2021 AMC 10A Problems/Problem 1: Difference between revisions
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~MRENTHUSIASM | ~MRENTHUSIASM | ||
==Solution 3 ( | ==Solution 3 (Overkill, Just for Fun)== | ||
< | We have | ||
<cmath>\begin{align*} | |||
(2^2-2)-(3^2-3)+(4^2-4) &= 2^2+4^2-3^2-2+3-4 \\ | |||
&=2^2+(4-3)(4+3)-3 \\ | |||
&=2^2+7-3=2^2+4 \\ | |||
&=4\cdot 2 \\ | |||
&=\boxed{\textbf{(D) } 8}.</cmath> | |||
-[[User:PureSwag|PureSwag]] | -[[User:PureSwag|PureSwag]] | ||
Revision as of 20:47, 8 August 2021
Problem
What is the value of ![\[(2^2-2)-(3^2-3)+(4^2-4)\]](http://latex.artofproblemsolving.com/f/b/f/fbf9a3889b146c23eb653b9dc16255c03a229dfe.png)
Solution 1
This corresponds to 
-happykeeper
Solution 2
We have
~MRENTHUSIASM
Solution 3 (Overkill, Just for Fun)
We have
\begin{align*}
(2^2-2)-(3^2-3)+(4^2-4) &= 2^2+4^2-3^2-2+3-4 \\
&=2^2+(4-3)(4+3)-3 \\
&=2^2+7-3=2^2+4 \\
&=4\cdot 2 \\
&=\boxed{\textbf{(D) } 8}. (Error compiling LaTeX. Unknown error_msg)
Video Solution 1 (Lightening Fast)
~ Education, the Study of everything
Video Solution 2
Video Solution 3 (Very Very Quick Computation)
https://www.youtube.com/watch?v=m0_UMI2mnZs&list=PLexHyfQ8DMuKqltG3cHT7Di4jhVl6L4YJ&index=2 ~North America Mathematic Contest Go Go Go
Video Solution 4 (Quick Computation)
https://youtu.be/C3n2hgBhyXc?t=37 ~ThePuzzlr
Video Solution 5 (Arithmetic Computation)
~ pi_is_3.14
Video Solution 6
~savannahsolver
Video Solution 7
~IceMatrix
Video Solution 8 (Problems 1-3)
~MathWithPi
Video Solution 9
~TheLearningRoyal
See Also
| 2021 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by First Problem |
Followed by Problem 2 | |
| 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 AMC 10 Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America. 
