2017 AMC 12A Problem 3
Problem 3 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 is “all right A.” An implication is equivalent only to its contrapositive: “not A not all right.”
“Not all right” means at least one question was wrong, which is exactly statement B. The converse and inverse do not follow, and getting “all wrong” is a much stronger claim than the negation.
Thus, the correct answer is B.