AMC8 2024

AMC8 2024 · Q9

AMC8 2024 · Q9. It mainly tests Ratios & proportions, Divisibility & factors.

All 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?

Maria 的所有弹珠都是红色的、绿色的或蓝色的。Maria 的红色弹珠数量是绿色弹珠数量的一半，蓝色弹珠数量是绿色弹珠数量的两倍。以下哪项可能是 Maria 弹珠集合的总数量？

(A) 24 24

(B) 25 25

(D) 27 27

(E) 28 28

Answer

Correct choice: (E)

正确答案：（E）

Solution

Since Maria has half as many red marbles as green, we can call the number of red marbles $x$, and the number of green marbles $2x$. Since she has half as many green marbles as blue, we can call the number of blue marbles $4x$. Adding them up, we have: $7x$ marbles. The number of marbles therefore must be a multiple of $7$, as $x$ represents an integer, so the only possible answer is $\boxed{\textbf{(E) 28}}.$ Minor Edit - Runningmouse

由于 Maria 的红色弹珠是绿色的一半，设红色为 $x$，绿色为 $2x$。蓝色是绿色的两倍，为 $4x$。总计：$7x$ 颗弹珠。因此总数必须是 $7$ 的倍数，故唯一可能答案是 $\boxed{\textbf{(E) 28}}$。

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