Question

At a certain beach if it is at least $80^{\circ} F$ and sunny, then the beach will be crowded. On June 10 the beach was not crowded. What can be concluded about the weather conditions on June 10?

The temperature was cooler than $80^{\circ}$ F and it was not sunny.

The temperature was cooler than $80^{\circ}$ F or it was not sunny.

If the temperature was at least $80^{\circ}$ F, then it was sunny.

If the temperature was cooler than $80^{\circ}$ F, then it was sunny.

If the temperature was cooler than $80^{\circ}$ F, then it was not sunny.

Solution:

The statement says that if the weather was at least $80^\circ F$ and sunny, then the beach was crowded.

Because the beach was not crowded, the two conditions could not both have been true. Therefore the temperature was cooler than $80^\circ F$ , or it was not sunny, or both.

Thus, B is the correct answer.

2011 AMC 10B Problem 8

Solution:

Problem 8 in Other Years