Difference between revisions of "2020 AMC 12B Problems/Problem 13"
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=== Solution 2 === | === Solution 2 === |
Revision as of 04:06, 15 February 2021
Contents
[hide]Problem
Which of the following is the value of
Solutions
Solution 1 (Logic)
Using the knowledge of the powers of and , we know that is greater than and is greater than Only choices and are greater than but is certainly incorrect--if we compare the squares of the original expression and they are clearly not equal. So, the answer is
Collaborators:
~Baolan
~Solasky (first edit on wiki!)
~chrisdiamond10
~MRENTHUSIASM (merged the thoughts of four people)
Solution 2
. If we call , then we have
. So our answer is .
~JHawk0224
Solution 3
From here, Finally, Answer: ~ TheBeast5520
Note that in this solution, even the most minor steps have been written out. In the actual test, this solution would be quite fast, and much of it could easily be done in your head.
Video Solution
~IceMatrix
Video Solution
https://youtu.be/RdIIEhsbZKw?t=1463
~ pi_is_3.14
Video Solution (Meta-Solving Technique)
https://youtu.be/GmUWIXXf_uk?t=1298
~ pi_is_3.14
See Also
2020 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 12 |
Followed by Problem 14 |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.