Question

在奥林匹克高中， $\tfrac25$ 的一年级学生和 $\tfrac45$ 的二年级学生参加了 AMC 10。已知参加考试的一年级学生人数和二年级学生人数相同。下列哪一项一定成立？

At Olympic High School, $\tfrac25$ of the freshmen and $\tfrac45$ of the sophomores took the AMC 10. Given that the number of freshmen and sophomore contestants was the same, which of the following must be true?

二年级学生人数是一年级学生人数的五倍。

There are five times as many sophomores as freshmen.

二年级学生人数是一年级学生人数的两倍。

There are twice as many sophomores as freshmen.

一年级学生人数和二年级学生人数相同。

There are as many freshmen as sophomores.

一年级学生人数是二年级学生人数的两倍。

There are twice as many freshmen as sophomores.

一年级学生人数是二年级学生人数的五倍。

There are five times as many freshmen as sophomores.

答案：D

知识点：比与比例一次方程

难度评级：1020

解答：

设一年级和二年级学生总人数分别为 $f$ 和 $s$ 。 $\tfrac25 f = \tfrac45 s.$

参加考试的人数相同。两边乘以 $5$ ，得 $2f = 4s$ ，所以 $f = 2s$ 。

所以正确答案是 D。

Let $f$ and $s$ be the numbers of freshmen and sophomores. The contestant counts are equal, so $\tfrac25 f = \tfrac45 s.$

Multiplying by $5$ gives $2f = 4s,$ so $f = 2s.$ There are twice as many freshmen as sophomores.

Thus, the correct answer is D.

2000 AMC 10 第 8 题

答案：D

难度评级：1020

解答：

其他年份的第 8 题