Difference between revisions of "2024 AMC 8 Problems/Problem 5"
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==Problem== | ==Problem== | ||
| + | Aaliyah rolls two standard 6-sided dice. She notices that the product of the two numbers rolled is a multiple of <math>6</math>. Which of the following integers cannot be the sum of the two numbers? | ||
| + | |||
| + | <math>\textbf{(A) } 5\qquad\textbf{(B) } 6\qquad\textbf{(C) } 7\qquad\textbf{(D) } 8\qquad\textbf{(E) } 9</math> | ||
==Solution 1== | ==Solution 1== | ||
| + | |||
| + | First, figure out all pairs of numbers whose product is 6. Then, using the process of elimination, we can find the following: | ||
| + | |||
| + | <math>\textbf{(A)}</math> is possible: <math>2\times 3</math> | ||
| + | |||
| + | <math>\textbf{(C)}</math> is possible: <math>1\times 6</math> | ||
| + | |||
| + | <math>\textbf{(D)}</math> is possible: <math>2\times 6</math> | ||
| + | |||
| + | <math>\textbf{(E)}</math> is possible: <math>3\times 6</math> | ||
| + | |||
| + | The only integer that cannot be the sum is <math>\boxed{\textbf{(B)\ 6}}.</math> | ||
| + | |||
| + | -ILoveMath31415926535 & countmath1 & Nivaar | ||
| + | |||
| + | ==Video Solution 1 (easy to digest) by Power Solve== | ||
| + | https://youtu.be/HE7JjZQ6xCk?si=2M33-oRy1ExY3_6l&t=239 | ||
| + | |||
| + | ==Video Solution by Math-X (First fully understand the problem!!!)== | ||
| + | https://youtu.be/BaE00H2SHQM?si=W8N4vwOx84KauOA6&t=1108 | ||
| + | |||
| + | ~Math-X | ||
| + | |||
| + | ==Video Solution by NiuniuMaths (Easy to understand!)== | ||
| + | https://www.youtube.com/watch?v=Ylw-kJkSpq8 | ||
| + | |||
| + | ~NiuniuMaths | ||
| + | |||
| + | ==Video Solution 2 by SpreadTheMathLove== | ||
| + | https://www.youtube.com/watch?v=L83DxusGkSY | ||
| + | |||
| + | == Video Solution by CosineMethod [🔥Fast and Easy🔥]== | ||
| + | |||
| + | https://www.youtube.com/watch?v=51pqs80PUnY | ||
| + | ==Video Solution by Interstigation== | ||
| + | https://youtu.be/ktzijuZtDas&t=296 | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC8 box|year=2024|num-b=4|num-a=6}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 09:35, 8 February 2024
Contents
- 1 Problem
- 2 Solution 1
- 3 Video Solution 1 (easy to digest) by Power Solve
- 4 Video Solution by Math-X (First fully understand the problem!!!)
- 5 Video Solution by NiuniuMaths (Easy to understand!)
- 6 Video Solution 2 by SpreadTheMathLove
- 7 Video Solution by CosineMethod [🔥Fast and Easy🔥]
- 8 Video Solution by Interstigation
- 9 See Also
Problem
Aaliyah rolls two standard 6-sided dice. She notices that the product of the two numbers rolled is a multiple of 
. Which of the following integers cannot be the sum of the two numbers?
Solution 1
First, figure out all pairs of numbers whose product is 6. Then, using the process of elimination, we can find the following:
is possible: 
is possible: 
is possible: 
is possible: 
The only integer that cannot be the sum is 
-ILoveMath31415926535 & countmath1 & Nivaar
Video Solution 1 (easy to digest) by Power Solve
https://youtu.be/HE7JjZQ6xCk?si=2M33-oRy1ExY3_6l&t=239
Video Solution by Math-X (First fully understand the problem!!!)
https://youtu.be/BaE00H2SHQM?si=W8N4vwOx84KauOA6&t=1108
~Math-X
Video Solution by NiuniuMaths (Easy to understand!)
https://www.youtube.com/watch?v=Ylw-kJkSpq8
~NiuniuMaths
Video Solution 2 by SpreadTheMathLove
https://www.youtube.com/watch?v=L83DxusGkSY
Video Solution by CosineMethod [🔥Fast and Easy🔥]
https://www.youtube.com/watch?v=51pqs80PUnY
Video Solution by Interstigation
https://youtu.be/ktzijuZtDas&t=296
See Also
| 2024 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
