Difference between revisions of "2024 AMC 8 Problems/Problem 4"
(→Solution 1) |
(→Solution 1) |
||
| (31 intermediate revisions by 8 users not shown) | |||
| Line 3: | Line 3: | ||
<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 | + | ==Solution 1== |
| − | |||
| − | |||
| − | + | 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. | |
| − | |||
| − | |||
| − | - | + | 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. |
| − | + | Therefore, the missing number is <math>\boxed{\textbf{(E) } \text{9}}</math>. | |
| − | |||
| − | + | ==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 | ||
| Line 58: | Line 34: | ||
== Video Solution by CosineMethod [🔥Fast and Easy🔥]== | == Video Solution by CosineMethod [🔥Fast and Easy🔥]== | ||
| − | + | noooooooooooooooooooooooooooooooooooooo!!!!!!!!!!!!!!!!!! | |
| + | |||
==Video Solution by Intersigation== | ==Video Solution by Intersigation== | ||
https://youtu.be/ktzijuZtDas&t=232 | https://youtu.be/ktzijuZtDas&t=232 | ||
Latest revision as of 22:46, 4 March 2024
Contents
- 1 Problem
- 2 Solution 1
- 3 Video Solution 1 (Simple and Fast) by Parshwa
- 4 Video Solution 2 (easy to digest) by Power Solve
- 5 Video Solution by Math-X (First fully understand the problem!!!)
- 6 Video Solution by NiuniuMaths (Easy to understand!)
- 7 Video Solution 2 by SpreadTheMathLove
- 8 Video Solution by CosineMethod [🔥Fast and Easy🔥]
- 9 Video Solution by Intersigation
- 10 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 1
The sum of the digits from 
are 
. Note that one of the answer choices (that is equal to Yunju's digits) subtracted from her sum of 
must equal a square.
Note that 
is a very close square to the sum of 45. Checking, we see that 
works.
Therefore, the missing number is 
.
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🔥]
noooooooooooooooooooooooooooooooooooooo!!!!!!!!!!!!!!!!!!
Video Solution by Intersigation
https://youtu.be/ktzijuZtDas&t=232
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. 
