Difference between revisions of "2021 AMC 12A Problems/Problem 4"
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<math>\textbf{(A) }</math> Purple snakes can add. | <math>\textbf{(A) }</math> Purple snakes can add. | ||
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<math>\textbf{(B) }</math> Purple snakes are happy. | <math>\textbf{(B) }</math> Purple snakes are happy. | ||
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<math>\textbf{(C) }</math> Snakes that can add are purple. | <math>\textbf{(C) }</math> Snakes that can add are purple. | ||
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<math>\textbf{(D) }</math> Happy snakes are not purple. | <math>\textbf{(D) }</math> Happy snakes are not purple. | ||
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<math>\textbf{(E) }</math> Happy snakes can't subtract. | <math>\textbf{(E) }</math> Happy snakes can't subtract. | ||
Revision as of 15:21, 11 February 2021
Problem
Tom has a collection of 
snakes, 
of which are purple and 
of which are happy. He observes that all of his happy snakes can add, none of his purple snakes can subtract, and all of his snakes that can't subtract also can't add. Which of these conclusions can be drawn about Tom's snakes?
Purple snakes can add.
Purple snakes are happy.
Snakes that can add are purple.
Happy snakes are not purple.
Happy snakes can't subtract.
Video Solution by Punxsutawney Phil
https://youtube.com/watch?v=MUHja8TpKGw&t=259s (Note that there's a slight error in the video I corrected in the description)
Solution 1
We know that purple snakes cannot subtract, thus they cannot add either. Since happy snakes must be able to add, the purple snakes cannot be happy. Therefore, we know that the happy snakes are not purple and the answer is 
.
--abhinavg0627
See also
| 2021 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 3 |
Followed by Problem 5 |
| 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 | |
| 2021 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
