2023 AMC 8 Problem 20
Attempt Problem 20 of the 2023 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2023 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
20.
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?
Answer: D
Small hint:
The original range is , so the new range must be
Big hint:
To keep the median , add one number below and one above
Video solution:
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Written solution:
The original range is so the new range must be To keep the median one added number must be less than and the other, must be greater than
If the minimum remains so the new maximum must be The value would change the mode, so Hence
If and then so If the maximum remains forcing and giving an even smaller sum. Therefore no case exceeds
The values and preserve the mode and median and give range so the maximum sum is
Thus, D is the correct answer.
Problem 20 in other years
- 1985 AMC 8
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- 1989 AMC 8
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