Difference between revisions of "User:Jiseop55406"

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Problem
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== Problem ==
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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?
  
 
<math>\text{(A)}\ 0.1 \qquad \text{(B)}\ 0.2 \qquad \text{(C)}\ 1 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 10</math>
 
<math>\text{(A)}\ 0.1 \qquad \text{(B)}\ 0.2 \qquad \text{(C)}\ 1 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 10</math>
  
== soulition 1 ==
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== Solution 1 ==
Helo,
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Hello,
 
<cmath>
 
<cmath>
 
\begin{align*}
 
\begin{align*}
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\end{align*}
 
\end{align*}
 
</cmath>
 
</cmath>
soo basicly the ansiwer is obviously <math>\text{(F)} \ 420.69</math>. <math>\mathbf{Q.E.D}</math>.<math>\blacksquare</math>
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So basically the answer is obviously <math>\text{(F)} \ 420.69</math>. <math>\mathbf{Q.E.D}</math>.<math>\blacksquare</math>
  
~Foogle and Hoogle, Members of the Ooga Booga Tribe of The Caveman Society
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~Foogle and Hoogle, Members of the Ooga Booga Tribe of The Caveman Society (aka Michaelwenquan)

Revision as of 09:51, 5 August 2022

Problem

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

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

Solution 1

Hello, \begin{align*} \frac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}} &= \frac{10^{2000}(1+10^2)}{10^{2000}(10+10)}\\ &= \frac{101}{20}\\ &= 5.05, \end{align*} So basically the answer is obviously $\text{(F)} \ 420.69$. $\mathbf{Q.E.D}$.$\blacksquare$

~Foogle and Hoogle, Members of the Ooga Booga Tribe of The Caveman Society (aka Michaelwenquan)