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**AMC 8,2023 Problem 1**

What is the value of $(8 \times 4+2)-(8+4 \times 2)$ ?

(A) 0

(B) 6

(C) 10

(D) 18

(E) 24

**AMC 8,2023 Problem **3

*Wind chill* is a measure of how cold people feel when exposed to wind outside. A good estimate for wind chill can be found using this calculation

(wind chill)=(air temperature)$-0.7 \times$ (wind speed)

where temperature is measured in degrees Fahrenheit $\left({ }^{\circ} \mathrm{F}\right)$

and the wind speed is measured in miles per hour (mph). Suppose the air temperature is $36^{\circ} \mathrm{F}$

and the wind speed is 18 mph. Which of the following is closest to the approximate wind chill?

(A) 18

(B) 23

(C) 28

(D) 32

(E) 35

**AMC 8,2023 Problem ** 5

A lake contains 250 trout, along with a variety of other fish. When a marine biologist catches and releases a sample of 180 fish from the lake, 30 are identified as trout. Assume that the ratio of trout to the total number of fish is the same in both the sample and the lake. How many fish are there in the lake?

(A) 1250

(B) 1500

(C) 1750

(D) 1800

(E) 2000

**AMC 8,2023 Problem **6

The digits 2,0,2, and 3 are placed in the expression below, one digit per box. What is the maximum possible value of the expression?

(A) 0

(B) 8

(C) 9

(D) 16

(E) 18

**AMC 8,2023 Problem **9

Malaika is skiing on a mountain. The graph below shows her elevation, in meters, above the base of the mountain as she skis along a trail. In total, how many seconds does she spend at an elevation between 4 and 7 meters?

(A) 6

(B) 8

(C) 10

(D) 12

(E) 14

**AMC 8,2023 Problem **10

Harold made a plum pie to take on a picnic. He was able to eat only $\frac{1}{4}$ of the pie, and he left the rest for his friends. A moose came by and ate $\frac{1}{3}$ of what Harold left behind. After that, a porcupine ate $\frac{1}{3}$ of what the moose left behind. How much of the original pie still remained after the porcupine left?

(A) $\frac{1}{12}$

(B) $\frac{1}{6}$

(C) $\frac{1}{4}$

(D) $\frac{1}{3}$

(E) $\frac{5}{12}$

**AMC 8,2023 Problem **11

NASA's Perseverance Rover was launched on July 30, 2020. After traveling 292,526,838 miles, it landed on Mars in Jezero Crater about 6.5 months later. Which of the following is closest to the Rover's average interplanetary speed in miles per hour?

(A) 6,000

(B) 12,000

(C) 60,000

(D) 120,000

(E) 600,000

**AMC 8,2023 Problem **13

Along the route of a bicycle race, 7 water stations are evenly spaced between the start and finish lines, as shown in the figure below. There are also 2 repair stations evenly spaced between the start and finish lines. The 3rd water station is located 2 miles after the 1 st repair station. How long is the race in miles?

(A) 8

(B) 16

(C) 24

(D) 48

(E) 96

**AMC 8,2023 Problem **14

Nicolas is planning to send a package to his friend Anton, who is a stamp collector. To pay for the postage, Nicolas would like to cover the package with a large number of stamps. Suppose he has a collection of 5 -cent, 10-cent, and 25 -cent stamps, with exactly 20 of each type. What is the greatest number of stamps Nicolas can use to make exactly \$7.10 in postage? (Note: The amount \$7.10 corresponds to 7 dollars and 10 cents. One dollar is worth 100 cents.)

(A) 45

(B) 46

(C) 51

(D) 54

(E) 55

**AMC 8,2023 Problem **15

Viswam walks half a mile to get to school each day. His route consists of 10 city blocks of equal length and he takes 1 minute to walk each block. Today, after walking 5 blocks, Viswam discovers he has to make a detour, walking 3 blocks of equal length instead of 1 block to reach the next corner. From the time he starts his detour, at what speed, in mph, must he walk, in order to get to school at his usual time?

(A) 4

(B) 4.2

(C) 4.5

(D) 4.8

(E) 5

**AMC 8,2023 Problem **22

In a sequence of positive integers, each term after the second is the product of the previous two terms. The sixth term is 4000

. What is the first term?

(A) 1

(B) 2

(C) 4

(D) 5

(E) 10

**AMC 8,2022 Problem 2**

Consider these two operations:

$$

\begin{gathered}

a \diamond b=a^2-b^2 \\

a \star b=(a-b)^2

\end{gathered}

$$

What is the value of $(5 \diamond 3) \star 6$ ?

(A) -20

(B) 4

(C) 16

(D) 100

(E) 220

**AMC 8,2022 Problem 5**

Anna and Bella are celebrating their birthdays together. Five years ago, when Bella turned 6 years old, she received a newborn kitten as a birthday present. Today the sum of the ages of the two children and the kitten is 30 years. How many years older than Bella is Anna?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

**AMC 8,2022 Problem 6**

Three positive integers are equally spaced on a number line. The middle number is 15 , and the largest number is 4 times the smallest number. What is the smallest of these three numbers?

