AMC 8 1991 Problem 14

Several students are competing in a series of three races. A student earns $5$ points for winning a race, $3$ points for finishing second and $1$ point for finishing third. There are no ties. What is the smallest number of points that a student must earn in the three races to be guaranteed of earning more points than any other student? $\text{(A)}\ 9 \text{(B)}\ 10 \text{(C)}\ 11 \text{(D)}\ 13 \text{(E)}\ 15$