2016/17 AHSMC Part 1 Problem 5

Since $n^2 + 3n + 2 = (n+1)(n+2)$ it must be even. Thus, $375$ is not attainable. The other four numbers in the list can be attained using $n = -1$, $n = 0$, $n = 9$ and $n = 19$, respectively. The answer is (D).