# Difference between revisions of "2000 AMC 10 Problems/Problem 8"

## Problem

At Olympic High School, $\frac{2}{5}$ of the freshmen and $\frac{4}{5}$ 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?

$\mathrm{(A)}$ There are five times as many sophomores as freshmen.

$\mathrm{(B)}$ There are twice as many sophomores as freshmen.

$\mathrm{(C)}$ There are as many freshmen as sophomores.

$\mathrm{(D)}$ There are twice as many freshmen as sophomores.

$\mathrm{(E)}$ There are five times as many freshmen as sophomores.

## Solution

Let $f$ be the number of freshman and s be the number of sophomores.

$\frac{2}{5}f=\frac{4}{5}s$

$f=2s$

There are twice as many freshman as sophomores. $\boxed{\text{D}}$