2019 AMC 8 Problems/Problem 12

Revision as of 15:57, 19 August 2020 by Sum-of-sums (talk | contribs) (Solution 3)


The faces of a cube are painted in six different colors: red $(R)$, white $(W)$, green $(G)$, brown $(B)$, aqua $(A)$, and purple $(P)$. Three views of the cube are shown below. What is the color of the face opposite the aqua face?


$\textbf{(A) }\text{red}\qquad\textbf{(B) }\text{white}\qquad\textbf{(C) }\text{green}\qquad\textbf{(D) }\text{brown}\qquad\textbf{(E) }\text{purple}$

Solution 1

$B$ is on the top, and $R$ is on the side, and $G$ is on the right side. That means that (image $2$) $W$ is on the left side. From the third image, you know that $P$ must be on the bottom since $G$ is sideways. That leaves us with the back, so the back must be $A$. The front is opposite of the back, so the answer is $\boxed{\textbf{(A)}\ R}$.~heeeeeeeheeeee

Solution 2

Looking closely we can see that all faces are connected with $R$ except for $A$. Thus the answer is $\boxed{\textbf{(A)}\ R}$.


Solution 3

Associated video - https://www.youtube.com/watch?v=K5vaX_EzjEM

Video Solution- https://youtu.be/Lw8fSbX_8FU ( Also explains problems 11-20)


2019 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 11
Followed by
Problem 13
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

Only two of the cubes are required to solve the problem.

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