2008 AMC 8 Problem 15
Attempt Problem 15 of the 2008 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 2008 AMC 8 solutions, or check the answer key.
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15.
In Theresa’s first basketball games, she scored and points. In her ninth game, she scored fewer than points and her points-per-game average for the nine games was an integer. Similarly in her tenth game, she scored fewer than points and her points-per-game average for the games was also an integer. What is the product of the number of points she scored in the ninth and tenth games?
Answer: B
Small hint:
First add Theresa’s scores from the first games.
Big hint:
The -game total must be a multiple of and the -game total must be a multiple of
Solution:
The sum of her first scores is Since the average of the first scores is an integer, the sum of the first scores is a multiple of
Since the score is less than the sum of the scores after games is between and and is a multiple of making the sum Thus, the score of the th game is
The sum of Theresa’s first scores is Since the average of the first scores is an integer, the sum of the first scores is a multiple of
Since the score is less than the sum of the scores after games is between and and is a multiple of making the sum Thus, the score of the th game is
Therefore, their product is
Thus, the answer is B .
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
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