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Difference between revisions of "2002 AMC 10A Problems/Problem 1"

(New page: ==Problem== The ratio <math>\frac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}</math> is closest to which of the following numbers? <math>\text{(A)}\ 0.1 \qquad \text{(B)}\ 0.2 \qquad \text{...)
 
 
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The ratio <math>\frac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}</math> is closest to which of the following numbers?
 
The ratio <math>\frac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}</math> is closest to which of the following numbers?
  
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<math>\text{(A)}\ 0.1 \qquad \text{(B)}\ 0.2 \qquad \text{(C)}\ 1 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 10</math>
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<math>\textbf{(A)}\ 0.1 \qquad \textbf{(B)}\ 0.2 \qquad \textbf{(C)}\ 1 \qquad \textbf{(D)}\ 5 \qquad \textbf{(E)}\ 10</math>
  
 
==Solution==
 
==Solution==
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We factor <math>\frac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}</math> as <math>\frac{10^{2000}(1+100)}{10^{2001}(1+1)}=\frac{101}{20}</math>. As <math>\frac{101}{20}=5.05</math>, our answer is <math>\text{(D)}\ 5 \qquad</math>.
+
We factor <math>\frac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}</math> as <math>\frac{10^{2000}(1+100)}{10^{2001}(1+1)}=\frac{101}{20}</math>. As <math>\frac{101}{20}=5.05</math>, our answer is <math>\boxed{\textbf{(D)}\ 5 }</math>.
 +
 
 +
==Video Solution by Daily Dose of Math==
 +
 
 +
https://youtu.be/VEW3sYvitGI
 +
 
 +
~Thesmartgreekmathdude
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==See Also==
 +
{{AMC10 box|year=2002|ab=A|before=First question|num-a=2}}
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[[Category:Introductory Number Theory Problems]]
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{{MAA Notice}}

Latest revision as of 23:38, 18 July 2024

Problem

The ratio $\frac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}$ is closest to which of the following numbers?

$\textbf{(A)}\ 0.1 \qquad \textbf{(B)}\ 0.2 \qquad \textbf{(C)}\ 1 \qquad \textbf{(D)}\ 5 \qquad \textbf{(E)}\ 10$

Solution

We factor $\frac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}$ as $\frac{10^{2000}(1+100)}{10^{2001}(1+1)}=\frac{101}{20}$. As $\frac{101}{20}=5.05$, our answer is $\boxed{\textbf{(D)}\ 5 }$.

Video Solution by Daily Dose of Math

https://youtu.be/VEW3sYvitGI

~Thesmartgreekmathdude

See Also

2002 AMC 10A (Problems • Answer Key • Resources)
Preceded by
First question 		Followed by
Problem 2
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

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