2021 AMC 12A Problem 4
Problem 4 of 25EasierLogic
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?
Answer choices
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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.
Tagged: logical deduction