1975 AMC 12 Problem 29
Attempt Problem 29 of the 1975 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 1975 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
29.
What is the smallest integer larger than
Answer: C
Small hint:
Pair the expression with its conjugate
Big hint:
Their sum is an integer, while the conjugate term lies strictly between and
Solution:
Let and Adding their sixth powers cancels all odd radical terms: Since we have Thus the smallest larger integer is
Therefore, the correct answer is C.
Problem 29 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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- 1971 AMC 12
- 1972 AMC 12
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