2023 AMC 8 Problems/Problem 1

Problem

What is the value of $(8 \times 4 + 2) - (8 + 4 \times 2)$?

$\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 6 \qquad \textbf{(C)}\ 10 \qquad \textbf{(D)}\ 18 \qquad \textbf{(E)}\ 24$

Solution 1

By the order of operations, we have \[(8 \times 4 + 2) - (8 + 4 \times 2) = (32+2) - (8+8) = 34 - 16 = \boxed{\textbf{(D)}\ 18}.\] ~apex304, TaeKim, peelybonehead, MRENTHUSIASM

Solution 2

We can simplify the expression above in another way: \[(8 \times 4 + 2) - (8 + 4 \times 2)=8\times4+2-8-4\times2=32+2-8-8=34-16=\boxed{\textbf{(D)}\ 18}.\]

~MathFun1000

Video Solution (How to Creatively Think!!!)

https://youtu.be/n2tl50HMkDw

~Education the Study of everything

Video Solution by Magic Square

https://youtu.be/-N46BeEKaCQ?t=5746

Video Solution by SpreadTheMathLove

https://www.youtube.com/watch?v=EcrktBc8zrM

Video Solution by Interstigation

https://youtu.be/DBqko2xATxs&t=41

Video Solution by WhyMath

https://youtu.be/macEkeMMM_w

~savannahsolver

Video Solution by harungurcan

https://www.youtube.com/watch?v=35BW7bsm_Cg&t=10s

~harungurcan

Video Solution by Math-X (Smart and Simple)

https://youtu.be/Ku_c1YHnLt0?si=RarnomIDE4gELDM3&t=62 ~Math-X

Video Explanation by MathTalks_Now

https://studio.youtube.com/video/PMOeiGLkDH0/edit

See Also

2023 AMC 8 (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 AJHSME/AMC 8 Problems and Solutions

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