Problem:
Bridget, Cassie, and Hannah are discussing the results of their last math test. Hannah shows Bridget and Cassie her test, but Bridget and Cassie don't show their tests to anyone. Cassie says, "I didn't get the lowest score in our class," and Bridget adds, "I didn't get the highest score." What is the ranking of the three girls from highest to lowest?
Answer Choices:
A. Hannah, Cassie, Bridget
B. Hannah, Bridget, Cassie
C. Cassie, Bridget, Hannah
D. Cassie, Hannah, Bridget
E. Bridget, Cassie, Hannah
Solution:
Cassie says, "I didn't get the lowest score," so her score is higher than Hannah's score. Bridget says, "I didn't get the highest score," so her score is lower than Hannah's score. Therefore the order, from highest to lowest, must be Cassie, Hannah, Bridget.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions