2017 AMC 10A Problem 6
Attempt Problem 6 of the 2017 AMC 10A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2017 AMC 10A solutions, or check the answer key.
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6.
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?
If Lewis did not receive an A, then he got all of the multiple choice questions wrong.
If Lewis did not receive an A, then he got at least one of the multiple choice questions wrong.
If Lewis got at least one of the multiple choice questions wrong, then he did not receive an A.
If Lewis received an A, then he got all of the multiple choice questions right.
If Lewis received an A, then he got at least one of the multiple choice questions right.
Answer: B
Solution:
The promise says that getting every multiple choice question right guarantees an A. Its contrapositive is that anyone who did not receive an A must not have gotten every multiple choice question right. In other words, that person got at least one multiple choice question wrong.
Thus, B is the correct answer.
Problem 6 in Other Years
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