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

m (Problem)
m (Solution 2)
 
(6 intermediate revisions by 5 users not shown)
Line 3: Line 3:
  
 
[[File:2019AMC8Prob12.png]]
 
[[File:2019AMC8Prob12.png]]
<math>(A)</math> red <math>(B)</math> white <math>(C)</math> green <math>(D)</math> brown <math>(E)</math> purple
+
 
 +
<math> \textbf{(A)}\ \text{red}\qquad\textbf{(B)}\ \text{white}\qquad\textbf{(C)}\ \text{green}\qquad\textbf{(D)}\ \text{brown}\qquad\textbf{(E)}\ \text{purple} </math>
  
 
==Solution 1==
 
==Solution 1==
Line 9: Line 10:
  
 
==Solution 2==
 
==Solution 2==
Looking closely we can see that all faces are connected with <math>R</math> except for <math>A</math>. Thus the answer is <math>\boxed{\textbf{(A)}\ R}</math>.
+
Looking closely, we can see that all faces are connected with <math>R</math> except for <math>A</math>. Thus, the answer is <math>\boxed{\textbf{(A)}\ R}</math>.
  
 
It is A, just draw it out!
 
It is A, just draw it out!
 
~phoenixfire
 
~phoenixfire
 +
 +
==Solution Explained==
 +
https://youtu.be/gOZOCFNXMhE ~ The Learning Royal
  
 
==Solution 3==
 
==Solution 3==
Line 20: Line 24:
  
 
Solution detailing how to solve the problem: https://www.youtube.com/watch?v=VXBqE-jh2WA&list=PLbhMrFqoXXwmwbk2CWeYOYPRbGtmdPUhL&index=13
 
Solution detailing how to solve the problem: https://www.youtube.com/watch?v=VXBqE-jh2WA&list=PLbhMrFqoXXwmwbk2CWeYOYPRbGtmdPUhL&index=13
 +
 +
==Video Solution==
 +
https://youtu.be/dru7MQO6jqs
 +
 +
~savannahsolver
  
 
==See also==
 
==See also==
 
{{AMC8 box|year=2019|num-b=11|num-a=13}}
 
{{AMC8 box|year=2019|num-b=11|num-a=13}}
Only two of the cubes are required to solve the problem.
 

Latest revision as of 01:12, 4 December 2022

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?

2019AMC8Prob12.png

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

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

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 Explained

https://youtu.be/gOZOCFNXMhE ~ The Learning Royal

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

Video Solution

https://youtu.be/dru7MQO6jqs

~savannahsolver

See also

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
Invalid username
Login to AoPS