2008 AMC 8 第 15 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
15.
特蕾莎前 场篮球比赛分别得了 、、、、、、 和 分。第九场她得分少于 分，并且九场比赛的场均得分是整数。类似地，第十场她得分少于 分，并且 场比赛的场均得分也是整数。她第九场和第十场得分的乘积是多少？
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?
小提示：
先把特蕾莎前 场的得分相加
First add Theresa’s scores from the first games.
大提示：
场总分必须是 的倍数， 场总分必须是 的倍数
The -game total must be a multiple of and the -game total must be a multiple of
解答：
她前 场的得分和为 。因为前 场的平均分是整数，所以前 场的总分是 的倍数。
由于第九场得分少于 ，前 场的总分在 到 之间，并且是 的倍数，因此总分为 。所以第 场得分为 。
特蕾莎前 场的总分是 。因为前 场的平均分是整数，所以前 场的总分是 的倍数。
由于第十场得分少于 ，前 场的总分在 到 之间，并且是 的倍数，因此总分为 。所以第 场得分为 。
因此乘积为 。
所以正确答案是 B。
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 .
其他年份的第 15 题
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