Problem 369

The room numbers of a hotel are all three-digit numbers. The first digit represents the floor and the last two digits represent the room number. The hotel has rooms on five floors, numbered 1 to 5. It has 35 rooms on each floor, numbered n01 to n35 where $n$ is the number of the floor. In numbering all the rooms, how many times will the digit 2 be used?

(A) $60$ (B) $65$ (C) $95$ (D) $100$ (E) $105$