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

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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?  
 
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?  
  
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<math>\mathrm{(A)}</math> There are five times as many sophomores as freshmen.  
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<math>\textbf{(A)}</math> There are five times as many sophomores as freshmen.  
  
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<math>\mathrm{(B)}</math> There are twice as many sophomores as freshmen.
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<math>\textbf{(B)}</math> There are twice as many sophomores as freshmen.
  
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<math>\mathrm{(C)}</math> There are as many freshmen as sophomores.
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<math>\textbf{(C)}</math> There are as many freshmen as sophomores.
  
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<math>\mathrm{(D)}</math> There are twice as many freshmen as sophomores.  
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<math>\textbf{(D)}</math> There are twice as many freshmen as sophomores.  
  
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<math>\mathrm{(E)}</math> There are five times as many freshmen as sophomores.
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<math>\textbf{(E)}</math> There are five times as many freshmen as sophomores.
  
 
==Solution==
 
==Solution==
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There are twice as many freshmen as sophomores.
 
There are twice as many freshmen as sophomores.
 
<math>\boxed{\text{D}}</math>
 
<math>\boxed{\text{D}}</math>
 +
 +
==Video Solution by Daily Dose of Math==
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 +
https://youtu.be/qFwbXU-guuA?si=Lm84VudzdQPJ301d
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~Thesmartgreekmathdude
  
 
==See Also==
 
==See Also==
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{{AMC10 box|year=2000|num-b=7|num-a=9}}
 
{{AMC10 box|year=2000|num-b=7|num-a=9}}
 
{{MAA Notice}}
 
{{MAA Notice}}
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[[Category:Introductory Algebra Problems]]
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[[Category:Introductory Number Theory Problems]]

Latest revision as of 23:41, 14 July 2024

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

See Also

2000 AMC 10 (Problems • Answer Key • 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
All AMC 10 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

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