AMC 12 2017a Problem 3

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?

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