2024 AMC 8 Problem 15
Attempt Problem 15 of the 2024 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 2024 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
15.
Let the letters represent distinct digits. Suppose is the greatest number that satisfies the equation What is the value of
Answer: C
Small hint:
Big hint:
The equation reduces to
Video solution:
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Written solution:
Firstly, note that and, similarly, so the equation can be simplified to
Because has three digits, The largest possible three-digit number at most with distinct digits is but repeats a digit and also reuses the digit
The next candidate is and The six digits and are all distinct, so is the greatest possible value of
Hence,
Thus, C is the correct answer.
Problem 15 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
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- 1991 AMC 8
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