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Carroll's Tests

Source: Problem #6 2017 AMC 10A

February 8, 2017
AMCAMC 10AMC 122017 AMC 12A2017 AMC 10A

Problem Statement

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 of these statements necessarily follows logically?
<spanclass=′latex−bold′>(A)</span><span class='latex-bold'>(A)</span> If Lewis did not receive an A, then he got all of the multiple choice questions wrong. \\ <spanclass=′latex−bold′>(B)</span><span class='latex-bold'>(B)</span> If Lewis did not receive an A, then he got at least one of the multiple choice questions wrong. \\ <spanclass=′latex−bold′>(C)</span><span class='latex-bold'>(C)</span> If Lewis got at least one of the multiple choice questions wrong, then he did not receive an A. \\ <spanclass=′latex−bold′>(D)</span><span class='latex-bold'>(D)</span> If Lewis received an A, then he got all of the multiple choice questions right. \\ <spanclass=′latex−bold′>(E)</span><span class='latex-bold'>(E)</span> If Lewis received an A, then he got at least one of the multiple choice questions right.
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