Difference between revisions of "2017 AMC 12A Problems/Problem 3"

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==Solution==
 
==Solution==
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Taking the contrapositive of the statement If he got all of them right, he got an A yields If he didn't get an A, he didn't get all of them right, making the answer B.
  
 
==See Also==
 
==See Also==
 
{{AMC12 box|year=2017|ab=A|num-b=2|num-a=4}}
 
{{AMC12 box|year=2017|ab=A|num-b=2|num-a=4}}

Revision as of 15:25, 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 on of these statements necessarily follows logically?

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

Solution

Taking the contrapositive of the statement If he got all of them right, he got an A yields If he didn't get an A, he didn't get all of them right, making the answer B.

See Also

2017 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions