Difference between revisions of "2010 AMC 12B Problems/Problem 8"
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== Solution == | == Solution == | ||
| + | There are <math>x</math> schools. This means that there are <math>3x</math> 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 <math>x</math> is an odd number. <math>x</math> cannot be less than 23, because there wouldn't be a 64th place if there were. <math>x</math> cannot be greater than 23 either, because that would tie Andrea and Beth. Thus, the only possible answer is <math>\boxed{23}</math> | ||
== See also == | == See also == | ||
{{AMC12 box|year=2010|num-b=12|num-a=14|ab=B}} | {{AMC12 box|year=2010|num-b=12|num-a=14|ab=B}} | ||
Revision as of 22:30, 2 September 2010
Problem 8
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 
th and 
th, respectively. How many schools are in the city?
Solution
There are 
schools. This means that there are 
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 is an odd number. cannot be less than 23, because there wouldn't be a 64th place if there were. cannot be greater than 23 either, because that would tie Andrea and Beth. Thus, the only possible answer is 
See also
| 2010 AMC 12B (Problems • Answer Key • Resources) | |
| 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 | |
