Difference between revisions of "2024 AMC 8 Problems/Problem 4"
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When Yunji added all the integers from <math>1</math> to <math>9</math>, she mistakenly left out a number. Her incorrect sum turned out to be a square number. What number did Yunji leave out? | When Yunji added all the integers from <math>1</math> to <math>9</math>, she mistakenly left out a number. Her incorrect sum turned out to be a square number. What number did Yunji leave out? | ||
| − | <math> | + | <math>\textbf{(A) } 5\qquad\textbf{(B) } 6\qquad\textbf{(C) } 7\qquad\textbf{(D) } 8\qquad\textbf{(E) } 9</math> |
| − | == | + | ==Solution== |
| − | + | Adding numbers 1 through 9 gives us 45. This was her expected sum, but what she got was a perfect square. Since she got that perfect square sum by forgetting a number, that sum is less than 45. The square number right under 45 is 36. So 45 - 36 = 9. So the solution is E[9]. | |
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| − | + | ~That_One_Dude | |
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| − | + | ==Video Solution (Goes through the full thought process)== | |
| + | https://youtu.be/dMX5_MXVkYs | ||
| − | + | ~mr_mathman | |
| − | + | ==Video Solution by Math-X (First fully understand the problem!!!)== | |
| + | https://youtu.be/BaE00H2SHQM?si=tzbzeCdEfXqROciK&t=907 | ||
| + | |||
| + | ~Math-X | ||
| − | ==Solution | + | ==Video Solution (A Clever Explanation You’ll Get Instantly)== |
| − | + | https://youtu.be/5ZIFnqymdDQ?si=bxVKQiul4AjzVUgC&t=331 | |
| − | + | ~hsnacademy | |
| − | ==Solution | + | ==Video Solution 1 (Simple and Fast) by Parshwa== |
| − | + | https://youtu.be/Qrf4GTDjjXs | |
| − | ==Video Solution | + | ==Video Solution 2 (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🔥]== | ||
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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 | ||
| + | |||
| + | ~Thesmartgreekmathdude | ||
| + | |||
| + | ==Video Solution by WhyMath== | ||
| + | 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 17:25, 21 December 2024
Contents
- 1 Problem
- 2 Solution
- 3 Video Solution (Goes through the full thought process)
- 4 Video Solution by Math-X (First fully understand the problem!!!)
- 5 Video Solution (A Clever Explanation You’ll Get Instantly)
- 6 Video Solution 1 (Simple and Fast) by Parshwa
- 7 Video Solution 2 (easy to digest) by Power Solve
- 8 Video Solution by Math-X (First fully understand the problem!!!)
- 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 Intersigation
- 13 Video Solution by Daily Dose of Math (Understandable, Logical, and Speedy)
- 14 Video Solution by WhyMath
- 15 See Also
Problem
When Yunji added all the integers from 
to 
, she mistakenly left out a number. Her incorrect sum turned out to be a square number. What number did Yunji leave out?
Solution
Adding numbers 1 through 9 gives us 45. This was her expected sum, but what she got was a perfect square. Since she got that perfect square sum by forgetting a number, that sum is less than 45. The square number right under 45 is 36. So 45 - 36 = 9. So the solution is E[9].
~That_One_Dude
Video Solution (Goes through the full thought process)
~mr_mathman
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
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
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. 
