AMC 10 2017b Problem 1

Mary thought of a positive two-digit number. She multiplied it by $3$ and added $11$. Then she switched the digits of the result, obtaining a number between $71$ and $75$, inclusive. What was Mary's number? $\textbf{(A)}\ 11 \textbf{(B)}\ 12 \textbf{(C)}\ 13 \textbf{(D)}\ 14 \textbf{(E)}\ 15$