AMC 12 2010b Problem 8

Every high school in the city of Euclid sent a team of $3$ students to a math contest. Each participant in the contest received a different score. Andrea's score was the median among all students, and hers was the highest score on her team. Andrea's teammates Beth and Carla placed $37$th and $64$th, respectively. How many schools are in the city?

\textbf{(A)}\ 22 \textbf{(B)}\ 23 \textbf{(C)}\ 24 \textbf{(D)}\ 25 \textbf{(E)}\ 26