2012 AMC 8 Problem 19
Attempt Problem 19 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).
19.
In a jar of red, green, and blue marbles, all but are red marbles, all but are green, and all but are blue. How many marbles are in the jar?
Answer: C
Small hint:
Translate each “all but” statement into a sum of two colors.
Big hint:
Adding the three equations counts every marble twice.
Video solution:
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Written solution:
Let be the number of red marbles, green marbles, and blue marbles respectively. We then know by the statements given. Adding these equations yields This would mean so Therefore, the sum of all of the marbles is
Thus, the answer is C .
Problem 19 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
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