AMC8 2017

AMC8 2017 · Q9

AMC8 2017 · Q9. It mainly tests Fractions, Divisibility & factors.

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?

马西所有的弹珠是蓝色、红色、绿色或黄色。她有三分之一的弹珠是蓝色，四分之一是红色，有 6 个是绿色。马西可能拥有的黄色弹珠最少是多少？

(A) 1 1

(B) 2 2

(D) 4 4

(E) 5 5

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): The total number of Marcy’s marbles must be divisible by both 3 and 4 thus it must be a multiple of 12. If she has just 12 marbles, then 4 are blue and 3 are red, leaving just 5 other marbles, so she could not have 6 green marbles. If she has 24 marbles, then 8 are blue and 6 are red, leaving 10 other marbles, so she could have 6 green marbles and 4 yellow marbles. The smallest number of yellow marbles that Marcy would have is 4.

9. 答案 (D)：Marcy 的弹珠总数必须同时能被 3 和 4 整除，因此它必须是 12 的倍数。如果她只有 12 颗弹珠，那么有 4 颗是蓝色、3 颗是红色，剩下只有 5 颗其他颜色，所以不可能有 6 颗绿色。如果她有 24 颗弹珠，那么有 8 颗蓝色、6 颗红色，剩下 10 颗其他颜色，因此可以有 6 颗绿色和 4 颗黄色。Marcy 可能有的黄色弹珠的最小数量是 4。

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