AMC12 2012 B

AMC12 2012 B · Q7

AMC12 2012 B · Q7. It mainly tests Unit conversion, Basic counting (rules of product/sum).

Small lights are hung on a string $6$ inches apart in the order red, red, green, green, green, red, red, green, green, green, and so on continuing this pattern of $2$ red lights followed by $3$ green lights. How many feet separate the 3rd red light and the 21st red light? Note: $1$ foot is equal to $12$ inches.

小灯挂在一根绳子上，相邻两盏灯相距 $6$ 英寸，按顺序为红、红、绿、绿、绿、红、红、绿、绿、绿，依此类推，持续重复“$2$ 盏红灯后接 $3$ 盏绿灯”的模式。第 $3$ 盏红灯与第 $21$ 盏红灯相隔多少英尺？注：$1$ 英尺等于 $12$ 英寸。

(A) 18 18

(B) 18.5 18.5

(D) 20.5 20.5

(E) 22.5 22.5

Answer

Correct choice: (E)

正确答案：（E）

Solution

We know the repeating section is made of $2$ red lights and $3$ green lights. The 3rd red light would appear in the 2nd section of this pattern, and the 21st red light would appear in the 11th section. There would then be a total of $44$ lights in between the 3rd and 21st red light, translating to $45$ $6$-inch gaps. Since the question asks for the answer in feet, the answer is $\frac{45*6}{12} \rightarrow \boxed{\textbf{(E)}\ 22.5}$.

重复单元由 $2$ 盏红灯和 $3$ 盏绿灯组成。第 $3$ 盏红灯出现在该模式的第 $2$ 个单元中，第 $21$ 盏红灯出现在第 $11$ 个单元中。因此在第 $3$ 盏与第 $21$ 盏红灯之间共有 $44$ 盏灯，对应 $45$ 个 $6$ 英寸的间隔。题目要求以英尺为单位，答案为 $\frac{45*6}{12} \rightarrow \boxed{\textbf{(E)}\ 22.5}$。

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