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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 10 Jan 2006, 13:13
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If n and m are positive integers, what is the remainder when 3^(4n+2) is divided by 10?

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

Shouldnt the answer be A .. but its B.

Please explain.

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 [#permalink] New post 10 Jan 2006, 14:39
Is this questions correct? Should it be 3^(4n+2m)?
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 [#permalink] New post 10 Jan 2006, 14:54
Yeah thats what I was wondering since m didnt feature anywhere in the question stem but thats the question! It is from one of the GmatPrep tests. Maybe its a typo .. didn't think GmatPrep would have typos!!!!!

Anyone else seen this?

:shock:

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 [#permalink] New post 10 Jan 2006, 15:10
Hmm. looks like a trick question.

3^(4n+2)/10 will always have a reminder of 9, as long as n is a +ve integer. How?

Rem :3^1/10 = 3
3^2/10 = 9
3^3/10 = 7
3^4/10 = 1
3^5/10 = 3
3^6/10 = 9 ---> 6th

The pattern, 3,9,7,1 repeats for every 4 numbers.

4n+2 will always be = 6, 10, 14 ....
For all of these powers of 3 the reminder when divided by 10 is always be 9.

Hence n is not required!! Hence A is not required => B!!

:shock: May be I am smoking something. :??? :drunk
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 [#permalink] New post 10 Jan 2006, 15:32
giddi77 wrote:
Hmm. looks like a trick question.

3^(4n+2)/10 will always have a reminder of 9, as long as n is a +ve integer. How?

Rem :3^1/10 = 3
3^2/10 = 9
3^3/10 = 7
3^4/10 = 1
3^5/10 = 3
3^6/10 = 9 ---> 6th

The pattern, 3,9,7,1 repeats for every 4 numbers.

4n+2 will always be = 6, 10, 14 ....
For all of these powers of 3 the reminder when divided by 10 is always be 9.

Hence n is not required!! Hence A is not required => B!!

:shock: May be I am smoking something. :??? :drunk



If the question asked for 3^(4n+2m).
B is correct, since the reminder is independent of A.

In fact if neither A or B is required to answer the question. Shouldn't it be E?
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 [#permalink] New post 10 Jan 2006, 17:37
I guess the question should be 3^(4n+2m). It just doesnt make any sense otherwise! :roll:

Arghhhh gmat's really getting to me!!! :boxer
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 [#permalink] New post 10 Jan 2006, 18:02
Agree, there may be a typo in the question. If 'm' is not given in the question, then definitely statement 2) m = 1 , doesn't make any sense.

If there is no typo, the question is as it is , then I would pick E.
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  [#permalink] 10 Jan 2006, 18:02
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