remainders

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.

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?

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

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