Difference between revisions of "2017 AMC 10A Problems/Problem 6"
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If that someone is Lewis the statement becomes: "if Lewis got all the multiple choice questions right, then he got an A on the exam." | If that someone is Lewis the statement becomes: "if Lewis got all the multiple choice questions right, then he got an A on the exam." | ||
The contrapositive: "If Lewis did not receive an A, then he got at least one of the multiple choice questions wrong (did not get all of them right)" must also be true leaving B as the correct answer. B is also equivalent to the contrapositive of the original statement, which implies that it must be true, so the answer is <math>\boxed{\textbf{(B)}\text{ If Lewis did not receive an A, then he got at least one of the multiple choice questions wrong.}}</math>. | The contrapositive: "If Lewis did not receive an A, then he got at least one of the multiple choice questions wrong (did not get all of them right)" must also be true leaving B as the correct answer. B is also equivalent to the contrapositive of the original statement, which implies that it must be true, so the answer is <math>\boxed{\textbf{(B)}\text{ If Lewis did not receive an A, then he got at least one of the multiple choice questions wrong.}}</math>. | ||
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| + | * Note that Answer choice (B) is the contrapositive of the given statement. We know that contrapositive is always true if the given statement is true. | ||
==See Also== | ==See Also== | ||
{{AMC10 box|year=2017|ab=A|num-b=5|num-a=7}} | {{AMC10 box|year=2017|ab=A|num-b=5|num-a=7}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 12:25, 9 February 2018
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?
Solution
Rewriting the given statement: "if someone got all the multiple choice questions right on the upcoming exam then he or she would receive an A on the exam."
If that someone is Lewis the statement becomes: "if Lewis got all the multiple choice questions right, then he got an A on the exam."
The contrapositive: "If Lewis did not receive an A, then he got at least one of the multiple choice questions wrong (did not get all of them right)" must also be true leaving B as the correct answer. B is also equivalent to the contrapositive of the original statement, which implies that it must be true, so the answer is 
.
- Note that Answer choice (B) is the contrapositive of the given statement. We know that contrapositive is always true if the given statement is true.
See Also
| 2017 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 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 10 Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
