How many three-digit numbers greater than 200 can be written using only the digits 1, 3, and 5?
(a) 10
(b) 12
(c) 14
(d) 15
(e) 18
The correct option is (e).

Since they are greater than 200, their hundreds digits can only be 3 or 5.

Starting with 3, we have 315 and 351 (which do not repeat digits) and 311, 313, 331, 335, 353, 333, and 355 (repeating digits), that is, nine numbers.

Starting with 5, it is enough to swap the 3 with the 5 in the numbers above. Therefore, we have 9 of these numbers. Thus, we have a total of 18 numbers that can be written using only the digits 1, 3, and 5.