2021 AMC 12A Spring Problem 4
Below is the professionally curated solution for Problem 4 of the 2021 AMC 12A Spring, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2021 AMC 12A Spring solutions, or check the answer key.
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Difficulty rating: 1200
4.
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:
A purple snake cannot subtract, and any snake that cannot subtract also cannot add. So every purple snake cannot add.
Every happy snake can add. Since purple snakes cannot add, no happy snake can be purple; that is, happy snakes are not purple.
Thus, the correct answer is D.
Problem 4 in Other Years
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