AMC 10 2014b Problem 11

For the consumer, a single discount of $n\%$ is more advantageous than any of the following discounts: (1) two successive $15\%$ discounts (2) three successive $10\%$ discounts (3) a $25\%$ discount followed by a $5\%$ discount What is the smallest possible positive integer value of $n$? $\textbf{(A)}\ \ 27 \textbf{(B)}\ 28 \textbf{(C)}\ 29 \textbf{(D)}\ 31 \textbf{(E)}\ 33$