2011 AMC 10B Problems/Problem 8

Problem

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?

$\textbf{(A)}\ \text{The temperature was cooler than } 80^{\circ} \text{F and it was not sunny.}$

$\textbf{(B)}\ \text{The temperature was cooler than } 80^{\circ} \text{F or it was not sunny.}$

$\textbf{(C)}\ \text{If the temperature was at least } 80^{\circ} \text{F, then it was sunny.}$

$\textbf{(D)}\ \text{If the temperature was cooler than } 80^{\circ} \text{F, then it was sunny.}$

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

Solution

The beach not being crowded only means that it is not both hot and sunny. Equivalently, it is either cool or cloudy, which means $\boxed{\textbf{(B)}}$ is correct.

It could be in fact cool and sunny, which would violate (A) and (E). It could also be cool and cloudy, which would violate (D), or warm and sunny, which would violate (C).

2011 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 9
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2011 AMC 10B Problems/Problem 8

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