2012 AMC 8 Problem 18
Attempt Problem 18 of the 2012 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2012 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
18.
What is the smallest positive integer that is neither prime nor square and that has no prime factor less than
Answer: A
Small hint:
The number must be composite but not a square.
Big hint:
Use the smallest two distinct primes that are at least .
Video solution:
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Written solution:
The number is composite, not prime, and has no prime factor below . The smallest possible prime factors are therefore , , , and so on.
A square such as is not allowed, and is much larger than . The smallest allowed nonsquare composite is .
Thus, the answer is A .
Problem 18 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
- 2001 AMC 8
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