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remainders

by GmatTakerNo.1 » Sun Apr 25, 2010 7:00 am
Hey, can you help me out with this one:

When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder when N is divided by 30?

The answer is 11.
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by tpr-becky » Sun Apr 25, 2010 7:30 am
having a remainder means that the original number is a multiple of the divisor + the remainder.

if the remainter is 1 when N is divided by 10 that means that the units digit of the number is 1. N is always a multiple of 10 +1.

If the remainder is 2 when divided by three that means it is a multiple of 3 +2.

When you look for the overlap you have 11, 21, 31, 41 for (10)x+1 and 11 and 41 overlap that for 3(y)+2

if you divide either 11 or 41 by 30 you get a remainder of 11.
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by eaakbari » Wed Apr 28, 2010 6:50 am
tpr-becky wrote:having a remainder means that the original number is a multiple of the divisor + the remainder.

if the remainter is 1 when N is divided by 10 that means that the units digit of the number is 1. N is always a multiple of 10 +1.

If the remainder is 2 when divided by three that means it is a multiple of 3 +2.

When you look for the overlap you have 11, 21, 31, 41 for (10)x+1 and 11 and 41 overlap that for 3(y)+2

if you divide either 11 or 41 by 30 you get a remainder of 11.
Well I had the same solution

Dividend = Divisor * quotient + Remainder
N= 10x + 1
N= 3y + 2

I did substitute some values of x and y and find 11 as remainder as Becky did, but there should be a better method than this. Someone please?
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by liferocks » Wed Apr 28, 2010 7:00 am
I did like this,
N=10x+1
=9x+(x+1)
since 9x is divisible by 3 when we divide x+1 by 3 reminder is 2 i.e x+1=3k+2 or x=3k+1

so N=10(3k+1)+1
or N=30k+11

hence when N is divided by 30 reminder is 11
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by eaakbari » Thu Apr 29, 2010 1:48 am
liferocks wrote:I did like this,
N=10x+1
=9x+(x+1)
since 9x is divisible by 3 when we divide x+1 by 3 reminder is 2 i.e x+1=3k+2 or x=3k+1

so N=10(3k+1)+1
or N=30k+11

hence when N is divided by 30 reminder is 11
Now thats a solution! Nice. Thanks
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