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2021 AMC 12A Problem 4

Problem 4 of 25Easier

Tom has a collection of 1313 snakes, 44 of which are purple and 55 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?

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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.

More practice

Concepts: logical deduction

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.