2025 AMC 8 Problem 9
Attempt Problem 9 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).
9.
Ningli looks at the pairs of numbers directly across from each other on a clock. She takes the average of each pair of numbers. What is the average of the resulting numbers?
Answer: B
Small hint:
The average of pair-averages equals the average of all numbers
Big hint:
The average of through is halfway between the endpoints
Video solution:
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Written solution:
The answer is the same as the average of all numbers. To understand why this is the case, it is actually generally true that if a whole bunch of numbers is split up into pairs, and each pair is averaged, and then all those pair-averages are averaged, the answer is the average of all the numbers.
To see why this is true, consider a smaller example of numbers and The average of the pair-averages is: and that is equal to The same type of simplification happens with numbers.
Since the numbers are equally spaced (in an arithmetic progression), the answer is the same as the average of the first and last number, which is or choice B.
Problem 9 in other years
- 1985 AMC 8
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