MathNet 2007-part-01 — 187 problems (EN–VI) Question 132

Let $A$ and $B$ be two subsets of $\{1, 2, 3, \dots, 100\}$, satisfying $|A| = |B|$ and $A \cap B = \emptyset$. If $n \in A$ always implies $2n + 2 \in B$, then the maximum of $|A \cup B|$ is ( ).