# 2021 AMC 12A Problems/Problem 4

## Problem

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.

## Video Solution by Punxsutawney Phil

https://youtube.com/watch?v=MUHja8TpKGw&t=259s (Note that there's a slight error in the video I corrected in the description)

## Solution 1

We know that purple snakes cannot subtract, thus they cannot add either. Since happy snakes must be able to add, the purple snakes cannot be happy. Therefore, we know that the happy snakes are not purple and the answer is $\boxed{\textbf{(D)}}$.

--abhinavg0627