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Divisibility of Integers, remainders

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calvinshmoe
 Post subject: Divisibility of Integers, remainders
 Post Posted: Fri Dec 02, 2011 6:07 am 
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Course Students


Posts: 1
The question is:

Integer n is divided by 3 the remainder is 2, when integer n is divided by 4 the remainder is 1, what is the remainder when n is divided by 12?

Help guys, and when it comes to this kind of question how to we approach first?

Thanks a million!
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stud.jatt
 Post subject: Re: Divisibility of Integers, remainders
 Post Posted: Sat Dec 03, 2011 5:06 pm 
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Students


Posts: 21
You have to find the series of numbers for which both the statements hold true and then divide any one of them by 12 to see what the remainder would be.

First Statement
When integer n is divided by 3 the remainder is 2
let a be the quotient when n is divided by 3, then n is of the form n = 3a+2

plugging a = 0,1,2,3,4...
we have

n = 2,5,8,11,14,17,20....

Second Statement
When integer n is divided by 4 the remainder is 1
let b be the quotient when n is divided by 4, then n is of the form n = 4b+1

plugging b = 0,1,2,3,4,5...
we have

n = 1,5,9,13,17,21.....

Now note that the only numbers in the series that satisfy both these equations are 5,17,29..... and if you divide any of these by 12 the remainder will always be 5.

Actually you do not have to plot both the series to a lot of terms, I did that just to make the explanation easier and lucid. Just find the first common term in the two series (for e.g. 5 here) and that will give you the answer

Hope this helps
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jnelson0612
 Post subject: Re: Divisibility of Integers, remainders
 Post Posted: Sun Dec 25, 2011 11:39 pm 
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ManhattanGMAT Staff


Posts: 1857
Excellent explanation, thank you!

_________________
Jamie Nelson
ManhattanGMAT Instructor
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