Question

If 160 is divided by x, then the remainder is 4. What is the remainder when 315 is divided by x?

Answer 1

Let us rewrite this equation as:
160/x = some number + 4/x
we can assume that some number of x's can fit into 160, but x is greater than 4 so we have a remainder.
We can figure out by using the remainder that x is completely divisible into (160-4) or 156. Knowing this we can assume that x is some factor of 156 that is greater than 4. 
Let us list the factors of 156
1,2,3,4,6,12,13,26,39,52,78,156
Now let us refer back to the restrictions we put on x.
x must be > 4 as anything less than 4 would divide at least 1 more time into it. So now we are left with a bunch of other factors. And the cool thing is that all of the factors excluding anything that is = or < 4 all work for getting a remainder of 4. Thus we can use the largest factor and set it equal to x.
So x = 156
then if we divide 315 by x or 315/x = 315/156 = 2 and a remainder of 3
so the answer would be 3.