AMC 8 2018

An amusement park has a collection of scale models, with ratio $1 : 20$ , of buildings and other sights from around the country. The height of the United States Capitol is 289 feet. What is the height in feet of its replica to the nearest whole number? $\textbf{(A) }14 \textbf{(B) }15 \textbf{(C) }16 \textbf{(D) }18 \textbf{(E) }20$

What is the value of the product $$\left(1+\frac{1}{1}\right)\cdot\left(1+\frac{1}{2}\right)\cdot\left(1+\frac{1}{3}\right)\cdot\left(1+\frac{1}{4}\right)\cdot\left(1+\frac{1}{5}\right)\cdot\left(1+\frac{1}{6}\right)?$$ $\textbf{(A) }\frac{7}{6} \textbf{(B) }\frac{4}{3} \textbf{(C) }\frac{7}{2} \textbf{(D) }7 \textbf{(E) }8$

Students Arn, Bob, Cyd, Dan, Eve, and Fon are arranged in that order in a circle. They start counting: Arn first, then Bob, and so forth. When the number contains a 7 as a digit (such as 47) or is a multiple of 7 that person leaves the circle and the counting continues. Who is the last one present in the circle? $\textbf{(A) } \text{Arn} \textbf{(B) }\text{Bob} \textbf{(C) }\text{Cyd} \textbf{(D) }\text{Dan} \textbf{(E) }\text{Eve}$

The twelve-sided figure shown has been drawn on $1 \text{ cm}\times 1 \text{ cm}$ graph paper. What is the area of the figure in $\text{cm}^2$ ?

$\textbf{(A) } 12 \textbf{(B) } 12.5 \textbf{(C) } 13 \textbf{(D) } 13.5 \textbf{(E) } 14$