2021 AMC 10A Problem 7

Problem 7 of 25EasierLogic

Tom has a collection of

13

snakes,

4

of which are purple and

5

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

Note that the third condition ensures that purple snakes can’t add. We also know that all happy snakes can add, which means that happy snakes can’t be purple as well. Thus, D is the correct answer.

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Tagged: logical deduction

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