2010 AMC 12B Problems/Problem 8

Revision as of 23:30, 2 September 2010 by Alberthyang (talk | contribs) (Solution)

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?

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


There are $x$ schools. This means that there are $3x$ people. Because no one's score was the same as another person's score, that means that there could only have been 1 median score. This implies that $x$ is an odd number. $x$ cannot be less than 23, because there wouldn't be a 64th place if there were. $x$ cannot be greater than 23 either, because that would tie Andrea and Beth. Thus, the only possible answer is $\boxed{23}$

See also

2010 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 12
Followed by
Problem 14
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions
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