(A) 4

(B) 5

(C) 6

(D) 7

(E) 8

**AMC 8,2022 Problem 7**

When the World Wide Web first became popular in the 1990 s, download speeds reached a maximum of about 56 kilobits per second. Approximately how many minutes would the download of a 4.2-megabyte song have taken at that speed? (Note that there are 8000 kilobits in a megabyte.)

(A) 0.6

(B) 10

(C) 1800

(D) 7200

(E) 36000

**AMC 8,2022 Problem 8**

What is the value of

$$

\frac{1}{3} \cdot \frac{2}{4} \cdot \frac{3}{5} \cdot \frac{18}{20} \cdot \frac{19}{21} \cdot \frac{20}{22} ?

$$

(A) $\frac{1}{462}$

(B) $\frac{1}{231}$

(C) $\frac{1}{132}$

(D) $\frac{2}{213}$

(E) $\frac{1}{22}$

**AMC 8,2022 Problem 9**

A cup of boiling water $\left(212^{\circ} \mathrm{F}\right)$ is placed to $\mathrm{cool}$ in a room whose temperature remains constant at $68^{\circ} \mathrm{F}$. Suppose the difference between the water temperature and the room temperature is halved every 5 minutes. What is the water temperature, in degrees Fahrenheit, after 15 minutes?

(A) 77

(B) 86

(C) 92

(D) 98

(E) 104

**AMC 8,2022 Problem 10**

One sunny day, Ling decided to take a hike in the mountains. She left her house at $8 \mathrm{AM}$, drove at a constant speed of 45 miles per hour, and arrived at the hiking trail at $10 \mathrm{AM}$. After hiking for 3 hours, Ling drove home at a constant speed of 60 miles per hour. Which of the following graphs best illustrates the distance between Ling's car and her house over the course of her trip?

**AMC 8,2022 Problem 11**

Henry the donkey has a very long piece of pasta. He takes a number of bites of pasta, each time eating 3 inches of pasta from the middle of one piece. In the end, he has 10 pieces of pasta whose total length is 17 inches. How long, in inches, was the piece of pasta he started with?

(A) 34

(B) 38

(C) 41

(D) 44

(E) 47

**AMC 8,2022 Problem 12**

The arrows on the two spinners shown below are spun. Let the number $N$ equal 10 times the number on Spinner $\mathrm{A}$, added to the number on Spinner B. What is the probability that $N$ is a perfect square number?

(A) $\frac{1}{16}$

(B) $\frac{1}{8}$

(C) $\frac{1}{4}$

(D) $\frac{3}{8}$

(E) $\frac{1}{2}$

**AMC 8,2022 Problem 15**

Laszlo went online to shop for black pepper and found thirty different black pepper options varying in weight and price, shown in the scatter plot below. In ounces, what is the weight of the pepper that offers the lowest price per ounce?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

**AMC 8,2022 Problem 16**

Four numbers are written in a row. The average of the first two is 21 , the average of the middle two is 26 , and the average of the last two is 30 . What is the average of the first and last of the numbers?

(A) 24

(B) 25

(C) 26

(D) 27

(E) 28

**AMC 8,2022 Problem 19**

Mr. Ramos gave a test to his class of 20 students. The dot plot below shows the distribution of test scores.

Later Mr. Ramos discovered that there was a scoring error on one of the questions. He regraded the tests, awarding some of the students 5 extra points, which increased the median test score to 85 . What is the minimum number of students who received extra points?

(Note that the median test score equals the average of the 2 scores in the middle if the 20 test scores are arranged in increasing order.)

(A) 2

(B) 3

(C) 4

(D) 5

(E) 6

**AMC 8,2022 Problem 20**

The grid below is to be filled with integers in such a way that the sum of the numbers in each row and the sum of the numbers in each column are the same. Four numbers are missing. The number $x$ in the lower left corner is larger than the other three missing numbers. What is the smallest possible value of $x$ ?

(A) -1

(B) 5

(C) 6

(D) 8

(E) 9

**AMC 8,2022 Problem 21**

Steph scored 15 baskets out of 20 attempts in the first half of a game, and 10 baskets out of 10 attempts in the second half. Candace took 12 attempts in the first half and 18 attempts in the second. In each half, Steph scored a higher percentage of baskets than Candace. Surprisingly they ended with the same overall percentage of baskets scored. How many more baskets did Candace score in the second half than in the first?

(A) 7

(B) 8

(C) 9

(D) 10

(E) 11

**AMC 8,2022 Problem 22**

A bus takes 2 minutes to drive from one stop to the next, and waits 1 minute at each stop to let passengers board. Zia takes 5 minutes to walk from one bus stop to the next. As Zia reaches a bus stop, if the bus is at the previous stop or has already left the previous stop, then she will wait for the bus. Otherwise she will start walking toward the next stop. Suppose the bus and Zia start at the same time toward the library, with the bus 3 stops behind. After how many minutes will Zia board the bus?

