AMC 8 2008 Problem 15
AMC8 2008 年第 15 题
余数与同余★★★☆☆
In Theresa's first 8 basketball games, she scored 7, 4, 3, 6, 8, 3, 1 and 5 points. In her ninth game, she scored fewer than 10 points and her points-per-game average for the nine games was an integer. Similarly in her tenth game, she scored fewer than 10 points and her points-per-game average for the 10 games was also an integer. What is the product of the number of points she scored in the ninth and tenth games?
在 Theresa 的前 8 场篮球比赛中，她的进球得分分别是 7，4，3，6，8，3，1 和 5 分。在她的第 9 场比赛中，她的得分少于 10 分，而她在这 9 场比赛中平均每场得分都是整数。同样，在她的第 10 场比赛中，她的得分少于 10 分，而她在这 10 场比赛中平均每场得分也都是整数。
那么她在第 9 场和第 10 场比赛中的得分的乘积是多少？
- A.35
- B.40
- C.48
- D.56
- E.72
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
The total number of points from the first 8 games is 7+4+3+6+8+3+1+5=37. We have to make this a multiple of 9 by scoring less than 10 points. The smallest multiple of 9 that is greater than 37 is 45. 45-37=8. Now we have to add a number to get a multiple of 10. The next multiple of 10 is 50, which means that we add 5. Multiplying these together, you get .
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