Difference between revisions of "2024 AMC 8 Problems/Problem 5"

Revision as of 10:49, 11 January 2025

1 Problem
2 Solution 1
3 Solution 2
4 Video Solution 1 (Detailed Explanation) 🚀⚡📊
5 Video Solution by Central Valley Math Circle (Goes through full thought process)
6 Video Solution by Math-X (MATH-X)
7 Video Solution (A Clever Explanation You’ll Get Instantly)
8 Video Solution (easy to digest) by Power Solve
9 Video Solution by NiuniuMaths (Easy to understand!)
10 Video Solution 2 by SpreadTheMathLove
11 Video Solution by CosineMethod [🔥Fast and Easy🔥]
12 Video Solution by Interstigation
13 Video Solution by Daily Dose of Math (Understandable, Quick, and Speedy)
14 Video Solution by WhyMath
15 See Also

Problem

Aaliyah rolls two standard 6-sided dice. She notices that the product of the two numbers rolled is a multiple of $6$ . Which of the following integers cannot be the sum of the two numbers?

$\textbf{(A) } 5\qquad\textbf{(B) } 6\qquad\textbf{(C) } 7\qquad\textbf{(D) } 8\qquad\textbf{(E) } 9$

Solution 1

First, figure out all pairs of numbers whose product is 6. Then, using the process of elimination, we can find the following:

$\textbf{(A)}$ is possible: $2\times 3$

$\textbf{(C)}$ is possible: $1\times 6$

$\textbf{(D)}$ is possible: $2\times 6$

$\textbf{(E)}$ is possible: $3\times 6$

The only integer that cannot be the sum is $\boxed{\textbf{(B) } 6}$ .

Solution 2

First, see that in order for the two numbers to have a product of 6, it must either have 6 as a factor or have factors that have a product of 6 $2\times 3$ .

When we look at the answer choices, we see that answers $C, D, E$ all are more than 6, so they can all be added as a sum of 6. Answer $A$ works because $2+3=5$ , so 6 is the only answer choice that doesn't work. Thus, the answer is $\boxed{\textbf{(B) } 6}$ .

Video Solution 1 (Detailed Explanation) 🚀⚡📊

Youtube Link ⬇️

https://youtu.be/SreOL9LLmiI

~ ChillGuyDoesMath :)

Video Solution by Central Valley Math Circle (Goes through full thought process)

https://youtu.be/SjMK0jrVgj0

~mr_mathman

Video Solution by Math-X (MATH-X)

https://youtu.be/BaE00H2SHQM?si=W8N4vwOx84KauOA6&t=1108

~Math-X

Video Solution (A Clever Explanation You’ll Get Instantly)

https://youtu.be/5ZIFnqymdDQ?si=eqTGEN2doXnn-oZE&t=443

~hsnacademy

Video Solution (easy to digest) by Power Solve

https://youtu.be/HE7JjZQ6xCk?si=2M33-oRy1ExY3_6l&t=239

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

Video Solution by Daily Dose of Math (Understandable, Quick, and Speedy)

https://youtu.be/bSPWqeNO11M?si=HIzlxPjMfvGM5lxR

~Thesmartgreekmathdude

Video Solution by WhyMath

https://youtu.be/QD016SsgJBQ

@@ Line 17: / Line 17: @@
 The only integer that cannot be the sum is <math>\boxed{\textbf{(B) } 6}</math>.
+==Solution 2==
+First, see that in order for the two numbers to have a product of 6, it must either have 6 as a factor or have factors that have a product of 6 <math>2\times 3</math>.
+When we look at the answer choices, we see that answers <math>C, D, E</math> all are more than 6, so they can all be added as a sum of 6. Answer <math>A</math> works because <math>2+3=5</math>, so 6 is the only answer choice that doesn't work. Thus, the answer is <math>\boxed{\textbf{(B) } 6}</math>.
 == Video Solution 1 (Detailed Explanation) 🚀⚡📊 ==

2024 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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