Let $A$ and $B$ be two subsets of $\{1, 2, 3, 4, ..., 100\}$, such that $|A| = |B|$ and $A\cap B =\emptyset$. If $n \in A$ implies that $2n + 2 \in B$, determine the largest possible value of $ |A \cup B|$.
Source: 2015 Cuba 1.4
Tags: number theory
Let $A$ and $B$ be two subsets of $\{1, 2, 3, 4, ..., 100\}$, such that $|A| = |B|$ and $A\cap B =\emptyset$. If $n \in A$ implies that $2n + 2 \in B$, determine the largest possible value of $ |A \cup B|$.