AMC数学竞赛真题2017年10B 11-12

AMC10数学竞赛是美国高中数学竞赛中的一项，是针对高中一年级及初中三年级学生的数学测试，该竞赛开始于2000年，分A赛和B赛，于每年的2月初和2月中举行，学生可任选参加一项即可。不管是对高校申请还是今后在数学领域的发展都极其有利！那么接下来跟随小编来看一下AMC10数学竞赛真题以及官方解答吧：

Problem 11

At Typico High School,  of the students like dancing, and the rest dislike it. Of those who like dancing,  say that they like it, and the rest say that they dislike it. Of those who dislike dancing,  say that they dislike it, and the rest say that they like it. What fraction of students who say they dislike dancing actually like it?

Solution

 of the people that claim that they dislike dancing actually like it, and . Therefore, the answer is .

Problem 12

Elmer's new car gives  percent better fuel efficiency, measured in kilometers per liter, than his old car. However, his new car uses diesel fuel, which is  more expensive per liter than the gasoline his old car used. By what percent will Elmer save money if he uses his new car instead of his old car for a long trip?

Solution

Suppose that his old car runs at  km per liter. Then his new car runs at  km per liter, or  km per  of a liter. Let the cost of the old car's fuel be , so the trip in the old car takes  dollars, while the trip in the new car takes . He saves 

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