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

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Manager
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If n and m are positive integers, what is the remainder when [#permalink]  26 May 2006, 10:25
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
Manager
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(1)m could be anything. INSUFFICIENT

(2)any even power of 3 that is not a multiple of 4 will end in a 9. ad 1 and the remainder when divided by 10 is always 0 SUFFICIENT

Senior Manager
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a) the reminder is 9+m - insuff
b) the reminder is 9+1 = 0 sufficient
Director
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Kudos [?]: 5 [0], given: 0

I agree B is sufficient.
Manager
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Kudos [?]: 3 [0], given: 0

OA is B.

Great job guys!
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(1) Insufficient, as remainder depends on "m"
(2) Sufficient, as the power is even.
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level of difficulty [#permalink]  09 Jun 2006, 23:25
vivek123 wrote:
(1) Insufficient, as remainder depends on "m"
(2) Sufficient, as the power is even.

Right. just if it is a multiple of 4, it will always end in 9. add 1 then you have the unit digit as 0. hence the remainder will always equal 0.

what level of difficulty do you think this problem would be?
level of difficulty   [#permalink] 09 Jun 2006, 23:25
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