CEMC Pascal

When $n=1$, the values of the five expressions are 2014, 2018, 2017, 2018, 2019.
When $n=2$, the values of the five expressions are 2011, 2019, 4034, 2021, 2021.
Only the fifth expression $(2017+2n)$ is odd for both of these choices of $n$, so this must be the correct answer.
We note further that since 2017 is an odd integer and $2n$ is always an even integer, then $2017+2n$ is always an odd integer, as required.