Question

Maria 收藏的弹珠全是红色、绿色或蓝色。红色弹珠数量是绿色的一半，蓝色弹珠数量是绿色的两倍。下列哪个数可能是 Maria 收藏弹珠的总数？

All of the marbles in Maria's collection are red, green, or blue. Maria has half as many red marbles as green marbles and twice as many blue marbles as green marbles. Which of the following could be the total number of marbles in Maria's collection?

$24$

$25$

$26$

$27$

$28$

答案：E

知识点：比与比例整除性

难度评级：870

视频讲解：

Click to load, then click again to play

文字解答：

设 Maria 有 $r$ 个红色弹珠。红色是绿色的一半，所以绿色有 $2r$ 个；蓝色是绿色的两倍，所以蓝色有 $2(2r) = 4r$ 个。总数为 $r + 2r + 4r = 7r$ ，必须是 $7$ 的倍数。选项中只有 $28$ 是 $7$ 的倍数。

正确答案是 E。

We can let $r$ be the number of red marbles that Maria has. Since Maria has half as many red marbles as green, then we know that she has $2r$ green marbles. Moreover, since she has twice as many blue marbles as green, then she will have $2(2r) = 4r$ blue marbles. Adding these together gives us $r + 2r + 4r = 7r,$ and so the answer must be a multiple of $7.$ Among the answer choices, only $28$ is a multiple of $7.$

Thus, E is the correct answer.

2024 AMC 8 第 9 题

答案：E

难度评级：870

视频讲解：

文字解答：

其他年份的第 9 题