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Revision as of 12:41, 5 February 2016
Problem
Each of the students in a certain summer camp can either sing, dance, or act. Some students have more than one talent, but no student has all three talents. There are
students who cannot sing,
students who cannot dance, and
students who cannot act. How many students have two of these talents?
Solution
Let be the number of students that can only sing,
can only dance, and
can only act.
Let be the number of students that can sing and dance,
can sing and act, and
can dance and act.
From the information given in the problem, and
.
Adding these equations together, we get .
Since there are a total of students,
.
Subtracting these equations, we get .
Our answer is
See Also
2016 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 10 |
Followed by Problem 12 |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.