2021 AMC10A Problem 1

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Professor-Mom

2109 posts

Professor-Mom

#1 h Feb 5, 2021, 5:38 PM • 6 Y

Y by samrocksnature, icematrix2, HWenslawski, jhu08, megarnie, Asmaa

What is the value of $(2^2-2) - (3^2-3) + (4^2-4)?$
$\textbf{(A) } 1 \qquad \textbf{(B) } 2 \qquad \textbf{(C) } 5 \qquad \textbf{(D) } 8 \qquad \textbf{(E) } 12$

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Dr.Mathematics

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Dr.Mathematics

#2 h Feb 5, 2021, 5:38 PM • 5 Y

Y by samrocksnature, icematrix2, megarnie, HWenslawski, jhu08

Professor-Mom wrote:

What is the value of $(2^2-2) - (3^2-3) + (4^2-4)?$
$\textbf{(A) } 1 \qquad \textbf{(B) } 2 \qquad \textbf{(C) } 5 \qquad \textbf{(D) } 8 \qquad \textbf{(E) } 12$

Answer is 8.
Since it would be 2 - 6 + 12 = 8 !

This post has been edited 2 times. Last edited by Dr.Mathematics, Feb 5, 2021, 5:39 PM

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math9990

450 posts

math9990

#3 h Feb 5, 2021, 5:39 PM • 2 Y

Y by samrocksnature, icematrix2

Dr.Mathematics wrote:

Professor-Mom wrote:

What is the value of $(2^2-2) - (3^2-3) + (4^2-4)?$
$\textbf{(A) } 1 \qquad \textbf{(B) } 2 \qquad \textbf{(C) } 5 \qquad \textbf{(D) } 8 \qquad \textbf{(E) } 12$

Answer is , 8!

Be careful with using exclamation marks after a number, it's fine here though cause it's obvious this time

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jasperE3

11107 posts

jasperE3

#4 h Feb 5, 2021, 5:41 PM • 3 Y

Y by samrocksnature, icematrix2, Mango247

$(2^2-2)-(3^2-3)+(4^2-4)=(4-2)-(9-3)+(16-4)=2-6+12=-4+12=\boxed{\mathbf{(D)}~8}$

This post has been edited 1 time. Last edited by jasperE3, Feb 5, 2021, 5:43 PM

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WorldPeace

176 posts

WorldPeace

#5 h Feb 5, 2021, 5:42 PM • 3 Y

Y by samrocksnature, icematrix2, megarnie

Yay, I got 8 lol

1 down 24 to go

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aaja3427

1918 posts

aaja3427

#6 h Feb 5, 2021, 5:45 PM • 5 Y

Y by samrocksnature, icematrix2, poplintos, megarnie, michaelwenquan

I sillied this somehow and got B while also legitimately solving #25
How sad...

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MinnesotaMath

3172 posts

MinnesotaMath

#7 h Feb 5, 2021, 7:03 PM • 3 Y

Y by samrocksnature, icematrix2, megarnie

aaja3427 wrote:

I sillied this somehow and got B while also legitimately solving #25
How sad...

omg I'm sorry

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Mathematician1010

3261 posts

Mathematician1010

#8 h Feb 5, 2021, 7:33 PM • 4 Y

Y by aidan0626, samrocksnature, icematrix2, megarnie

WorldPeace wrote:

Yay, I got 8 lol

1 down 24 to go

Yo same. Now I know my score is at least above 6 points

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centslordm

4736 posts

centslordm

#9 h Feb 5, 2021, 7:34 PM • 7 Y

Y by nikitadas, Natsuki, samrocksnature, icematrix2, megarnie, Mango247, Mango247

2 - 6 + 12 = 8

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franzliszt

23531 posts

franzliszt

#10 h Feb 5, 2021, 7:45 PM • 4 Y

Y by samrocksnature, icematrix2, megarnie, Mango247

Well here's the classic opening arithmetic. Just make sure to distribute for the 3s. You get $4-2-9+3+16-4=8$ so pick $D$ .

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lakecomo224

3837 posts

lakecomo224

#11 h Feb 5, 2021, 7:54 PM • 4 Y

Y by centslordm, samrocksnature, icematrix2, megarnie

Solution

This post has been edited 2 times. Last edited by lakecomo224, Feb 5, 2021, 7:55 PM

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jasperE3

11107 posts

jasperE3

#12 h Feb 5, 2021, 7:58 PM • 4 Y

Y by samrocksnature, icematrix2, megarnie, Pengu14

$a^2-a-((a+1)^2-a-1)+((a+2)^2-a-2)$
$=a^2-a-(a^2+2a+1-a-1)+(a^2+4a+4-a-2)$
$=a^2-a-(a^2+a)+(a^2+3a+2)$
$=-2a+a^2+3a=2=a^2+a+2$
$a=2$
$2^2+2+2=8$ .
The general form is kinda decent.

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lakecomo224

3837 posts

lakecomo224

#13 h Feb 5, 2021, 7:59 PM • 3 Y

Y by samrocksnature, icematrix2, Pengu14

that's too rigorous, I don't like working with polynomials

you can use difference of squares, my solution is up there

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Arr0w

2908 posts

Arr0w

#14 h Feb 5, 2021, 8:00 PM • 2 Y

Y by samrocksnature, icematrix2

Evaluate within the parenthesis and add the results. The answer is 8, or option D.

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lakecomo224

3837 posts

lakecomo224

#15 h Feb 5, 2021, 8:02 PM • 3 Y

Y by centslordm, samrocksnature, icematrix2

I disagree, my solution is much cleaner.

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pog

4917 posts

pog

#43 h Nov 24, 2021, 5:52 PM

Y by

mahaler wrote:

We need @pog to write an overly complicated solution for this.

i already wrote one

This post has been edited 2 times. Last edited by pog, Nov 24, 2021, 5:52 PM

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mahaler

3084 posts

mahaler

#44 h Nov 24, 2021, 5:53 PM

Y by

pog wrote:

mahaler wrote:

We need @pog to write an overly complicated solution for this.

i already wrote one

Oh I thought I saw it somewhere...Thanks!

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TheSocialPi

5 posts

TheSocialPi

#45 h Dec 8, 2021, 12:10 PM

Y by

Well yeah its 8.

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NTistrulove

183 posts

NTistrulove

#46 h Dec 9, 2021, 2:19 PM

Y by

math9990 wrote:

Dr.Mathematics wrote:

Professor-Mom wrote:

What is the value of $(2^2-2) - (3^2-3) + (4^2-4)?$
$\textbf{(A) } 1 \qquad \textbf{(B) } 2 \qquad \textbf{(C) } 5 \qquad \textbf{(D) } 8 \qquad \textbf{(E) } 12$

Answer is , 8!

Be careful with using exclamation marks after a number, it's fine here though cause it's obvious this time

Get excited, but carefully!!!

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