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

m
(Problem)
Line 1: Line 1:
 
==Problem==
 
==Problem==
 +
 +
At Olympic High School, <math>\frac{2}{5}</math> of the freshmen and <math>\frac{4}{5}</math> 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?
 +
 +
<math>\mathrm{(A)}</math> There are five times as many sophomores as freshmen.
 +
 +
<math>\mathrm{(B)}</math> There are twice as many sophomores as freshmen.
 +
 +
<math>\mathrm{(C)}</math> There are as many freshmen as sophomores.
 +
 +
<math>\mathrm{(D)}</math> There are twice as many freshmen as sophomores.
 +
 +
<math>\mathrm{(E)}</math> There are five times as many freshmen as sophomores.
  
 
==Solution==
 
==Solution==

Revision as of 22:48, 8 January 2009

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. $\boxed{\text{D}}$

See Also

2000 AMC 10 (ProblemsAnswer KeyResources)
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
All AMC 10 Problems and Solutions
Invalid username
Login to AoPS