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?

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

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

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

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

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

Solution

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

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

$2f = 4s$

$f=2s$

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

Video Solution by Daily Dose of Math

https://youtu.be/qFwbXU-guuA?si=Lm84VudzdQPJ301d

~Thesmartgreekmathdude

2000 AMC 10 (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 9
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All AMC 10 Problems and Solutions

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2000 AMC 10 Problems/Problem 8

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Solution

Video Solution by Daily Dose of Math

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