2006 AMC 8

Mindy made three purchases for $\$1.98$, $\$5.04$, and $\$9.89$. What was her total, to the nearest dollar?

On the AMC $8$ contest Billy answers $13$ questions correctly, answers $7$ questions incorrectly and doesn’t answer the last $5.$ What is his score?

Elisa swims laps in the pool. When she first started, she completed $10$ laps in $25$ minutes. Now, she can finish $12$ laps in $24$ minutes. By how many minutes has she improved her lap time?

Initially, a spinner points west. Chenille moves it clockwise $ 2 \frac{1}{4}$ revolutions and then counterclockwise $ 3 \frac{3}{4}$ revolutions. In what direction does the spinner point after the two moves?

Points $A,$ $B,$ $C$ and $D$ are midpoints of the sides of the larger square. If the larger square has area $60,$ what is the area of the smaller square?

The letter T is formed by placing two $2 \times 4$ inch rectangles next to each other, as shown. What is the perimeter of the T, in inches?

Circle $X$ has a radius of $\pi.$ Circle $Y$ has a circumference of $8 \pi.$ Circle $Z$ has an area of $9 \pi.$ List the circles in order from smallest to largest radius.

The table shows some of the results of a survey by radio station KAMC. What percentage of the males surveyed listen to the station?

What is the product of $$
\dfrac{3}{2}\times\dfrac{4}{3}\times\dfrac{5}{4}\times\cdots\times\dfrac{2006}{2005}?
$$

Jorge’s teacher asks him to plot all the ordered pairs $(w, l)$ of positive integers for which $w$ is the width and $l$ is the length of a rectangle with area $12.$ What should his graph look like?

**(A)**

**(B)**

**(C)**

**(D)**

**(E)**

How many two-digit numbers have digits whose sum is a perfect square?

Antonette gets $70 \%$ on a $10$-problem test, $80 \%$ on a $20$-problem test and $90 \%$ on a $30$-problem test. If the three tests are combined into one $60$-problem test, which percent is closest to her overall score?

Cassie leaves Escanaba at $8:30$ AM heading for Marquette on her bike. She bikes at a uniform rate of $12$ miles per hour. Brian leaves Marquette at $9:00$ AM heading for Escanaba on his bike. He bikes at a uniform rate of $16$ miles per hour. They both bike on the same $62$-mile route between Escanaba and Marquette. At what time in the morning do they meet?

Problems $14,$ $15,$ and $16$ involve Mrs. Reed’s English assignment.

A Novel Assignment

The students in Mrs. Reed’s English class are reading the same $760$-page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in $20$ seconds, Bob reads a page in $45$ seconds and Chandra reads a page in $30$ seconds.

If Bob and Chandra both read the whole book, Bob will spend how many more seconds reading than Chandra?

Chandra and Bob, who each have a copy of the book, decide that they can save time by “team reading” the novel. In this scheme, Chandra will read from page $1$ to a certain page and Bob will read from the next page through page $760,$ finishing the book. When they are through they will tell each other about the part they read. What is the last page that Chandra should read so that she and Bob spend the same amount of time reading the novel?

Before Chandra and Bob start reading, Alice says she would like to team read with them. If they divide the book into three sections so that each reads for the same length of time, how many seconds will each have to read?

Jeff rotates spinners $P,$ $Q$ and $R$ and adds the resulting numbers. What is the probability that his sum is an odd number?

A cube with $3$-inch edges is made using $27$ cubes with $1$-inch edges. Nineteen of the smaller cubes are white and eight are black. If the eight black cubes are placed at the corners of the larger cube, what fraction of the surface area of the larger cube is white?

Triangle $ABC$ is an isosceles triangle with $\overline{AB}=\overline{BC}.$ Point $D$ is the midpoint of both $\overline{BC}$ and $\overline{AE},$ and $\overline{CE}$ is $11$ units long. Triangle $ABD$ is congruent to triangle $ECD.$ What is the length of $\overline{BD}?$

A singles tournament had six players. Each player played every other player only once, with no ties. If Helen won $4$ games, Ines won $3$ games, Janet won $2$ games, Kendra won $2$ games and Lara won $2$ games, how many games did Monica win?