Question 11
A sequence of $2016$ terms is constructed as follows: The first two terms of the sequence are both equal to $3$. Starting from the third term, each subsequent term is the sum of the preceding two terms. Each of the terms of this sequence $3$, $3$, $6$, $9$, $...$ is now divided by $2$ and the remainders are added. What is the sum of all the remainders of the $2016$ terms?
(A) $504$ (B) $1\,008$ (C) $1\,344$ (D) $1\,512$ (E) $2\,016$
(A) $504$ (B) $1\,008$ (C) $1\,344$ (D) $1\,512$ (E) $2\,016$