15. Observing the calendar, Chiara noticed that the current year 2016 has a particularity: if $x=2016$ is the year number, then $x+1$ is a multiple of $1, x+2$ is a multiple of $2, x+3$ is a multiple of $3$, and $x+4$ is a multiple of $4$. How many other positive integers, less than 2016, have the same particularity?
(A) 154
(B) 83
(C) 167
(D) 24
(E) 162
Problem 15. The answer is (C).

The statement is equivalent to saying that $x$ is a multiple of $1, 2, 3,$ and $4$, and thus a multiple of their least common multiple, which is 12. We need to count the positive integers less than 2016 that are multiples of 12. Since $2016 / 12 = 168$, there will be exactly 167 such numbers.

(Problem proposed by E. Tron)