Difference between revisions of "2020 AMC 10A Problems/Problem 3"
MRENTHUSIASM (talk | contribs) (Ordered the video solutions. Also, I fixed the coding in Solution 3 so that the -1's are on top of the factors instead of appearing in the same row as the numerator. Relatively, this version is clearer.) |
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Revision as of 21:17, 17 April 2021
Contents
Problem
Assuming , , and , what is the value in simplest form of the following expression?
Solution 1
Note that is times . Likewise, is times and is times . Therefore, the product of the given fraction equals .
Solution 2
Substituting values for , we see that if each of them satisfy the inequalities above, the value goes to be . Therefore, the product of the given fraction equals .
Solution 3
It is known that for . We use this fact to cancel out the terms:
~CoolJupiter (Solution)
~MRENTHUSIASM ( Adjustment)
Video Solution 1
~IceMatrix
Video Solution 2
Education, The Study of Everything
Video Solution 3
https://www.youtube.com/watch?v=7-3sl1pSojc
~bobthefam
Video Solution 4
~savannahsolver
Video Solution 5
https://youtu.be/ba6w1OhXqOQ?t=956
~ pi_is_3.14
See Also
2020 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.