考题3-4 2015 AMC 12B

AMC12是针对高中学生的数学测验，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。其主要目的在于激发学生对数学的兴趣，参予AMC12的学生应该不难发现测验的问题都很具挑战性，但测验的题型都不会超过学生的学习范围。这项测验希望每个考生能从竞赛中享受数学。那么接下来跟随小编来看一下AMC12的官方真题以及官方解答吧：

Problem 3

Isaac has written down one integer two times and another integer three times. The sum of the five numbers is 100, and one of the numbers is 28. What is the other number?

Solution

Let  be the number written two times, and  the number written three times. Then . Plugging in  doesn't yield an integer for , so it must be that , and we get . Solving for , we obtain .

Problem 4

David, Hikmet, Jack, Marta, Rand, and Todd were in a 12-person race with 6 other people. Rand finished 6 places ahead of Hikmet. Marta finished 1 place behind Jack. David finished 2 places behind Hikmet. Jack finished 2 places behind Todd. Todd finished 1 place behind Rand. Marta finished in 6th place. Who finished in 8th place?

Solution 1

Let  denote any of the 6 racers not named. Then the correct order following all the logic looks like:

Clearly the 8th place runner is .

Solution 2

We can list these out vertically to ensure clarity, starting with Marta and working from there.

Thus our answer is .

以上就是小编对AMC12数学竞赛试题以及解析的介绍，希望对你有所帮助，更多学习资料请持续关注AMC数学竞赛网！