1982 AMC 12 Problem 30
Attempt Problem 30 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).
30.
Find the units digit in the decimal expansion of
none of these
Answer: D
Small hint:
Pair with its conjugate
Big hint:
The integers satisfy a short recurrence, while
Solution:
Let and so The integers satisfy hence for every Therefore is a multiple of minus a positive number less than Its integer part therefore ends in
Therefore, the correct answer is D.
Problem 30 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
- 1958 AMC 12
- 1959 AMC 12
- 1960 AMC 12
- 1961 AMC 12
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- 1963 AMC 12
- 1964 AMC 12
- 1965 AMC 12
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