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.