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2011 AMC 10B Problem 8

Problem 8 of 25Easier

At a certain beach if it is at least 80F80^{\circ} F and sunny, then the beach will be crowded. On June 1010 the beach was not crowded. What can be concluded about the weather conditions on June 10?10?

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Solution

The statement says that if the weather was at least 80F80^\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 80F80^\circ F, or it was not sunny, or both. Thus, B is the correct answer.

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Concepts: logical deduction

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.