Difference between revisions of "2020 AMC 12A Problems/Problem 1"
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<math>\textbf{(A)}\ 10\%\qquad\textbf{(B)}\ 15\%\qquad\textbf{(C)}\ 20\%\qquad\textbf{(D)}\ 30\%\qquad\textbf{(E)}\ 35\%</math> | <math>\textbf{(A)}\ 10\%\qquad\textbf{(B)}\ 15\%\qquad\textbf{(C)}\ 20\%\qquad\textbf{(D)}\ 30\%\qquad\textbf{(E)}\ 35\%</math> | ||
| − | ==Solution== | + | ==Solution 1== |
| + | If Carlos took <math>70\%</math> of the pie, there must be <math>(100 - 70)\% = 30\%</math> left. After Maria takes <math>\frac{1}{3}</math> of the remaining <math>30\%, \ 1 - \frac{1}{3} = \frac{2}{3}</math> of the remaining <math>30\%</math> is left. | ||
| + | |||
| + | Therefore, the answer is <math>30\% \cdot \frac{2}{3} = \boxed{\textbf{(C)}\ 20\%}.</math> | ||
| + | |||
| + | ~Awesome2.1 (Solution) | ||
| + | |||
| + | ~quacker88 (<math>\LaTeX</math> Adjustments) | ||
| + | |||
| + | ==Solution 2== | ||
| + | Like solution 1, it is clear that there is <math>30\%</math> of the pie remaining. Since Maria takes <math>\frac{1}{3}</math> of the remainder, she takes <math>\frac{1}{3} \cdot 30\% = 10\%,</math> meaning that there is <math>30\% - 10\% = \boxed{\textbf{(C)}\ 20\%}</math> left. | ||
| + | |||
| + | ~DBlack2021 | ||
| + | |||
| + | ==Solution 3 (One Sentence)== | ||
| + | We have <cmath>\left(100\%-70\%\right)\cdot\left(1-\frac13\right)=30\%\cdot\frac23=\boxed{\textbf{(C)}\ 20\%}</cmath> of the whole pie left. | ||
| + | |||
| + | ~MRENTHUSIASM | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/qJF3G7_IDgc | ||
| + | |||
| + | ~IceMatrix | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://www.youtube.com/watch?v=1fkJ2Mm55Ls | ||
| + | |||
| + | ~The Power of Logic | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/HtVPh8AE5dI | ||
| + | |||
| + | ~Education, the Study of Everything | ||
==See Also== | ==See Also== | ||
Latest revision as of 03:17, 7 October 2022
Contents
Problem
Carlos took 
of a whole pie. Maria took one third of the remainder. What portion of the whole pie was left?
Solution 1
If Carlos took of the pie, there must be 
left. After Maria takes 
of the remaining 
of the remaining 
is left.
Therefore, the answer is 
~Awesome2.1 (Solution)
~quacker88 (
Adjustments)
Solution 2
Like solution 1, it is clear that there is of the pie remaining. Since Maria takes of the remainder, she takes 
meaning that there is 
left.
~DBlack2021
Solution 3 (One Sentence)
We have ![\[\left(100\%-70\%\right)\cdot\left(1-\frac13\right)=30\%\cdot\frac23=\boxed{\textbf{(C)}\ 20\%}\]](http://latex.artofproblemsolving.com/0/c/e/0ce11cb93c4b54ee4c2318644ba2ce6fb8c76f81.png)
of the whole pie left.
~MRENTHUSIASM
Video Solution
~IceMatrix
Video Solution
https://www.youtube.com/watch?v=1fkJ2Mm55Ls
~The Power of Logic
Video Solution
~Education, the Study of Everything
See Also
| 2020 AMC 12A (Problems • Answer Key • Resources) | |
| 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 12 Problems and Solutions | |
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
