Difference between revisions of "2021 AMC 10A Problems/Problem 1"

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~MRENTHUSIASM
 
~MRENTHUSIASM
  
==Video Solution (Lightening Fast)==
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==Video Solution 1 (Lightening Fast)==
 
https://youtu.be/cAMg15KhK6E
 
https://youtu.be/cAMg15KhK6E
  
 
~ Education, the Study of everything
 
~ Education, the Study of everything
  
 
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==Video Solution 2==
 
 
==Video Solution ==
 
 
https://youtu.be/cAMg15KhK6E
 
https://youtu.be/cAMg15KhK6E
  
==Video Solution #0(Very Very Quick Computation) ==
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==Video Solution 3 (Very Very Quick Computation) ==
 
https://www.youtube.com/watch?v=m0_UMI2mnZs&list=PLexHyfQ8DMuKqltG3cHT7Di4jhVl6L4YJ&index=2
 
https://www.youtube.com/watch?v=m0_UMI2mnZs&list=PLexHyfQ8DMuKqltG3cHT7Di4jhVl6L4YJ&index=2
 
~North America Mathematic Contest Go Go Go
 
~North America Mathematic Contest Go Go Go
  
==Video Solution #1(Quick Computation) ==
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==Video Solution 4 (Quick Computation) ==
 
https://youtu.be/C3n2hgBhyXc?t=37
 
https://youtu.be/C3n2hgBhyXc?t=37
 
~ThePuzzlr
 
~ThePuzzlr
  
== Video Solution (Arithmetic Computation) ==
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== Video Solution 5 (Arithmetic Computation) ==
 
https://youtu.be/0VvM_f-IDvE
 
https://youtu.be/0VvM_f-IDvE
  
 
~ pi_is_3.14
 
~ pi_is_3.14
  
==Video Solution 5==
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==Video Solution 6==
 
https://youtu.be/4dkzuRHJieQ
 
https://youtu.be/4dkzuRHJieQ
  
 
~savannahsolver
 
~savannahsolver
  
==Video Solution 6==
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==Video Solution 7==
 
https://youtu.be/50CThrk3RcM
 
https://youtu.be/50CThrk3RcM
  
 
~IceMatrix
 
~IceMatrix
  
==Video Solution (Problems 1-3)==
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==Video Solution 8 (Problems 1-3)==
 
https://youtu.be/CupJpUzKPB0
 
https://youtu.be/CupJpUzKPB0
  
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== See Also ==
 
== See Also ==
 
 
{{AMC10 box|year=2021|ab=A|before=First Problem|num-a=2}}
 
{{AMC10 box|year=2021|ab=A|before=First Problem|num-a=2}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 19:00, 26 May 2021

Problem

What is the value of \[(2^2-2)-(3^2-3)+(4^2-4)\]

$\textbf{(A) } 1 \qquad\textbf{(B) } 2 \qquad\textbf{(C) } 5 \qquad\textbf{(D) } 8 \qquad\textbf{(E) } 12$

Solution 1

$(4-2)-(9-3)+(16-4)=2-6+12=8.$ This corresponds to $\boxed{\textbf{(D) } 8}$

-happykeeper

Solution 2

We have \begin{align*} (2^2-2)-(3^2-3)+(4^2-4) &= 2(2-1)-3(3-1)+4(4-1) \\ &= 2(1)-3(2)+4(3) \\ &= 2-6+12 \\ &= \boxed{\textbf{(D) } 8}. \end{align*} ~MRENTHUSIASM

Video Solution 1 (Lightening Fast)

https://youtu.be/cAMg15KhK6E

~ Education, the Study of everything

Video Solution 2

https://youtu.be/cAMg15KhK6E

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)

https://youtu.be/0VvM_f-IDvE

~ pi_is_3.14

Video Solution 6

https://youtu.be/4dkzuRHJieQ

~savannahsolver

Video Solution 7

https://youtu.be/50CThrk3RcM

~IceMatrix

Video Solution 8 (Problems 1-3)

https://youtu.be/CupJpUzKPB0

~MathWithPi

See Also

2021 AMC 10A (ProblemsAnswer KeyResources)
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

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