Problem:
Alice, Bob, and Charlie were on a hike and were wondering how far away the nearest town was. When Alice said, "We are at least 6 miles away," Bob replied, "We are at most 5 miles away." Charlie then remarked, "Actually the nearest town is at most miles away." It turned out that none of the three statements was true. Let be the distance in miles to the nearest town. Which of the following intervals is the set of all possible values of
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Because the statements of Alice, Bob, and Charlie are all incorrect, the actual distance satisfies , and . Hence the actual distance lies in the interval .
The problems on this page are the property of the MAA's American Mathematics Competitions