The remainder question that is divided by 5 will have a cycle of 4. In other words, (~2)^1=~2, (~2)^2=~4, (~2)^3=~8, (~2)^4=~6. Hence, it has a cycle of
4-> 2->4->8->6->2->4->8->6.
If we modify the original condition and the question, when we divide 2^4x+2+y by 5, we do not have to know 4x in 4x+2. Hence, from 2^2+y, we only have to know y. The correct answer choice is, thus, B.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.