(A) 17

(B) 19

(C) 20

(D) 21

(E) 23

**AMC 8,2022 Problem 23**

A $\Delta$ or $\bigcirc$ is placed in each of the nine squares in a 3 -by- 3 grid. Shown below is a sample configuration with three $\Delta s$ in a line.

How many configurations will have three $\Delta s$ in a line and three $\bigcirc$ s in a line?

(A) 39

(B) 42

(C) 78

(D) 84

(E) 96

**AMC 8,2020 Problem 1**

Luka is making lemonade to sell at a school fundraiser. His recipe requires $4$ times as much water as sugar and twice as much sugar as lemon juice. He uses $3$ cups of lemon juice. How many cups of water does he need?

(A) $6$

(B) $8$

(C) $12$

(D) $18$

(E) $24$

**AMC 8,2020 Problem 2**

Four friends do yardwork for their neighbors over the weekend, earning $\$ 15, \$ 20, \$ 25$, and $\$ 40$, respectively. They decide to split their earnings equally among themselves. In total how much will the friend who earned $\$ 40$ give to the others?

(A) $\$ 5$

(B) $\$ 10$

(C) $\$ 15$

(D) $\$ 20$

(E) $\$ 25$

**AMC 8,2020 Problem 3**

Carrie has a rectangular garden that measures $6$ feet by $8$ feet. She plants the entire garden with strawberry plants. Carrie is able to plant $4$ strawberry plants per square foot, and she harvests an average of $10$ strawberries per plant. How many strawberries can she expect to harvest?

(A) $560$

(B) $960$

(C) $1120$

(D) $1920$

(E) $3840$

**AMC 8,2020 Problem 5**

Three fourths of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of $5$ cups. What percent of the total capacity of the pitcher did each cup receive?

(A) $5$

(B) $10$

(C) $15$

(D) $20$

(E) $25$

**AMC 8,2020 Problem 8**

Ricardo has $2020$ coins, some of which are pennies (1-cent coins) and the rest of which are nickels ( $(5$ -cent coins). He has at least one penny and at least one nickel. What is the difference in cents between the greatest possible and least possible amounts of money that Ricardo can have?

(A) $8062$

(B) $8068$

(C) $8072$

(D) $8076$

(E) $8082$

**AMC 8,2020 Problem 13**

Jamal has a drawer containing $6$ green socks, 18 purple socks, and $12$ orange socks. After adding more purple socks, Jamal noticed that there is now a $60 \%$ chance that a sock randomly selected from the drawer is purple. How many purple socks did Jamal add?

(A) $46$

(B) $9$

(C) $12$

(D) $18$

(E) $24$

**AMC 8,2020 Problem 15**

Suppose $15 \%$ of $x$ equals $20 \%$ of $y$. What percentage of $x$ is $y$ ?

(A) $5$

(B) $35$

(C) $75$

(D) $133 \frac{1}{3}$

(E) $300$

**AMC 8,2019 Problem 1**

Ike and Mike go into a sandwich shop with a total of $\$ 30.00$ to spend. Sandwiches cost $\$ 4.50$ each and soft drinks cost $\$ 1.00$ each. Ike and Mike plan to buy as many sandwiches as they can, and use any remaining money to buy soft drinks. Counting both sandwiches and soft drinks, how many items will they buy?

(A) $6$

(B) $7$

(C) $8$

(D) $9$

(E) $10$

**AMC 8,2019 Problem 3**

Which of the following is the correct order of the fractions $\frac{15}{11}, \frac{19}{15}$, and $\frac{17}{13}$, from least to greatest?

(A) $\frac{15}{11}<\frac{17}{13}<\frac{19}{15}$

(B) $\frac{15}{11}<\frac{19}{15}<\frac{17}{13}$

(C) $\frac{17}{13}<\frac{19}{15}<\frac{15}{11}$

(D) $\frac{19}{15}<\frac{15}{11}<\frac{17}{13}$

(E) $\frac{19}{15}<\frac{17}{13}<\frac{15}{11}$

**AMC 8,2019 Problem 8**

Gilda has a bag of marbles. She gives $20 \%$ of them to her friend Pedro. Then Gilda gives $10 \%$ of what is left to another friend, Ebony. Finally, Gilda gives $25 \%$ of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself?

(A) $20$

(B) $33 \frac{1}{3}$

(C) $38$

(D) $45$

(E) $54$

**AMC 8,2019 Problem 9**

Alex and Felicia each have cats as pets. Alex buys cat food in cylindrical cans that are $6 \mathrm{~cm}$ in diameter and $12 \mathrm{~cm}$ high. Felicia buys cat food in cylindrical cans that are $12 \mathrm{~cm}$ in diameter and $6 \mathrm{~cm}$ high. What is the ratio of the volume one of Alex's cans to the volume one of Felicia's cans?

