Problem:
AT Olympic High School, of the freshmen and of the sophomores took the . Given that the number of freshmen and sophomore contestants was the same, which of the following must be true?
Answer Choices:
A. There are five times as many sophomores as freshmen.
B. There are twice as many sophomores as freshmen.
C. There are as many freshmen as sophomores.
D. There are twice as many freshmen as sophomores.
E. There are five times as many freshmen as sophomores.
Solution:
Let and represent the numbers of freshmen and sophomores at the school, respectively. According to the given condition, . Thus, . That is, there are twice as many freshmen as sophomores.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions