Difference between revisions of "2020 AMC 12B Problems/Problem 13"
Pi is 3.14 (talk | contribs) (→Video Solution) |
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== Video Solution == | == Video Solution == | ||
https://youtu.be/RdIIEhsbZKw?t=1463 | 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 | ~ pi_is_3.14 |
Revision as of 21:10, 24 January 2021
Contents
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 . So that means . Since is the only option greater than , it's the answer. ~Baolan
Answer Choice E is also greater than but it’s obvious that it’s too big.
~Solasky (first edit on wiki!)
Specifically, verify Choice E is too big by squaring the expression in the question and squaring choice (E) and then comparing.
Actually, this solution is incomplete, as is also greater than 2. ~chrisdiamond10
Solution 2
. If we call , then we have
. So our answer is .
~JHawk0224
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.