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| − | Problem | + | == Problem == |
| + | |||
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> | ||
| + | |||
| + | == Solution 1 == | ||
| + | Hello, | ||
| + | <cmath> | ||
| + | \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*} | ||
| + | </cmath> | ||
| + | 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 (aka Michaelwenquan) | ||
Revision as of 09:51, 5 August 2022
Problem
The ratio 
is closest to which of the following numbers?
Solution 1
Hello,
So basically the answer is obviously 
. 
.
~Foogle and Hoogle, Members of the Ooga Booga Tribe of The Caveman Society (aka Michaelwenquan)
