2012 AMC 8 Problem 15
Attempt Problem 15 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).
15.
The smallest number greater than that leaves a remainder of when divided by or lies between what numbers?
and
and
and
and
and
Answer: D
Small hint:
Subtract from the unknown number.
Big hint:
The result must be a common multiple of , , , and .
Video solution:
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Written solution:
Let the number be Since it leaves a remainder of when divided by , , , and we know is a multiple of , , , and This means is a multiple of , which is Therefore, must be a multiple of The next number such that this occurs is when
Thus, the answer is D .
Problem 15 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
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