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

(Solution 3)
m (Video Solution (A Clever Explanation You’ll Get Instantly))
 
(36 intermediate revisions by 17 users not shown)
Line 2: Line 2:
 
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>Yunji is dumb</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].
  ./              o \          .-----.
 
/./\  )______  \__ \        ( help! )
 
./  / /\ \  | \ \  \ \      /`-----'
 
  / /  \ \  | |\ \  \7--- ooo ooo ooo ooo ooo ooo
 
  
==wapjgpoaewhgawehgoihewoighoiwhg[owrh[oigawh[oghw[aw==
+
~That_One_Dude
Roses are red
 
  
violets are blue
+
==Video Solution (Goes through the full thought process)==
 +
https://youtu.be/dMX5_MXVkYs
  
Grass is green
+
~mr_mathman
  
Chair
+
==Video Solution by Math-X (First fully understand the problem!!!)==
:skull:
+
https://youtu.be/BaE00H2SHQM?si=tzbzeCdEfXqROciK&t=907
  
==Solution 3==
+
~Math-X
🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿🗿
 
 
 
-iamcalifornia'sresidentidiot
 
bleeeeeeeeeeeeeeeeeeeeeeeeep!!!!!
 
 
 
==Solution 4==
 
using the theory of relativity, 1+5 is 4 so therefore Mark Zuckerburg is a lizard person and the earth is actually flat, which proves the pythagorean theorom
 
  
-by random_uwu_gamer_girl (roblox edater)
+
==Video Solution (A Clever Explanation You’ll Get Instantly)==
 +
https://youtu.be/5ZIFnqymdDQ?si=bxVKQiul4AjzVUgC&t=331
  
BAN ME I DARE YOU I ACTUALLY DARE
+
~hsnacademy
  
 
==Video Solution 1 (Simple and Fast) by Parshwa==
 
==Video Solution 1 (Simple and Fast) by Parshwa==
Line 56: Line 46:
 
== Video Solution by CosineMethod [🔥Fast and Easy🔥]==
 
== Video Solution by CosineMethod [🔥Fast and Easy🔥]==
  
https://www.youtube.com/watch?v=9v5q5DxeriM
 
 
==Video Solution by Intersigation==
 
==Video Solution by Intersigation==
 
https://youtu.be/ktzijuZtDas&t=232
 
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==
 
==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

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

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)

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

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 (ProblemsAnswer KeyResources)
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