(A) $1: 4$

(B) $1: 2$

(C) $1: 1$

(D) $2: 1$

(E) $4: 1$

**AMC 8,2019 Problem 11**

The eighth grade class at Lincoln Middle School has $93$ students. Each student takes a math class or a foreign language class or both. There are $70$ eighth graders taking a math class, and there are $54$ eighth graders taking a foreign language class. How many eighth graders take only a math class and not a foreign language class?

(A) $16$

(B) $23$

(C) $31$

(D) $39$

(E) $70$

**AMC 8,2019 Problem 13**

A palindrome is a number that has the same value when read from left to right or from right to left. (For example, $12321$ is a palindrome.) Let $N$ be the least three-digit integer which is not a palindrome but which is the sum of three distinct two-digit palindromes. What is the sum of the digits of $N$ ?

(A) $2$

(B) $3$

(C) $4$

(D) $5$

(E) $6$

**AMC 8,2019 Problem 16**

Qiang drives $15$ miles at an average speed of $30$ miles per hour. How many additional miles will he have to drive at $55$ miles per hour to average $50$ miles per hour for the entire trip?

(A) $45$

(B) $62$

(C) $90$

(D) $110$

(E) $135$

**AMC 8,2019 Problem 17**

What is the value of the product

$$

\left(\frac{1 \cdot 3}{2 \cdot 2}\right)\left(\frac{2 \cdot 4}{3 \cdot 3}\right)\left(\frac{3 \cdot 5}{4 \cdot 4}\right) \cdots\left(\frac{97 \cdot 99}{98 \cdot 98}\right)\left(\frac{98 \cdot 100}{99 \cdot 99}\right) ?

$$

(A) $\frac{1}{2}$

(B) $\frac{50}{99}$

(C) $\frac{9800}{9801}$

(D) $\frac{100}{99}$

(E) $50$

**AMC 8,2019 Problem 20**

How many different real numbers $x$ satisfy the equation

$$

\left(x^{2}-5\right)^{2}=16 ?

$$

(A) $0$

(B) $1$

(C) $2$

(D) $4$

(E) $8$

**AMC 8,2019 Problem 23**

After Euclid High School's last basketball game, it was determined that $\frac{1}{4}$ of the team's points were scored by Alexa and $\frac{2}{7}$ were scored by Brittany. Chelsea scored $15$ points. None of the other $47$ team members scored more than $42$ points. What was the total number of points scored by the other $7$ team members?

(A) $10$

(B) $11$

(C) $12$

(D) $13$

(E) $14$

**AMC 8, 2019, Problem 24**

In triangle $ABC$, point $D$ divides side $\overline{AC}$ so that $AD:DC=1:2$. Let $E$ be the midpoint of $\overline{BD}$ and let $F$ be the point of intersection of line $BC$ and line $AE$. Given that the area of $\triangle ABC$ is $360$, what is the area of $\triangle EBF$?

**AMC 8, 2018, Problem 1**

An amusement park has a collection of scale models, with a ratio $1: 20$, of buildings and other sights from around the country. The height of the United States Capitol is $289$ feet. What is the height in feet of its duplicate to the nearest whole number?

(A) $14$

(B) $15$

(C) $16$

(D) $18$

(E) $20$

**AMC 8, 2018, Problem 2**

What is the value of the product

$$

\left(1+\frac{1}{1}\right) \cdot\left(1+\frac{1}{2}\right) \cdot\left(1+\frac{1}{3}\right) \cdot\left(1+\frac{1}{4}\right) \cdot\left(1+\frac{1}{5}\right) \cdot\left(1+\frac{1}{6}\right)

$$

(A) $\frac{7}{6}$

(B) $\frac{4}{3}$

(C) $\frac{7}{2}$

(D) $7$

(E) $8$

**AMC 8, 2018, Problem 6**

On a trip to the beach, Anh traveled $50$ miles on the highway and $10$ miles on a coastal access road. He drove three times as fast on the highway as on the coastal road. If Anh spent $30$ minutes driving on the coastal road, how many minutes did his entire trip take?

(A) $50$

(B) $70$

(C) $80$

(D) $904$

(E) $100$

**AMC 8, 2018, Problem 9**

Bob is tiling the floor of his $12$ foot by $16$ foot living room. He plans to place one-foot by one-foot square tiles to form a border along the edges of the room and to fill in the rest of the floor with two-foot by two-foot square tiles. How many tiles will he use?

(A) $48$

(B) $87$

(C) $89$

(D) $96$

(E) $120$

**AMC 8, 2018, Problem 10**

The harmonic mean of a set of non-zero numbers is the reciprocal of the average of the reciprocals of the numbers. What is the harmonic mean of $1,2$ , and $4$ ?

(A) $\frac{3}{7}$

(B) $\frac{7}{12}$

(C) $\frac{12}{7}$

(D) $\frac{7}{4}$

(E) $\frac{7}{3}$

**AMC 8, 2018, Problem 12**

The clock in Sri's car, which is not accurate, gains time at a constant rate. One day as he begins shopping he notes that his car clock and his watch (which is accurate) both say $12: 00$ noon. When he is done shopping, his watch says $12: 30$ and his car clock says $12: 35$. Later that day, Sri loses his watch. He looks at his car clock and it says $7:00$. What is the actual time?

