Difference between revisions of "2019 AMC 8 Problems/Problem 12"
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The faces of a cube are painted in six different colors: red <math>(R)</math>, white <math>(W)</math>, green <math>(G)</math>, brown <math>(B)</math>, aqua <math>(A)</math>, and purple <math>(P)</math>. Three views of the cube are shown below. What is the color of the face opposite the aqua face? | The faces of a cube are painted in six different colors: red <math>(R)</math>, white <math>(W)</math>, green <math>(G)</math>, brown <math>(B)</math>, aqua <math>(A)</math>, and purple <math>(P)</math>. Three views of the cube are shown below. What is the color of the face opposite the aqua face? | ||
| − | [[File:2019AMC8Prob12.png] | + | [[File:2019AMC8Prob12.png]] |
| + | |||
| + | <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== | ||
| − | <math>B</math> is on the top, and <math>R</math> is on the side, and <math>G</math> is on the right side. That means that (image <math>2</math>) <math>W</math> is on the left side. From the third image, you know that <math>P</math> must be on the bottom since <math>G</math> is sideways. That leaves us with the back, so the back must be <math>A</math>. The front is opposite of the back, so the answer is <math>\boxed{\textbf{(A)}\ R}</math>. | + | <math>B</math> is on the top, and <math>R</math> is on the side, and <math>G</math> is on the right side. That means that (image <math>2</math>) <math>W</math> is on the left side. From the third image, you know that <math>P</math> must be on the bottom since <math>G</math> is sideways. That leaves us with the back, so the back must be <math>A</math>. The front is opposite of the back, so the answer is <math>\boxed{\textbf{(A)}\ R}</math>. |
==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 3== | ||
| + | From pic 1 and 2, we know that the G's opposite is W. From pic 1 and 3, the B's opposite is P. So the <math>A</math>'s opposite is <math>\boxed{\textbf{(A)}\ R}</math>. | ||
| + | |||
| + | ==Video Solution by Math-X (Simple Visualization!!!)== | ||
| + | https://youtu.be/IgpayYB48C4?si=uPWa04P5Bi6wEZB-&t=3752 | ||
| + | |||
| + | ~Math-X | ||
| + | |||
| + | ==Solution Explained== | ||
| + | https://youtu.be/gOZOCFNXMhE ~ The Learning Royal | ||
==Solution 3== | ==Solution 3== | ||
Associated video - https://www.youtube.com/watch?v=K5vaX_EzjEM | Associated video - https://www.youtube.com/watch?v=K5vaX_EzjEM | ||
| − | Video Solution- https://youtu.be/ | + | == 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 | ||
| + | |||
| + | ==Video Solution (CREATIVE ANALYSIS!!!)== | ||
| + | https://youtu.be/kD4V_InGI_g | ||
| + | |||
| + | ~Education, the Study of Everything | ||
| + | |||
| + | ==Video Solution by The Power of Logic(Problem 1 to 25 Full Solution)== | ||
| + | https://youtu.be/Xm4ZGND9WoY | ||
| + | |||
| + | ~Hayabusa1 | ||
| − | == | + | ==See also== |
{{AMC8 box|year=2019|num-b=11|num-a=13}} | {{AMC8 box|year=2019|num-b=11|num-a=13}} | ||
| − | |||
Revision as of 02:08, 5 March 2024
Contents
Problem
The faces of a cube are painted in six different colors: red 
, white 
, green 
, brown 
, aqua 
, and purple 
. Three views of the cube are shown below. What is the color of the face opposite the aqua face?
Solution 1
is on the top, and 
is on the side, and 
is on the right side. That means that (image 
) 
is on the left side. From the third image, you know that 
must be on the bottom since is sideways. That leaves us with the back, so the back must be 
. The front is opposite of the back, so the answer is 
.
Solution 2
Looking closely, we can see that all faces are connected with except for . Thus, the answer is .
It is A, just draw it out! ~phoenixfire
Solution 3
From pic 1 and 2, we know that the G's opposite is W. From pic 1 and 3, the B's opposite is P. So the 's opposite is .
Video Solution by Math-X (Simple Visualization!!!)
https://youtu.be/IgpayYB48C4?si=uPWa04P5Bi6wEZB-&t=3752
~Math-X
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
~savannahsolver
Video Solution (CREATIVE ANALYSIS!!!)
~Education, the Study of Everything
Video Solution by The Power of Logic(Problem 1 to 25 Full Solution)
~Hayabusa1
See also
| 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 | ||
