2003 AMC 8

Jamie counted the number of edges of a cube, Jimmy counted the number of corners, and Judy counted the number of faces. They then added the three numbers. What was the resulting sum?

Which of the following numbers has the smallest prime factor?

A burger at Ricky C’s weighs $120$ grams, of which $30$ grams are filler. What percent of the burger is not filler?

A group of children riding on bicycles and tricycles rode past Billy Bob’s house. Billy Bob counted $7$ children and $19$ wheels. How many tricycles were there?

If $20 \%$ of a number is $12,$ what is $30\%$ of the same number?

Given the areas of the three squares in the figure, what is the area of the interior triangle?

Blake and Jenny each took four $100$-point tests. Blake averaged $78$ on the four tests. Jenny scored $10$ points higher than Blake on the first test, $10$ points lower than him on the second test, and $20$ points higher on both the third and fourth tests. What is the difference between Jenny’s average and Blake’s average on these four tests?

Problems $8,$ $9,$ and $10$ use the data found in the accompanying paragraph and figures.

**Bake Sale**

Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.

• Art’s cookies are trapezoids:



• Roger’s cookies are rectangles:



• Paul’s cookies are parallelograms:



• Trisha’s cookies are triangles:



Each friend uses the same amount of dough, and Art makes exactly $12$ cookies.

Who gets the fewest cookies from one batch of cookie dough?

Art’s cookies sell for $60$¢ each. To earn the same amount from a single batch, how much should one of Roger’s cookies cost?

How many cookies will be in one batch of Trisha’s cookies?

Business is a little slow at Lou’s Fine Shoes, so Lou decides to have a sale. On Friday, Lou increases all of Thursday’s prices by $10 \%.$ Over the weekend, Lou advertises the sale: “Ten percent off the listed price. Sale starts Monday.” How much does a pair of shoes cost on Monday that cost $\$40$ on Thursday?

When a fair six-sided die is tossed on a table top, the bottom face cannot be seen. What is the probability that the product of the numbers on the five faces that can be seen is divisible by $6?$

Fourteen white cubes are put together to form the figure on the right. The complete surface of the figure, including the bottom, is painted red. The figure is then separated into individual cubes. How many of the individual cubes have exactly four red faces?

In this addition problem, each letter stands for a different digit. $$
\begin{array}{cccc}&T & W & O\\ +&T & W & O\\ \hline F& O & U & R\end{array}
$$ If $T = 7$ and the letter $O$ represents an even number, what is the only possible value for $W?$

A figure is constructed from unit cubes. Each cube shares at least one face with another cube. What is the minimum number of cubes needed to build a figure with the front and side views shown?

Ali, Bonnie, Carlo and Dianna are going to drive together to a nearby theme park. The car they are using has four seats: one driver’s seat, one front passenger seat and two back seats. Bonnie and Carlo are the only two who can drive the car. How many possible seating arrangements are there?

The six children listed below are from two families of three siblings each. Each child has blue or brown eyes and black or blond hair. Children from the same family have at least one of these characteristics in common. Which two children are Jim’s siblings?

Child Eye Color Hair Color Benjamin Blue Black Jim Brown Blond Nadeen Brown Black Austin Blue Blond Tevyn Blue Black Sue Blue Blond

Each of the twenty dots on the graph below represents one of Sarah’s classmates. Classmates who are friends are connected with a line segment. For her birthday party, Sarah is inviting only the following: all of her friends and all of those classmates who are friends with at least one of her friends. How many classmates will not be invited to Sarah’s party?

How many integers between $1000$ and $2000$ have all three of the numbers $15,$ $20,$ and $25$ as factors?

What is the measure of the acute angle formed by the hands of a clock at $4{:}20$ a.m.?