2018 AMC12A 真题

2018 AMC 12A

Problem 1

A large urn contains balls, of which are red and the rest are blue. How many of the blue balls must be removed so that the percentage of red balls in the urn will be ? (No red balls are to be removed.)

一个大瓮包含 100 个球，其中 36% 的球是红色的，其余的球是蓝色的。必须要移除多少个蓝 球，才能使得大瓮中的红球的比例变为 72% ？ （红球不会被移除。）

(A) 28 (B) 32 (C) 36 (D) 50 (E) 64

Problem 2

While exploring a cave, Carl comes across a collection of -pound rocks worth each, -pound rocks worth each, and -pound rocks worth each. There are at least of each size. He can carry at most pounds. What is the maximum value, in dollars, of the rocks he can carry out of the cave?

Carl 在一个山洞里探险，他发现了一些 5 磅重的石头每块价值 14 美元， 磅重的石头每块价值 4 11 美元，以及 1 磅重的石头每块价值 2 美元。每种大小的石头各至少有 20 块。他最多能 18 磅。 他可以从山洞中带走的岩石的最大价值是多少美元？

(A) 48 (B) 49 (C) 50 (D) 51 (E) 52

Problem 3

How many ways can a student schedule mathematics courses -- algebra, geometry, and number theory -- in a -period day if no two mathematics courses can be taken in consecutive periods? (What courses the student takes during the other periods is of no concern here.)

一个学生想要在一天的 6 堂课中安排 3 门数学课 代数，几何和数论，要求任何两堂数学课不能连 -续安排（其他三堂课如何安排无需考虑），请问有多少种安排方法？

(A) 3 (B) 6 (C) 12 (D) 18 (E) 24