AMC 10 2021a Problem 7

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? $\textbf{(A) }$ Purple snakes can add. $\textbf{(B) }$ Purple snakes are happy. $\textbf{(C) }$ Snakes that can add are purple. $\textbf{(D) }$ Happy snakes are not purple. $\textbf{(E) }$ Happy snakes can't subtract.