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2017 AMC 10A Problem 6

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2017 AMC 10A Problem 6AMC 10 Step by Step
Name:                             Date: October 28, 2026
Logic Puzzles · difficulty 1 of 5 · about 1 min · position P1-10

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?

  1. A)If Lewis did not receive an A, then he got all of the multiple choice questions wrong.\text{If Lewis did not receive an A, then he got all of the multiple choice questions wrong.}
  2. B)If Lewis did not receive an A, then he got at least one of the multiple choice questions wrong.\text{If Lewis did not receive an A, then he got at least one of the multiple choice questions wrong.}
  3. C)If Lewis got at least one of the multiple choice questions wrong, then he did not receive an A. \text{If Lewis got at least one of the multiple choice questions wrong, then he did not receive an A. }
  4. D)If Lewis received an A, then he got all of the multiple choice questions right.\text{If Lewis received an A, then he got all of the multiple choice questions right.}
  5. E)If Lewis received an A, then he got at least one of the multiple choice questions right.\text{If Lewis received an A, then he got at least one of the multiple choice questions right.}

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