When a number Y is divided by X - it leaves a remainder of 11.
When Y is divided by 8X , the remainder is 92.
What is the remainder when Y is divided by 4X ?
Let Y = aX + 11 = 8bX + 92
Then X = 81/(a-8b)
But 8X must be > 92, because dividing by 8X leaves a remainder of 92, so X > 11.5
Since (a-8b) is an integer, X can only be 81/n where n between 1 and 7 inclusive. If n > 7, then X is < 11.5.
Then Y can be 92 +8m(81/n) where m = any integer.
Here are the remainders (Y mod 4X) for each of the possible n.
The remainder is independent of m, so I only need to calculate 92 Mod (4*81/n)
n remainder
1 92
2 92
3 92
4 11
5 27.2
6 38
7 45 + 5/7
The remainder can be any one of 5 values. If X is an integer, then n = 1 or 3, and the remainder must by 92, as demonstrated by Charlie.
Analytical solution yields 5 possible remainders
