from: category_eng

Num of Equations

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

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

Paula the painter had just enough paint for 30 identically sized rooms. Unfortunately, on the way to work, three cans of paint fell off her truck, so she had only enough paint for 25 rooms. How many cans of paint did she use for the 25 rooms?

$mathrm{(A)} 10qquadmathrm{(B)} 12qquadmathrm{(C)} 15qquadmathrm{(D)} 18qquadmathrm{(E)} 25$

1. 5:4

2.	Application

3.

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 $oxed{ ext{(D)} 5 }$ .

4.

Losing three cans of paint corresponds to being able to paint five fewer rooms. So $frac 35 cdot 25 = oxed{15}$ . The answer is $mathrm{(C)}$ .