# Difference between revisions of "2020 AMC 12A Problems/Problem 1"

## Problem

Carlos took $70\%$ of a whole pie. Maria took one third of the remainder. What portion of the whole pie was left? $\textbf{(A)}\ 10\%\qquad\textbf{(B)}\ 15\%\qquad\textbf{(C)}\ 20\%\qquad\textbf{(D)}\ 30\%\qquad\textbf{(E)}\ 35\%$

## Solution 1

If Carlos took $70\%$ of the pie, there must be $(100 - 70) = 30\%$ left. After Maria takes $\frac{1}{3}$ of the remaining $30\%,$ $1 - \frac{1}{3} = \frac{2}{3}$ of the remaining $30\%$ is left.

Therefore: $30\% \cdot \frac{2}{3} = \boxed{\textbf{C) }20\%}$

-Contributed by YOur dad, one dude

## Solution 2

Like solution 1, it is clear that there is $30\%$ of the pie remaining. Since Maria takes $\frac{1}{3}$ of the remainder, she takes $\frac{1}{3} \cdot 30\% = 10\%$ meaning that there is $30\% - 10\% = 20\%$ left $\implies \boxed{\textbf{C}}$.

~DBlack2021

## Solution 3 (One Sentence)

We have $$\left(100\%-70\%\right)\cdot\left(1-\frac13\right)=30\%\cdot\frac23=\boxed{\textbf{(C)}\ 20\%}$$ of the whole pie left.

~MRENTHUSIASM

~IceMatrix

## See Also

 2020 AMC 12A (Problems • Answer Key • Resources) Preceded byFirst Problem Followed byProblem 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 12 Problems and Solutions

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