2014 AMC 10B 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\qquad\textbf{(B)}\ 28\qquad\textbf{(C)}\ 29\qquad\textbf{(D)}\ 31\qquad\textbf{(E)}\ 33

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