User:Jiseop55406

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)

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