(A) $5: 50$

(B) $6: 00$

(C) $6: 30$

(D) $6: 55$

(E) $8: 10$

**AMC 8, 2018, Problem 25**

How many perfect cubes lie between $2^{8}+1$ and $2^{15}+1$, inclusive?

(A) $4$

(B) $9$

(C) $10$

(D) $57$

(E) $58$

**AMC 8, 2017, Problem 1**

Which of the following values is largest?

(A) $2+0+1+7$

(B) $2 \times 0+1+7$

(C) $2+0 \times 1+7$

(D) $2+0+1 \times 7$

(E) $2 \times 0 \times 1 \times 7$

**AMC 8, 2017, Problem 3**

What is the value of the expression $\sqrt{16 \sqrt{8 \sqrt{4}}}$ ?

(A) $4$

(B) $4 \sqrt{2}$

(C) $8$

(D) $8 \sqrt{2}$

(E) $16$

**AMC 8, 2017, Problem 4**

When $0.000315$ is multiplied by $7,928,564$ the product is closest to which of the following?

(A) $210$

(B) $240$

(C) $2100$

(D) $2400$

(E) $24000$

**AMC 8, 2017, Problem 5**

What is the value of the expression $\frac{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8}{1+2+3+4+5+6+7+8} ?$

(A) $1020$

(B) $1120$

(C) $1220$

(D) $2240$

(E) $3360$

**AMC 8, 2017, Problem 6**

If the degree measures of the angles of a triangle are in the ratio $3: 3: 4$, what is the degree measure of the largest angle of the triangle?

(A) $18$

(B) $36$

(C) $60$

(D) $72$

(E) $90$

**AMC 8, 2017, Problem 9**

All of Marcy's marbles are blue, red, green, or yellow. One third of her marbles are blue, one fourth of them are red, and six of them are green. What is the smallest number of yellow marbles that Macy could have?

(A) $1$

(B) $2$

(C) $3$

(D) $4$

(E) $5$

**AMC 8, 2017, Problem 11**

A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is $37$ , how many tiles cover the floor?

(A) $148$

(B) $3244$

(C) $361$

(D) $1296$

(E) $1369$

**AMC 8, 2017, Problem 14**

Chloe and Zoe are both students in Ms. Demeanor's math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to only $80 \%$ of the problems she solved alone, but overall $88 \%$ of her answers were correct. Zoe had correct answers to $90 \%$ of the problems she solved alone. What was Zoe's overall percentage of correct answers?

(A) $89$

(B) $92$

(C) $93$

(D) $96$

(E) $98$

**AMC 8, 2017, Problem 17**

Starting with some gold coins and some empty treasure chests, I tried to put $9$ gold coins in each treasure chest, but that left $2$ treasure chests empty. So instead I put $6$ gold coins in each treasure chest, but then I had $3$ gold coins left over. How many gold coins did I have?

(A) $9$

(B) $27$

(C) $45$

(D) $63$

(E) $81$

**AMC 8, 2017, Problem 23**

Each day for four days, Linda traveled for one hour at a speed that resulted in her traveling one mile in an integer number of minutes. Each day after the first, her speed decreased so that the number of minutes to travel one mile increased by $5$ minutes over the preceding day. Each of the four days, her distance traveled was also an integer number of miles. What was the total number of miles for the four trips?

(A) $10$

(B) $15$

(C) $25$

(D) $50$

(E) $82$

**AMC 8, 2016, Problem 1**

The longest professional tennis match ever played lasted a total of $11$ hours and $5$ minutes. How many minutes was this?

(A) $605$

(B) $655$

(C) $665$

(D) $1005$

(E) $1105$

**AMC 8, 2016, Problem 3**

Four students take an exam. Three of their scores are $70,80$ , and $90$. If the average of their four scores is $70$ , then what is the remaining score?

(A) $40$

(B) $50$

(C) $55$

(D) $60$

(E) $70$

**AMC 8, 2016, Problem 4**

When Cheenu was a boy he could run $15$ miles in $3$ hours and $30$ minutes. As an old man he can now walk $10$ miles in $4$ hours. How many minutes longer does it take for him to walk a mile now compared to when he was a boy?

(A) $6$

(B) $10$

(C) $15$

(D) $18$

(E) $30$

**AMC 8, 2016, Problem 7**

Which of the following numbers is not a perfect square?

(A) $1^{2016}$

(B) $2^{2017}$

(C) $3^{2018}$

(D) $4^{2019}$

(E) $5^{2020}$

**AMC 8, 2016, Problem 10**

Suppose that $a * b$ means $3 a-b$. What is the value of $x$ if

$$

2 *(5 * x)=1

$$

(A) $\frac{1}{10}$

(B) $2$

(C) $\frac{10}{3}$

(D) $10$

(E) $14$

**AMC 8, 2016, Problem 11**

Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by reversing its digits, the sum is $132$ .

