All of Marcy's marbles are blue, red, green, or yellow. One third of her marbles are blue, one fourth of them are red, and six of them are green. What is the smallest number of yellow marbles that Marcy could have?

A. 1

B. 2

C. 3

D. 4

E. 5

1. 2017 AMC 8 官方解析

翻译：马西的所有小球有四种颜色，分别是蓝色、红色、绿色和黄色. 其中蓝色的占了$\frac{1}{3}$，红色的占了$\frac{1}{4}$，绿色的球有6个. 那么数量最少的黄色球有（　）个.
总数未知，但总数肯定是3和4的倍数，也就是12的倍数，
如果总数是12，黄色球$12 - 12 \times \frac{1}{3} - 12 \times \frac{1}{4} - 6 = -1$（舍）；
如果总数24，黄色球$24 - 24 \times \frac{1}{3} - 24 \times \frac{1}{4} - 6 = 4$，选D；
如果总数36，黄色球$36 - 36 \times \frac{1}{3} - 36 \times \frac{1}{4} - 6 = 9$（此时黄球数量不是最少的，舍去）.