2017 AMC 10A Problem 6
Below is the professionally curated solution for Problem 6 of the 2017 AMC 10A, 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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Difficulty rating: 900
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.
Solution:
There is no stipulation on how to get an A other than that getting all the multiple choice right guarantees an A.
This means that it is possible to get an A without getting all the multiple choice questions right.
It is also possible to not get an A even if all but one of the multiple choice questions are answered correctly.
This rules out A , C , D , and E .
Thus, B is the correct answer.
Problem 6 in Other Years
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