2012 AMC 12A Problem 7
Attempt Problem 7 of the 2012 AMC 12A 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 2012 AMC 12A solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
7.
Mary divides a circle into sectors. The central angles of these sectors, measured in degrees, are all integers and they form an arithmetic sequence. What is the degree measure of the smallest possible sector angle?
Answer: C
Small hint:
The twelve angles sum to
Big hint:
With first term and common difference so
Solution:
Let be the smallest angle and the common difference. The sum of the angles is so
To make small, take large. Since must be even, is even, and gives so A larger even makes non-positive.
Thus, the correct answer is C.
Problem 7 in other years
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