1. When you divide an integer by a positive integer N, the possible remainders range from 0 to (N- 1). There are thus N possible remainders.

2. You can add and subtract remainders directly, as long as you correct excess or negative remainders. so to correct the negative remainder, which is unacceptable remainder, add and extra 8. you get 7 as the answer.

Please note here that excess and negative remainders are not acceptable. for more, please refer chapter 10 of manhattan math book 1.

pacifist85 wrote:

I think we could also use the last digits of the numbers like this:

47 * 49 = 7*9 = 63.

63/8 = 7,... and leaves a remainder of 7.

One question on one of the solutions above:

Another way

(48-1)(48+1)/8

(48^2-1^2)/8

remainder when 48^2/8 is 0

remainder when -1^2/8 is -1 ie 7

Why does this tell us that the remainder is 7? I read the post about remainder tricks and tips, but it is not that clear to me...

There are two things for you to note

1) the method of calculating remainder by calculating unit digits and dividing by divisor is fundamentally wrong if the divisors are not 2 or 5 or 10.

Just luckily the answer is matching so please don't use this method because it fits to one question by chance.

2) remainder can be written in two forms either positive or negative. The understanding of positive and negative remainders are as follows

Remainder of 7 when a number divided by 8 means the number has 7 extra else the no. Would have been divisible by 8

Remainder of -1 when a number divided by 8 means the number is short by 1 else the no. Would have been divisible by 8

So technically they are sane and remainder of -1 is same as remainder of 7 for a divisor 8

Similarly, remainder of -2 is same as remainder of 6 for a divisor 8

Similarly, remainder of -4 is same as remainder of 5 for a divisor 9

Similarly, remainder of -5 is same as remainder of 7 for a divisor 12

I hope it clears your doubt!