1990 AMC 8 Problem 22
Attempt Problem 22 of the 1990 AMC 8 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 1990 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
22.
Several students are seated at a large circular table. They pass around a bag containing pieces of candy. Each person receives the bag, takes one piece of candy, and then passes the bag to the next person. If Chris takes the first and the last piece of candy, then the number of students at the table could be
Answer: B
Small hint:
Chris takes piece and piece , so after Chris’s first piece, the remaining pieces bring the bag exactly back to Chris
Big hint:
The number of students must divide evenly
Solution:
Chris takes the first piece, and then the bag goes around until Chris takes the last (th) piece. So the pieces after Chris’s first must be exactly a whole number of trips around the table back to Chris.
This means the number of students divides . Among the choices, only divides .
Thus, the correct answer is B .
Problem 22 in other years
- 1985 AMC 8
- 1986 AMC 8
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- 1989 AMC 8
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