2000 AMC 10 Problems/Problem 8

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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.

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

$2f = 4s$

$f=2s$

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

2000 AMC 10 (Problems • Resources)
Preceded by Problem 7	Followed by Problem 9
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25

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2000 AMC 10 Problems/Problem 8

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