Problem:
After Euclid High School's last basketball game, it was determined that of the team's points were scored by Alexa and were scored by Brittany. Chelsea scored points. None of the other team members scored more than points. What was the total number of points scored by the other team members?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Answer (B): The total number of points scored by players other than Alexa and Brittany was at least 15 and at most . The fraction of the team's points scored by those players was , so the number of points that they scored was a multiple of . The only multiple of between and is , so the number of points scored by the players other than Alexa, Brittany, and Chelsea was .
The total number of points scored by the team was a multiple of both and and thus was a multiple of . If the total was , then Alexa scored and Brittany scored , and so Chelsea could not have scored . If the total was , where , then Alexa scored and Brittany scored . With Chelsea scoring , this leaves points for the remaining team members. But then at least one of them scored more than points. So the only possible score was . Then Alexa scored , Brittany scored , Chelsea scored , and the remaining team members scored a total of points.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions