Difference between revisions of "2021 AMC 12A Problems/Problem 4"
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<math>\text{(3) Cannot subtract}\Rightarrow\text{cannot add}</math> | <math>\text{(3) Cannot subtract}\Rightarrow\text{cannot add}</math> | ||
| − | Combining the last two statements, we have < | + | Combining the last two statements, we have |
| + | |||
| + | <math>\text{(1) Happy}\Rightarrow\text{can add}</math> | ||
| + | |||
| + | <math>\text{(*) Purple}\Rightarrow\text{cannot subtract}\Rightarrow\text{cannot add}</math> | ||
| + | |||
| + | Clearly, the answer is <math>\boxed{\textbf{(D)}}.</math> | ||
~MRENTHUSIASM | ~MRENTHUSIASM | ||
Revision as of 05:01, 12 February 2021
Contents
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.
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
Solution 2 (Arrows)
We are given that
Combining the last two statements, we have
Clearly, the answer is 
~MRENTHUSIASM
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)
Video Solution by Hawk Math
https://www.youtube.com/watch?v=P5al76DxyHY
Video Solution (Using logic to eliminate choices)
~ pi_is_3.14
See also
| 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 | ||
| 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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
