Problem:
At a certain beach if it is at least and sunny, then the beach will be crowded. On June the beach was not crowded. What can be concluded about the weather conditions on June ?
Answer Choices:
A. The temperature was cooler than and it was not sunny.
B. The temperature was cooler than or it was not sunny.
C. If the temperature was at least , then it was sunny.
D. If the temperature was cooler than , then it was sunny.
E. If the temperature was cooler than , then it was not sunny.
Solution:
Because the beach was not crowded on June , at least one of the conditions was not met. That is, the weather might have been cooler than and sunny, at least and cloudy, or cooler than and cloudy. The first possibility shows that and are invalid, the second shows that is invalid, and the third shows that is invalid. Only conclusion is consistent with all three possibilities.
The problems on this page are the property of the MAA's American Mathematics Competitions