2017 AMC 10A Problem 20

Let S(n) equal the sum of the digits of positive integer n. For example, S(1507) = 13. For a particular positive integer n, S(n) = 1274. Which of the following could be the value of S(n+1)?

\textbf{(A)}\ 1 \qquad\textbf{(B)}\ 3\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 1239\qquad\textbf{(E)}\ 1265

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.