(A) $5$

(B) $7$

(C) $9$

(D) $11$

(E) $12$

**AMC 8, 2016, Problem 12**

Jefferson Middle School has the same number of boys and girls. $\frac{3}{4}$ of the girls and $\frac{2}{3}$ of the boys went on a field trip. What fraction of the students on the field trip were girls?

(A) $\frac{1}{2}$

(B) $\frac{9}{17}$

(C) $\frac{7}{13}$

(D) $\frac{2}{3}$

(E) $\frac{14}{15}$

**AMC 8, 2016, Problem 14**

Karl's car uses a gallon of gas every $35$ miles, and his gas tank holds $14$ gallons when it is full. One day, Karl started with a full tank of gas, drove $350$ miles, bought $8$ gallons of gas, and continued driving to his destination. When he arrived, his gas tank was half full. How many miles did Karl drive that day?

(A) $525$

(B) $560$

(C) $595$

(D) $665$

(E) $735$

**AMC 8, 2016, Problem 16**

Annie and Bonnie are running laps around a $400$-meter oval track. They started together, but Annie has pulled ahead, because she runs $25 \%$ faster than Bonnie. How many laps will Annie have run when she first passes Bonnie?

(A) $1 \frac{1}{4}$

(B) $3 \frac{1}{3}$

(C) $4$

(D) $5$

(E) $25$

**AMC 8, 2015, Problem 3**

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?

(A) $5$

(B) $6$

(C) $8$

(D) $9$

(E) $10$

**AMC 8, 2015, Problem 9**

On her first day of work, Janabel sold one widget. On day two, she sold three widgets. On day three, she sold five widgets, and on each succeeding day, she sold two more widgets than she had sold on the previous day. How many widgets in total had Janabel sold after working $20$ days?

(A) $39$

(B) $40$

(C) $210$

(D) $400$

(E) $401$

**AMC 8, 2015, Problem 16**

In a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No ninth grader is assigned more than one sixth-grade buddy. If $\frac{1}{3}$ of all the ninth graders are paired with $\frac{2}{5}$ of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy?

(A) $\frac{2}{15}$

(B) $\frac{4}{11}$

(C) $\frac{11}{30}$

(D) $\frac{3}{8}$

(E) $\frac{11}{15}$

**AMC 8, 2015, Problem 17**

Jeremy's father drives him to school in rush hour traffic in $20$ minutes. One day there is no traffic, so his father can drive him $18$ miles per hour faster and gets him to school in $12$ minutes. How far in miles is it to school?

(A) $44$

(B) $6$

(C) $8$

(D) $9$

(E) $12$

**AMC 8, 2015, Problem 20**

Ralph went to the store and bought $12$ pairs of socks for a total of $\$ 24$. Some of the socks he bought cost $\$ 1$ a pair, some of the socks he bought cost $\$ 3$ a pair, and some of the socks he bought cost $\$ 4$ a pair. If he bought at least one pair of each type, how many pairs of $\$ 1$ socks did Ralph buy?

(A) $4$

(B) $5$

(C) $6$

(D) $7$

(E) $8$

**AMC 8, 2014, Problem 1**

Harry and Terry are each told to calculate $8-(2+5)$. Harry gets the correct answer. Terry ignores the parentheses and calculates $8-2+5$. If Harry's answer is $H$ and Terry's answer is $T$, what is $H-T$ ?

(A) $-10$

(B) $-6$

(C) $0$

(D) $6$

(E) $10$

**AMC 8, 2014, Problem 2**

Paul owes Paula $35$ cents and has a pocket full of $5$ -cent coins, $10$ -cent coins, and $25$ -cent coins that he can use to pay her. What is the difference between the largest and the smallest number of coins he can use to pay her?

(A) $1$

(B) $2$

(C) $3$

(D) $4$

(E) $5$

**AMC 8, 2014, Problem 3**

Isabella had a week to read a book for a school assignment. She read an average of $36$ pages per day for the first three days and an average of $44$ pages per day for the next three days. She then finished the book by reading $10$ pages on the last day. How many pages were in the book?

(A) $240$

(B) $250$

(C) $260$

(D) $270$

(E) $280$

**AMC 8, 2014, Problem 4**

The sum of two prime numbers is $85$ . What is the product of these two prime numbers?

(A) $85$

(B) $91$

(C) $115$

(D) $133$

(E) $166$

**AMC 8, 2015, Problem 5**

Margie's car can go $32$ miles on a gallon of gas, and gas currently costs $\$ 4$ per gallon. How many miles can Margie drive on $\$ 20$ worth of gas?

(A) $64$

(B) $128$

(C) $160$

(D) $320$

(E) $640$

**AMC 8, 2015, Problem 6**

Six rectangles each with a common base width of $2$ have lengths of $1,4,9,16,25$, and $36$ . What is the sum of the areas of the six rectangles?

(A) $91$

(B) $93$

(C) $162$

(D) $182$

(E) $202$

**AMC 8, 2015, Problem 7**

There are four more girls than boys in Ms. Raub's class of $28$ students. What is the ratio of number of girls to the number of boys in her class?

