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

(→‎Video Solution by CosineMethod [🔥Fast and Easy🔥])
 
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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>
  
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==Solution 1==
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==Solution==
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You have to add the sum of the numbers 1 through 9, which is 45. After that, you can use the elimination method with subtraction to each number to determine that the answer is 9.
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-TheRealEinstein24
  
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The sum of the digits from <math>1-9</math> are <math>1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45</math>. Note that one of the answer choices (that is equal to Yunju's digits) subtracted from her sum of <math>45</math> must equal a square.
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==Video Solution by Math-X (First fully understand the problem!!!)==
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https://youtu.be/BaE00H2SHQM?si=tzbzeCdEfXqROciK&t=907
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~Math-X
  
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Note that <math>6^2 = 36</math> is a very close square to the sum of 45. Checking, we see that <math>45 - 9 = 36 = 6^2</math> works.
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==Video Solution (A Clever Explanation You’ll Get Instantly)==
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https://youtu.be/5ZIFnqymdDQ?si=bxVKQiul4AjzVUgC&t=331
  
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Therefore, the missing number is <math>\boxed{\textbf{(E) } \text{9}}</math>.
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~hsnacademy
  
 
==Video Solution 1 (Simple and Fast) by Parshwa==
 
==Video Solution 1 (Simple and Fast) by Parshwa==
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==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)==
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https://youtu.be/bSPWqeNO11M?si=HIzlxPjMfvGM5lxR
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~Thesmartgreekmathdude
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==Video Solution by WhyMath==
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https://youtu.be/PCvkqxz0f0I
  
 
==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 06:22, 15 November 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

You have to add the sum of the numbers 1 through 9, which is 45. After that, you can use the elimination method with subtraction to each number to determine that the answer is 9. -TheRealEinstein24

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

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

~Math-X

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

https://youtu.be/5ZIFnqymdDQ?si=bxVKQiul4AjzVUgC&t=331

~hsnacademy

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

Video Solution by WhyMath

https://youtu.be/PCvkqxz0f0I

See Also

2024 AMC 8 (Problems • Answer Key • Resources)
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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

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