1982 AMC 12 Problem 28
Attempt Problem 28 of the 1982 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1982 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
28.
A set of consecutive positive integers beginning with is written on a blackboard. One number is erased. The average (arithmetic mean) of the remaining numbers is What number was erased?
can not be determined
Answer: B
Small hint:
If the last written number is the remaining count is
Big hint:
Use the bounds on the erased value to narrow the possible values of
Solution:
The new average is below the original average but differs from it by less than forcing or Since the remaining sum must be integral, is divisible by so The erased number is
Therefore, the correct answer is B.
Problem 28 in other years
- 1950 AMC 12
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