2024 AMC 8 Problems/Problem 4
Contents
- 1 Problem
- 2 Solution 1
- 3 Solution 2
- 4 Solution 3
- 5 Video Solution by Math-X (First fully understand the problem!!!)
- 6 Video Solution 1 (easy to digest) by Power Solve
- 7 Video Solution by NiuniuMaths (Easy to understand!)
- 8 Video Solution 2 by SpreadTheMathLove
- 9 Video Solution by CosineMethod [🔥Fast and Easy🔥]
- 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 numbers from to
is
Denote the number left out when adding to be
. Thus,
is a perfect square. We also know that
must be between
and
inclusive. We can now start to find the closest perfect square to 45. We can immediately see that 36 is the closest, so we can just subtract both numbers to get our final answer of
.
~ Nivaar
Solution 2
Since we have all the answer choices, we can check and see which one works. Testing, we have that leaving out works, so the answer is
.
~andliu766
-rnatog337
Solution 3
Recall from AMC12A 2022 Problem 16, that . Hence removing
works and our answer is
.
-SahanWijetunga
Video Solution by Math-X (First fully understand the problem!!!)
https://youtu.be/BaE00H2SHQM?si=9ZUxEGmGam7il9xr&t=907
~Math-X
Video Solution 1 (easy to digest) by Power Solve
https://youtu.be/HE7JjZQ6xCk?si=sTC7YNSmfEOMe4Sn&t=179
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=9v5q5DxeriM
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.