(A) $3: 4$

(B) $4: 3$

(C) $3: 2$

(D) $7: 4$

(E) $2: 1$

**AMC 8, 2015, Problem 10**

The first AMC 8 was given in $1985$ and it has been given annually since that time. Samantha turned $12$ years old the year that she took the seventh AMC 8 . In what year was Samantha born?

(A) $1979$

(B) $1980$

(C) $1981$

(D) $1982$

(E) $1983$

**AMC 8, 2014, Problem 17**

George walks $1$ mile to school. He leaves home at the same time each day, walks at a steady speed of $3$ miles per hour, and arrives just as school begins.

Today he was distracted by the pleasant weather and walked the first $\frac{1}{2}$ mile at a speed of only $2$ miles per hour. At how many miles per hour must George run the last $\frac{1}{2}$ mile in order to arrive just as school begins today?

(A) $4$

(B) $6$

(C) $8$

(D) $10$

(E) $12$

**AMC 8, 2014, Problem 19**

A cube with $3$ -inch edges is to be constructed from $27$ smaller cubes with $1$ -inch edges. Twenty-one of the cubes are colored red and $6$ are colored white. If the $3$ -inch cube is constructed to have the smallest possible white surface area showing, what fraction of the surface area is white?

(A) $\frac{5}{54}$

(B) $\frac{1}{9}$

(C) $\frac{5}{27}$

(D) $\frac{2}{9}$

(E) $\frac{1}{3}$

**AMC 8, 2014, Problem 24**

One day the Beverage Barn sold $252$ cans of soda to 100 customers, and every customer bought at least one can of soda. What is the maximum possible median number of cans of soda bought per customer on that day?

(A) $2.5$

(B) $3.0$

(C) $3.5$

(D) $4.0$

(E) $4.5$

**AMC 8, 2013, Problem 1**

Danica wants to arrange her model cars in rows with exactly $6$ cars in each row. She now has $23$ model cars. What is the smallest number of additional cars she must buy in order to be able to arrange all her cars this way?

(A) $1$

(B) $2$

(C) $3$

(D) $4$

(E) $5$

**AMC 8, 2013, Problem 2**

A sign at the fish market says, "$50\%$ off, today only: half-pound packages for just $\$ 3$ per package." What is the regular price for a full pound of fish, in dollars?

(A) $6$

(B) $9$

(C) $10$

(D) $12$

(E) $15$

**AMC 8, 2013, Problem 4**

Eight friends ate at a restaurant and agreed to share the bill equally. Because Judi forgot her money, each of her seven friends paid an extra $\$ 2.50$ to cover her portion of the total bill. What was the total bill?

(A) $\$ 120$

(B) $\$ 128$

(C) $\$ 140$

(D) $\$ 144$

(E) $\$ 160$

**AMC 8, 2013, Problem 7**

Trey and his mom stopped at a railroad crossing to let a train pass. As the train began to pass, Trey counted $6$ cars in the first $10$ seconds. It took the train $2$ minutes and $45$ seconds to clear the crossing at a constant speed. Which of the following was the most likely number of cars in the train?

(A) $60$

(B) $80$

(C) $100$

(D) $120$

(E) $140$

**AMC 8, 2013, Problem 10**

What is the ratio of the least common multiple of $180$ and $594$ to the greatest common factor of $180$ and $594$ ?

(A) $110$

(B) $165$

(C) $330$

(D) $625$

(E) $660$

**AMC 8, 2013, Problem 11**

Ted's grandfather used his treadmill on $3$ days this week. He went $2$ miles each day. On Monday he jogged at a speed of $5$ miles per hour. He walked at the rate of $3$ miles per hour on Wednesday and at $4$ miles per hour on Friday. If Grandfather had always walked at $4$ miles per hour, he would have spent less time on the treadmill. How many minutes less?

(A) $1$

(B) $2$

(C) $3$

(D) $4$

(E) $5$

**AMC 8, 2013, Problem 12**

At the $2013$ Winnebago County Fair a vendor is offering a 'fair special" on sandals. If you buy one pair of sandals at the regular price of $\$ 50$, you get a second pair at a $40 \%$ discount, and a third pair at half the regular price. Javier took advantage of the "fair special" to buy three pairs of sandals. What percentage of the $\$ 150$ regular price did he save?

(A) $25$

(B) $30$

(C) $33$

(D) $404$

(E) $45$

**AMC 8, 2013, Problem 13**

When Clara totaled her scores, she inadvertently reversed the units digit and the tens digit of one score. By which of the following might her incorrect sum have differed from the correct one?

(A) $45$

(B) $46$

(C) $47$

(D) $48$

(E) $49$

**AMC 8, 2013, Problem 14**

If $3^{p}+3^{4}=90,2^{r}+44=76$, and $5^{3}+6^{s}=1421$, what is the product of $p, r$, and $s$ ?

