Difference between revisions of "2024 AMC 8 Problems/Problem 4"

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<math>\textbf{(A) } 5\qquad\textbf{(B) } 6\qquad\textbf{(C) } 7\qquad\textbf{(D) } 8\qquad\textbf{(E) } 9</math>
 
<math>\textbf{(A) } 5\qquad\textbf{(B) } 6\qquad\textbf{(C) } 7\qquad\textbf{(D) } 8\qquad\textbf{(E) } 9</math>
==solution one very fast and efficient must see==
 
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⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀
 
⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀
 
⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀
 
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⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀
 
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀
 
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀
 
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋
 
  
==wapjgpoaewhgawehgoihewoighoiwhg[owrh[oigawh[oghw[aw==
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==Solution==
Roses are red
+
The sum of the integers from <math>1</math> to <math>9</math> is <math>45</math>. Since the nearest square number less than <math>45</math> is <math>36</math>, the answer is <math>45 - 36 = \boxed{9}.</math>
violets are blue
 
Grass is green
 
Chair
 
  
==Solution 3==
+
==Video Solution 1 (Simple and Fast) by Parshwa==
Recall from AMC12A 2022 Problem 16, that <math>1+2+\dots+8 = 6^2</math>. Hence removing <math>9</math> works and our answer is <math>\boxed{\textbf{(E) }9}</math>.
+
https://youtu.be/Qrf4GTDjjXs
  
-SahanWijetunga
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==Video Solution 2 (easy to digest) by Power Solve==
 
 
==Solution 4==
 
We can add all the numbers from 1 through 9 using Gauss's trick, and find that the answer is 45. Since we know that all the square numbers below 45 are 36, 25, 16, 9, 4, 1, and 0, and 36 is the only square number that is within 10 numbers from 45, we can conclude that the answer is 45-36, hence the answer is <math>\boxed{\textbf{(E) }9}</math>.
 
 
 
~PK-10
 
 
 
==Video Solution 1 (easy to digest) by Power Solve==
 
 
https://youtu.be/HE7JjZQ6xCk?si=sTC7YNSmfEOMe4Sn&t=179
 
https://youtu.be/HE7JjZQ6xCk?si=sTC7YNSmfEOMe4Sn&t=179
  
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== Video Solution by CosineMethod [🔥Fast and Easy🔥]==
 
== Video Solution by CosineMethod [🔥Fast and Easy🔥]==
  
https://www.youtube.com/watch?v=9v5q5DxeriM
 
 
==Video Solution by Intersigation==
 
==Video Solution by Intersigation==
 
https://youtu.be/ktzijuZtDas&t=232
 
https://youtu.be/ktzijuZtDas&t=232
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 +
==Video Solution by Daily Dose of Math (Understandable, Logical, and Speedy)==
 +
 +
https://youtu.be/bSPWqeNO11M?si=HIzlxPjMfvGM5lxR
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 +
~Thesmartgreekmathdude
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2024|num-b=3|num-a=5}}
 
{{AMC8 box|year=2024|num-b=3|num-a=5}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 18:30, 26 July 2024

Problem

When Yunji added all the integers from $1$ to $9$, she mistakenly left out a number. Her incorrect sum turned out to be a square number. What number did Yunji leave out?

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

Solution

The sum of the integers from $1$ to $9$ is $45$. Since the nearest square number less than $45$ is $36$, the answer is $45 - 36 = \boxed{9}.$

Video Solution 1 (Simple and Fast) by Parshwa

https://youtu.be/Qrf4GTDjjXs

Video Solution 2 (easy to digest) by Power Solve

https://youtu.be/HE7JjZQ6xCk?si=sTC7YNSmfEOMe4Sn&t=179

Video Solution by Math-X (First fully understand the problem!!!)

https://youtu.be/BaE00H2SHQM?si=9ZUxEGmGam7il9xr&t=907

~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🔥]

Video Solution by Intersigation

https://youtu.be/ktzijuZtDas&t=232

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

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

~Thesmartgreekmathdude

See Also

2024 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
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

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