AMC10 2000 A

AMC10 2000 A · Q8

AMC10 2000 A · Q8. It mainly tests Ratios & proportions.

At Olympic High School, 2/5 of the freshmen and 4/5 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?

在奥林匹克高中，$2/5$ 的新生和 $4/5$ 的二年级生参加了 AMC 10。已知新生和二年级参赛人数相同，下列哪项一定正确？

(A) There are five times as many sophomores as freshmen. 二年级生是新生数的五倍。

(B) There are twice as many sophomores as freshmen. 二年级生是新生数的两倍。

(D) There are twice as many freshmen as sophomores. 新生是二年级生数的两倍。

(E) There are five times as many freshmen as sophomores. 新生是二年级生数的五倍。

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): Let $f$ and $s$ represent the numbers of freshmen and sophomores at the school, respectively. According to the given condition, $(2/5)f=(4/5)s$. Thus, $f=2s$. That is, there are twice as many freshmen as sophomores.

答案（D）：设 $f$ 和 $s$ 分别表示学校中新生和二年级学生的人数。根据给定条件，$(2/5)f=(4/5)s$。因此，$f=2s$。也就是说，新生人数是二年级学生人数的两倍。

Topics

AR.004 Ratios & proportions