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

Revision as of 20:49, 15 July 2024

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 Video Solution by Daily Dose of Math (Understandable, Quick, and Speedy)
11 See Also

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 1

The sum of the digits from $1-9$ are $1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45$ . Note that one of the answer choices (that is equal to Yunju's digits) subtracted from her sum of $45$ must equal a square.

Note that $6^2 = 36$ is a very close square to the sum of 45. Checking, we see that $45 - 9 = 36 = 6^2$ works.

Therefore, the missing number is $\boxed{\textbf{(E) } \text{9}}$ .

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, Quick, and Speedy)

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

~Thesmartgreekmathdude

@@ Line 36: / Line 36: @@
 ==Video Solution by Intersigation==
 https://youtu.be/ktzijuZtDas&t=232
+==Video Solution by Daily Dose of Math (Understandable, Quick, and Speedy)==
+https://youtu.be/bSPWqeNO11M?si=HIzlxPjMfvGM5lxR
+~Thesmartgreekmathdude
 ==See Also==
 {{AMC8 box|year=2024|num-b=3|num-a=5}}
 {{MAA Notice}}

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

Page

Toolbox

Search