Problem:
Every high school in the city of Euclid sent a team of 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 and , respectively. How many schools are in the city?
Answer Choices:
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E.
Solution:
If there are schools in the city, then there are contestants, so , and . Because Andrea received the median score and each student received a different score, is odd, so . Andrea's position is , and Andrea finished ahead of Beth, so , and . Because is an odd integer, . Therefore .
The problems on this page are the property of the MAA's American Mathematics Competitions