Question 68
Determine the largest integer $n$ with this property: there exist $n$ distinct positive integers $a_{1}, \ldots, a_{n}$ such that, however two distinct ones are chosen among them, neither their sum nor their difference is divisible by $100$.
(A) $49$
(B) $50$
(C) $51$
(D) $99$
(E) $100$ .
(A) $49$
(B) $50$
(C) $51$
(D) $99$
(E) $100$ .