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2017 AMC 10A Problem 6

Problem 6 of 25Easier

Ms. Carroll promised that anyone who got all the multiple choice questions right on the upcoming exam would receive an A on the exam. Which one of these statements necessarily follows logically?

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Solution

The promise says that getting every multiple choice question right guarantees an A. Its contrapositive is that anyone who did not receive an A must not have gotten every multiple choice question right. In other words, that person got at least one multiple choice question wrong. 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.