Art of Problem Solving

2017 AMC 10A Problems/Problem 6: Difference between revisions

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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?
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?


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


==Solution==
==Solution==


==See Also==
==See Also==

Revision as of 18:07, 8 February 2017

Problem

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?

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

Solution

See Also