Difference between revisions of "2023 AMC 8 Problems/Problem 20"
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==Video Solution by Math-X (Let's first Understand the question)== | ==Video Solution by Math-X (Let's first Understand the question)== |
Revision as of 22:32, 18 November 2023
Contents
[hide]- 1 Problem
- 2 Solution 1
- 3 Video Solution
- 4 Video Solution by Math-X (Let's first Understand the question)
- 5 Video Solution (CREATIVE THINKING!!!)
- 6 Animated Video Solution
- 7 Video Solution by OmegaLearn (Using Smart Sequence Analysis)
- 8 Video Solution by Magic Square
- 9 Video Solution by Interstigation
- 10 Video Solution by WhyMath
- 11 Video Solution
- 12 Video Solution by harungurcan
- 13 See Also
Problem
Two integers are inserted into the list to double its range. The mode and median remain unchanged. What is the maximum possible sum of the two additional numbers?
Solution 1
To double the range, we must find the current range, which is , to then double to: . Since we do not want to change the median, we need to get a value less than (as would change the mode) for the smaller, making fixed for the larger. Remember, anything less than is not beneficial to the optimization. So, taking our optimal values of and , we have an answer of .
~apex304, SohumUttamchandani, wuwang2002, TaeKim, CrystalFlower
Video Solution
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Video Solution by Math-X (Let's first Understand the question)
https://youtu.be/Ku_c1YHnLt0?si=1UUKWUVIPwomTx84&t=4411 ~Math-X
Video Solution (CREATIVE THINKING!!!)
~Education, the Study of Everything
Animated Video Solution
~Star League (https://starleague.us)
Video Solution by OmegaLearn (Using Smart Sequence Analysis)
Video Solution by Magic Square
https://youtu.be/-N46BeEKaCQ?t=3136
Video Solution by Interstigation
https://youtu.be/1bA7fD7Lg54?t=1970
Video Solution by WhyMath
~savannahsolver
Video Solution
Please like and subscribe!!
Video Solution by harungurcan
https://www.youtube.com/watch?v=Ki4tPSGAapU&t=534s
~harungurcan
See Also
2023 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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 AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.