2026 AMC 8 Problem 22
Attempt Problem 22 of the 2026 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 2026 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
22.
The integers from through are arbitrarily separated into five groups of numbers each. The median of each group is identified. Let equal the median of the five medians. What is the least possible value of
Answer: A
Small hint:
A group median at most needs at least numbers at most
Big hint:
Three small medians would require too many small numbers
Video solution:
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Written solution:
If a group has median at most , then at least numbers in that group are at most . For the median of the five medians to be at most , at least groups would need such medians, requiring at least numbers at most , impossible. Thus . This is attainable, for example with group medians : use groups , , , , and . Hence the least possible value is .
Problem 22 in other years
- 1985 AMC 8
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