2021 AMC 12A Problems/Problem 1

Problem

What is the value of\[2^{1+2+3}-(2^1+2^2+2^3)?\]$\textbf{(A) }0 \qquad \textbf{(B) }50 \qquad \textbf{(C) }52 \qquad \textbf{(D) }54 \qquad \textbf{(E) }57$

Solution

We evaluate the given expression to get that \[2^{1+2+3}-(2^1+2^2+2^3)=2^6-(2^1+2^2+2^3)=64-2-4-8=50 \implies \boxed{\text{(B)}}\]

Video Solution by Aaron He

https://www.youtube.com/watch?v=xTGDKBthWsw&t=8

Video Solution by Punxsutawney Phil

https://www.youtube.com/watch?v=MUHja8TpKGw

Video Solution by Hawk Math

https://www.youtube.com/watch?v=P5al76DxyHY

Video Solution by OmegaLearn (Using computation)

https://youtu.be/90OIMAWAwNg

~ pi_is_3.14

Video Solution by TheBeautyofMath

https://youtu.be/rEWS75W0Q54

~IceMatrix

See also

2021 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
First problem
Followed by
Problem 2
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All AMC 12 Problems and Solutions

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