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Art of Problem Solving

2011 AMC 8 Problems

From AoPSWiki

Contents

1 Problem 1

2 Problem 2

3 Problem 3

4 Problem 4

5 Problem 5

6 Problem 6

7 Problem 7

8 Problem 8

9 Problem 910 Problem 1011 Problem 1112 Problem 1213 Problem 1314 Problem 1415 Problem 1516 Problem 1617 Problem 1718 Problem 1819 Problem 1920 Problem

2021 Problem 2122 Problem 22

23 Problem 2324 Problem 2425 Problem

2526 See Also

Problem 1

Margie bought

apples at a cost of cents per apple. She paid with a 5-dollar bill. How m uch change did

Margie recieve?

Solution

Problem 2

Karl's rectangular vegetable garden is feet by

feet, and Makenna's is

feet by

feet. Whose

garden is larger in area?

Solution

Problem 3

Extend the square pattern of 8 black and 17 white square tiles by attaching a border of black tiles around the square. What is the ratio of black tiles to white tiles in the extended pattern?

Solution

Problem 4

Here is a list of the num bers of fish that Tyler caught in nine outings last sum m er:

Which statem ent about the m ean, m edian, and m ode is true?

Solution

Problem 5

What tim e was it m inutes after m idnight on January 1, 2011?

Solution

Problem 6

In a town of 351 adults, every adult owns a car, m otorcycle, or both. If 331 adults own cars and 45 adults own m otorcycles, how m any of the car owners do not own a m otorcycle?

Solution

Problem 7

Each of the following four large congruent squares is subdivided into com binations of congruent triangles or rectangles and is partially bolded. What percent of the total area is partially bolded?

Solution

Problem 8

Bag A has three chips labeled 1, 3, and 5. Bag B has three chips labeled 2, 4, and 6. If one chip is drawn from each bag, how m any different values are possible for the sum of the two num bers on the chips?

Solution

Problem 9

Carm en takes a long bike ride on a hilly highway. The graph indicates the m iles traveled during the tim e of her ride. What is Carm en's average speed for her entire ride in m iles per hour?

Solution

Problem 10

The taxi fare in Gotham City is $2.40 for the first m ile and additional m ileage charged at the rate $0.20 for each additional 0.1 m ile. You plan to give the driver a $2 tip. How m any m iles can you ride for $10?

Solution

The graph shows the num ber of m inutes studied by both Asha (black bar) and Sasha (grey bar) in one week. On the average, how m any m ore m inutes per day did Sasha study than Asha?

Solution

Problem 12

Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the probability that Angie and Carlos are seated opposite each other?

Solution

Problem 13

Two congruent squares, and , have side length . They overlap to form the by

rectangle shown. What percent of the area of rectangle is shaded?

Solution

Problem 14

There are students at Colfax Middle School, where the ratio of boys to girls is . There are

students at Winthrop Middle School, where the ratio of boys to girls is . The two schools hold a dance

and all students from both schools attend. What fraction of the students at the dance are girls?

Solution

Problem 15

How m any digits are in the product ?

Solution

Let be the area of the triangle with sides of length , and . Let be the area of the triangle with

sides of length and . What is the relationship between and ?

Solution

Problem 17

Let , , , and be whole num bers. If , then what does equal?

Solution

Problem 18

A fair 6-sided die is rolled twice. What is the probability that the first num ber that com es up is greater than or equal to the second num ber?

Solution

Problem 19

How m any rectangles are in this figure?

Solution

Problem 20

Quadrilateral is a trapezoid, , , , and the altitude is . What is the

area of the trapeziod?

Solution

Problem 21

Students guess that Norb's age is , and . Norb says, "At least half of you

guessed too low, two of you are off by one, and m y age is a prim e num ber." How old is Norb?

Solution

Problem 22

What is the

tens digit of ?

Solution

Problem 23

How m any 4-digit positive integers have four different digits, where the leading digit is not zero, the integer is a m ultiple of 5, and 5 is the largest digit?

Solution

Problem 24

In how m any ways can 10001 be written as the sum of two prim es?

Solution

Problem 25

A circle with radius is inscribed in a square and circum scribed about another square as shown. Which fraction is closest to the ratio of the circle's shaded area to the area between the two squares?

Solution