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More remainder problems

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mrblack
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More remainder problems [#permalink] New post   08 Jan 2010, 07:59
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If n is divided by 3, the remainder is 1.
If n is divided by 4, the remainder is 1.

What is the remainder if n is divided by 12?



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Re: More remainder problems [#permalink] New post   08 Jan 2010, 15:45
Hi,

Since the remainder is 1 in both cases can we just find the LCM of 3 and 4 and add 1.
LCM of 4 and 3 =12. So n has to be 12k+1, for k=0,1,2,3....
Remainder when n is divided by 12 is 1..

IMO remainder =1.
Please post the OA.
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Re: More remainder problems [#permalink] New post   08 Jan 2010, 17:09
what if remainders were different in both cases, as in divisibility by 3 and 4 separately yielded different remainders?

There should be a common strategy or formula with which these questions should be answered I guess.
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Re: More remainder problems [#permalink] New post   08 Jan 2010, 20:36
acegre wrote:
Hi,

Since the remainder is 1 in both cases can we just find the LCM of 3 and 4 and add 1.
LCM of 4 and 3 =12. So n has to be 12k+1, for k=0,1,2,3....
Remainder when n is divided by 12 is 1..

IMO remainder =1.
Please post the OA.


Sorry but there is no OA. I just made the question up. Your reasoning makes sense though.

Checking with n=13:
13/3 = remainder 1
13/4 = remainder 1
13/12 = remainder 1



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Re: More remainder problems [#permalink]
08 Jan 2010, 20:36
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