2013 AMC 8 Problem 16
Attempt Problem 16 of the 2013 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 2013 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
16.
A number of students from Fibonacci Middle School are taking part in a community service project. The ratio of th-graders to th-graders is and the ratio of th-graders to th-graders is What is the smallest number of students that could be participating in the project?
Answer: E
Small hint:
The number of eighth-graders must fit both ratios.
Big hint:
Use the least common multiple of and .
Video solution:
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Written solution:
The number of th-graders must be a multiple of and which means that it is at least Using this number, we get that the number of th-graders is Similarly, the number of th-graders is
The total number of students is therefore
Thus, E is the correct answer.
Problem 16 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
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