2021 AMC 12A Problems/Problem 4
- The following problem is from both the 2021 AMC 10A #7 and 2021 AMC 12A #4, so both problems redirect to this page.
Contents
- 1 Problem
- 2 Solution 1
- 3 Solution 2 (Explains Solution 1 Using Arrows)
- 4 Solution 3
- 5 Video Solution (Simple & Quick)
- 6 Video Solution by Aaron He (Sets)
- 7 Video Solution by Punxsutawney Phil
- 8 Video Solution by Hawk Math
- 9 Video Solution (Using logic to eliminate choices)
- 10 Video Solution 6
- 11 Video Solution by TheBeautyofMath
- 12 See also
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 (Explains Solution 1 Using Arrows)
We are given that
Combining and
into
below, we have
Clearly, the answer is
~MRENTHUSIASM
Solution 3
We can also see this through the process of elimination.
Statement is false because purple snakes cannot add.
is false as well because since happy snakes can add and purple snakes can not add, purple snakes are not happy snakes.
is false using the same reasoning, purple snakes are not happy snakes so happy snakes can subtract since purple snakes cannot subtract.
is false since snakes that can add are happy, not purple. That leaves statement D.
is the only correct statement.
~Bakedpotato66
Video Solution (Simple & Quick)
~ Education the Study of Everything
Video Solution by Aaron He (Sets)
https://www.youtube.com/watch?v=xTGDKBthWsw&t=164
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
Video Solution 6
~savannahsolver
Video Solution by TheBeautyofMath
https://youtu.be/s6E4E06XhPU?t=202 (AMC10A)
https://youtu.be/rEWS75W0Q54?t=353 (AMC12A)
~IceMatrix
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.