Difference between revisions of "2019 AMC 8 Problems/Problem 12"

Revision as of 19:33, 17 July 2020

Problem

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 $\boxed{\textbf{(A)}\ R}$ .

~phoenixfire

Solution 4

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

Note

2019 AMC 8 (Problems • Answer Key • Resources)
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.

@@ Line 15: / Line 15: @@
 ~phoenixfire
+==Solution 4==
-Video solution: https://www.youtube.com/watch?v=K5vaX_EzjEM
+Associated video - https://www.youtube.com/watch?v=K5vaX_EzjEM
 ==Note==
 {{AMC8 box|year=2019|num-b=11|num-a=13}}
 Only two of the cubes are required to solve the problem.

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