2011 AMC 10B Problem 8

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.

Use the contrapositive of “hot and sunny implies crowded”

Not crowded means at least one of the two conditions failed

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.

Problem 8 in other years