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

Revision as of 16:07, 2 July 2021

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?

$(A)$ red $(B)$ white $(C)$ green $(D)$ brown $(E)$ 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 $\boxed{\textbf{(A)}\ R}$ .

Solution 2

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

It is A, just draw it out! ~phoenixfire

Solution 3

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

Video Solution

Solution detailing how to solve the problem: https://www.youtube.com/watch?v=VXBqE-jh2WA&list=PLbhMrFqoXXwmwbk2CWeYOYPRbGtmdPUhL&index=13

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 3: / Line 3: @@
 [[File:2019AMC8Prob12.png]]
+<math>(A)</math> red <math>(B)</math> white <math>(C)</math> green <math>(D)</math> brown <math>(E)</math> purple
 ==Solution 1==

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