AMC 8 2015

How many square yards of carpet are required to cover a rectangular floor that is $12$ feet long and $9$ feet wide? (There are 3 feet in a yard.) $\textbf{(A) }12 \textbf{(B) }36 \textbf{(C) }108 \textbf{(D) }324 \textbf{(E) }972$

Point $O$ is the center of the regular octagon $ABCDEFGH$ , and $X$ is the midpoint of the side $\overline{AB}.$ What fraction of the area of the octagon is shaded? $\textbf{(A) }\frac{11}{32} \textbf{(B) }\frac{3}{8} \textbf{(C) }\frac{13}{32} \textbf{(D) }\frac{7}{16} \textbf{(E) }\frac{15}{32}$

$A$ $B$ $C$ $D$ $E$ $F$ $G$ $H$ $X$ $O$

Jack and Jill are going swimming at a pool that is one mile from their house. They leave home simultaneously. Jill rides her bicycle to the pool at a constant speed of $10$ miles per hour. Jack walks to the pool at a constant speed of $4$ miles per hour. How many minutes before Jack does Jill arrive? $\textbf{(A) }5 \textbf{(B) }6 \textbf{(C) }8 \textbf{(D) }9 \textbf{(E) }10$

The Centerville Middle School chess team consists of two boys and three girls. A photographer wants to take a picture of the team to appear in the local newspaper. She decides to have them sit in a row with a boy at each end and the three girls in the middle. How many such arrangements are possible? $\textbf{(A) }2 \textbf{(B) }4 \textbf{(C) }5 \textbf{(D) }6 \textbf{(E) }12$