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AMC10 2011b Test Paper
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Sample Question 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?

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

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

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

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

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




Answer Keys

Question 8: B


Solutions

Question 8
Step 1: Analyze the given condition that if the beach is at least \(80^{\circ} F\) and sunny, then it will be crowded.

Step 2: Understand that on June 10, the beach was not crowded.

Step 3: Determine that this means that the weather conditions on June 10 did not meet both criteria - it was not both hot and sunny.

Step 4: Realize that this means it could have been cooler or cloudy, not necessarily both. It might have been cool and sunny, or it might have been warm but cloudy. Thus, option \( \textbf{(B)} \) is the correct choice.

Step 5: Understand that all other options are invalidated by the various situations which could have occurred on June 10. This includes cool and sunny (violating \(\textbf{(A)}\) and \(\textbf{(E)}\)), cool and cloudy (violating \(\textbf{(D)}\)), or hot and cloudy (violating \(\textbf{(C)}\)).