1964 AMC 12 Problem 28
Attempt Problem 28 of the 1964 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 1964 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
28.
The sum of terms of an arithmetic progression is and the common difference is If the first term is an integer, and then the number of possible values for is:
Answer: D
Small hint:
If the first term is the sum is
Big hint:
List the divisors of that exceed
Solution:
The arithmetic-series formula simplifies to Thus must divide and every such gives an integer The divisors greater than are and so there are five possibilities.
Therefore, the correct answer is D.
Problem 28 in other years
- 1950 AMC 12
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