2009 AMC 8

Bridget bought a bag of apples at the grocery store. She gave half of the apples to Ann. Then she gave Cassie $3$ apples, keeping $4$ apples for herself. How many apples did Bridget buy?

On average, for every $4$ sports cars sold at the local car dealership, $7$ sedans are sold. The dealership predicts that it will sell $28$ sports cars next month. How many sedans does it expect to sell?

The graph shows the constant rate at which Suzanna rides her bike. If she rides a total of half an hour at the same speed, how many miles will she have ridden?

The five pieces shown below can be arranged to form four of the five figures below. Which figure **cannot** be formed?



**(A)**

**(B)**

**(C)**

**(D)**

**(E)**

A sequence of numbers starts with $1,$ $2,$ and $3.$ The fourth number of the sequence is the sum of the previous three numbers in the sequence: $1 + 2 + 3 = 6.$ In the same way, every number after the fourth is the sum of the previous three numbers. What is the eighth number in the sequence?

Steve’s empty swimming pool will hold $24{,}000$ gallons of water when full. It will be filled by $4$ hoses, each of which supplies $2.5$ gallons of water per minute. How many hours will it take to fill Steve’s pool?

The triangular plot of land $ACD$ lies between Aspen Road, Brown Road and a railroad. Main Street runs east and west, and the railroad runs north and south. The numbers in the diagram indicate distances in miles. The width of the railroad track can be ignored. How many square miles are in the plot of land $ACD?$

The length of a rectangle is increased by $10\%$ and the width is decreased by $10\%.$ What percent of the old area is the new area?

Construct a square on one side of an equilateral triangle. On one non-adjacent side of the square, construct a regular pentagon, as shown. On a non-adjacent side of the pentagon, construct a regular hexagon. Continue to construct regular polygons in the same way, until you construct an octagon. How many sides does the resulting polygon have?

On a checkerboard composed of $64$ unit squares, what is the probability that a randomly chosen unit square does **not** touch the outer edge of the board?

The Amaco Middle School bookstore sells pencils costing a whole number of cents. Some seventh graders each bought a pencil, paying a total of $1.43$ dollars. Some of the $30$ sixth graders each bought a pencil, and they paid a total of $1.95$ dollars. How many more sixth graders than seventh graders bought a pencil?

The two spinners shown are spun once and each lands on one of the numbered sectors. What is the probability that the sum of the numbers in the two sectors is prime?

A three-digit integer contains one of each of the digits $1,$ $3,$ and $5.$ What is the probability that the integer is divisible by $5?$

Austin and Temple are $50$ miles apart along Interstate $35.$ Bonnie drove from Austin to her daughter’s house in Temple, averaging $60$ miles per hour. Leaving the car with her daughter, Bonnie rode a bus back to Austin along the same route and averaged $40$ miles per hour on the return trip. What was the average speed for the round trip, in miles per hour?

A recipe that makes $5$ servings of hot chocolate requires $2$ squares of chocolate, $\dfrac{1}{4}$ cup sugar, $1$ cup water and $4$ cups milk. Jordan has $5$ squares of chocolate, $2$ cups of sugar, lots of water, and $7$ cups of milk. If she maintains the same ratio of ingredients, what is the greatest number of servings of hot chocolate she can make?

How many $3$-digit positive integers have digits whose product equals $24?$

The positive integers $x$ and $y$ are the two smallest positive integers for which the product of $360$ and $x$ is a square and the product of $360$ and $y$ is a cube. What is the sum of $x$ and $y?$

The diagram represents a $7$-foot-by-$7$-foot floor that is tiled with $1$-square-foot shaded tiles and unshaded tiles. Notice that the corners have unshaded tiles. If a $15$-foot-by-$15$-foot floor is to be tiled in the same manner, how many unshaded tiles will be needed?

Two angles of an isosceles triangle measure $70^\circ$ and $x^\circ.$ What is the sum of the three possible values of $x?$

How many non-congruent triangles have vertices at three of the eight points in the array shown below?