2011 AMC 10B Problems/Problem 8

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Problem 8

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

$C, D,$ and $E$ can not be right because the sun intensity of June 10 does not depend at all on the temperature.

If it was cooler than $80^\circ$ but it was still sunny, it would not meet the conditions of $A,$ but the beach would still be not crowded.

However, $B$ means that if either condition was not met, then the beach would not be crowded. Therefore, the correct answer is $\boxed{\textbf{(B)}}$

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