Difference between revisions of "2020 AMC 12B Problems/Problem 13"
MRENTHUSIASM (talk | contribs) (→Solution 1 (Logic)) |
MRENTHUSIASM (talk | contribs) (→Solution 1 (Logic)) |
||
Line 19: | Line 19: | ||
For A, B, C, D, only D is greater than 2. | For A, B, C, D, only D is greater than 2. | ||
E is certainly incorrect--if we compare the squares of the original expression and E, they are clearly not equal. | E is certainly incorrect--if we compare the squares of the original expression and E, they are clearly not equal. | ||
− | So, the answer is <math>\boxed{\textbf{(D)}.</math> ~MRENTHUSIASM | + | So, the answer is <math>\boxed{\textbf{(D)}}.</math> ~MRENTHUSIASM |
=== Solution 2 === | === Solution 2 === |
Revision as of 18:29, 2 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 . 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
Using the approximations mentioned above, the original expression is greater than 2. For A, B, C, D, only D is greater than 2. E is certainly incorrect--if we compare the squares of the original expression and E, they are clearly not equal. So, the answer is ~MRENTHUSIASM
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.