Difference between revisions of "2021 Fall AMC 10B Problems/Problem 3"
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==Solution== | ==Solution== | ||
We write the given expression as a single fraction: <cmath>\frac{2021}{2020} - \frac{2020}{2021} = \frac{2021\cdot2021-2020\cdot2020}{2020\cdot2021}</cmath> by cross multiplication. Then by factoring the numerator, we get <cmath>\frac{2021\cdot2021-2020\cdot2020}{2020\cdot2021}=\frac{(2021-2020)(2021+2020)}{2020\cdot2021}.</cmath> The question is asking for the numerator, so our answer is <math>2021+2020=4041,</math> giving answer choice <math>\boxed{\textbf{(E)}}.</math> | We write the given expression as a single fraction: <cmath>\frac{2021}{2020} - \frac{2020}{2021} = \frac{2021\cdot2021-2020\cdot2020}{2020\cdot2021}</cmath> by cross multiplication. Then by factoring the numerator, we get <cmath>\frac{2021\cdot2021-2020\cdot2020}{2020\cdot2021}=\frac{(2021-2020)(2021+2020)}{2020\cdot2021}.</cmath> The question is asking for the numerator, so our answer is <math>2021+2020=4041,</math> giving answer choice <math>\boxed{\textbf{(E)}}.</math> | ||
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+ | ~[[User:Aops-g5-gethsemanea2|Aops-g5-gethsemanea2]] |
Revision as of 19:06, 22 November 2021
Problem
The expression is equal to the fraction in which and are positive integers whose greatest common divisor is . What is
Solution
We write the given expression as a single fraction: by cross multiplication. Then by factoring the numerator, we get The question is asking for the numerator, so our answer is giving answer choice