AM-GM Inequality — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses AM-GM Inequality — a algebra concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.
AMC 10
AMC 12
1951 AMC 12 Problem 43 • 1952 AMC 12 Problem 45 • 1958 AMC 12 Problem 46 • 1964 AMC 12 Problem 37 • 1965 AMC 12 Problem 34 • 1968 AMC 12 Problem 28 • 1969 AMC 12 Problem 25 • 1979 AMC 12 Problem 29 • 2000 AMC 12 Problem 12 • 2003 AMC 12A Problem 24 • 2016 AMC 12A Problem 24 • 2016 AMC 12B Problem 15 • 2023 AMC 12A Problem 23