1978 AMC 12 Problem 27
Attempt Problem 27 of the 1978 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 1978 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
27.
There is more than one integer greater than which, when divided by any integer such that has a remainder of What is the difference between the two smallest such integers?
none of these
Answer: C
Small hint:
Each desired integer is more than a common multiple of every integer from through
Big hint:
The difference of consecutive such integers is the least common multiple of those divisors
Solution:
A qualifying integer is congruent to modulo every integer from through hence modulo The two smallest qualifying integers greater than are and whose difference is
Therefore, the correct answer is C.
Problem 27 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
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