2025 AMC 8 Problem 14
Attempt Problem 14 of the 2025 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 2025 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
14.
A number is inserted into the list The mean is now twice as great as the median. What is
Answer: E
Small hint:
Since every choice is at least the median stays fixed
Big hint:
Make the total sum equal to times twice the median
Video solution:
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Written solution:
After inserting into the list, there will be total numbers. That is even, so the median will be the average of the middle two numbers.
All of the answer choices are at least so when they are inserted into the list, the middle two numbers will be and It is convenient that the median will always be no matter which answer choice is picked.
The mean becomes twice the median, which is
To have a total of numbers with mean their sum must become
The sum of the original numbers is so the answer is which is choice E.
Problem 14 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
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- 1993 AMC 8
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- 1998 AMC 8
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