 3^4n * 9

now if u observe the progression of different powers of 3 you observe that the units digit follows a pattern 3,9,7,1

therefore 3^4n will always have 1 in its unit place

and 3^4n*9 will always have 9 in its units place.

Thus the value of m=1 brings 0 in the units place of the complete expression 3^(4n+2) +m

Hence the expression is completely divisible by 10 ie remainder 0

thus B is sufficient.
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