(A) $27$

(B) $40$

(C) $50$

(D) $70$

(E) $90$

**AMC 8, 2013, Problem 16**

A number of students from Fibonacci Middle School are taking part in a community service project. The ratio of $8^{\text {th }}$ -graders to $6^{\text {th }}$ -graders is $5: 3$, and the the ratio of $8^{\text {th }}$ -graders to $7^{\text {th. }}$ -graders is $8: 5$. What is the smallest number of students that could be participating in the project?

(A) $16$

(B) $40$

(C) $55$

(D) $79$

(E) $89$

**AMC 8, 2012, Problem 1**

Rachelle uses 3 pounds of meat to make 8 hamburgers for her family. How many pounds of meat does she need to make 24 hamburgers for a neighbourhood picnic?

(A) $6$

(B) $6 \frac{2}{3}$

(C) $7 \frac{1}{2}$

(D) $8$

(E) $9$

**AMC 8, 2012, Problem 2**

In the country of East Westmore, statisticians estimate there is a baby born every $8$ hours and a death every day. To the nearest hundred, how many people are added to the population of East Westmore each year?

(A) $600$

(B) $700$

(C) $800$

(D) $900$

(E) $1000$

**AMC 8, 2012, Problem 3**

On February 13 The Oshkosh Northwester listed the length of daylight as $10$ hours and $24$ minutes, the sunrise was $6: 57 \mathrm{AM}$, and the sunset as $8: 15 \mathrm{PM}$. The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set?

(A) $5: 10 \mathrm{PM}$

(B) $5: 21 \mathrm{PM}$

(C) $5: 41 \mathrm{PM}$

(D) $5: 57 \mathrm{PM}$

(E) $6: 03 \mathrm{PM}$

**AMC 8, 2012, Problem 4**

Peter's family ordered a $12$-slice pizza for dinner. Peter ate one slice and shared another slice equally with his brother Paul. What fraction of the pizza did Peter eat?

(A) $\frac{1}{24}$

(B) $\frac{1}{12}$

(C) $\frac{1}{8}$

(D) $\frac{1}{6}$

(E) $\frac{1}{4}$

**AMC 8, 2012, Problem 8**

A shop advertises everything is "half price in today's sale." In addition, a coupon gives a $20 \%$ discount on sale prices. Using the coupon, the price today represents what percentage off the original price?

(A) $10$

(B) $33$

(C) $40$

(D) $60$

(E) $70$

**AMC 8, 2012, Problem 9**

The Fort Worth Zoo has a number of two-legged birds and a number of four-legged mammals. On one visit to the zoo, Margie counted 200 heads and 522 legs. How many of the animals that Margie counted were two-legged birds?

(A) $61$

(B) $122$

(C) $139$

(D) $150$

(E) $161$

**AMC 8, 2012, Problem 13**

Jamar bought some pencils costing more than a penny each at the school bookstore and paid $\$ 1.43$. Sharona bought some of the same pencils and paid $\$ 1.87$. How many more pencils did Sharona buy than Jamar?

(A) $2$

(B) $3$

(C) $4$

(D) $5$

(E) $6$

**AMC 8, 2012, Problem 20**

What is the correct ordering of the three numbers $\frac{5}{19}, \frac{7}{21}$, and $\frac{9}{23}$, in increasing order?

(A) $\frac{9}{23}<\frac{7}{21}<\frac{5}{19}$

(B) $\frac{5}{19}<\frac{7}{21}<\frac{9}{23}$

(C) $\frac{9}{23}<\frac{5}{19}<\frac{7}{21}$

(D) $\frac{5}{19}<\frac{9}{23}<\frac{7}{21}$

(E) $\frac{7}{21}<\frac{5}{19}<\frac{9}{23}$

**AMC 8, 2011, Problem 1**

Margie bought $3$ apples at a cost of $50$ cents per apple. She paid with a $5$-dollar bill. How much change did Margie receive?

(A) $\$ 1.50$

(B) $\$ 2.00$

(C) $\$ 2.50$

(D) $\$ 3.00$

(E) $\$ 3.50$

**AMC 8, 2011, Problem 6**

In a town of $351$ adults, every adult owns a car, motorcycle, or both. If $331$ adults own cars and $45$ adults own motorcycles, how many of the car owners do not own a motorcycle?

(A) $20$

(B) $25$

(C) $45$

(D) $306$

(E) $351$

**AMC 8, 2011, Problem 10**

The taxi fare in Gotham City is $\$ 2.40$ for the first $\frac{1}{2}$ mile and additional mileage charged at the rate $\$ 0.20$ for each additional $0.1$ mile. You plan to give the driver a $\$ 2$ tip. How many miles can you ride for $\$ 10 ?$

(A) $3.0$

(B) $3.25$

(C) $3.3$

(D) $3.5$

(E) $3.75$

**AMC 8, 2011, Problem 14**

There are 270 students at Colfax Middle School, where the ratio of boys to girls is $5: 4$. There are 180 students at Winthrop Middle School, where the ratio of boys to girls is $4: 5$. The two schools hold a dance and all students from both schools attend. What fraction of the students at the dance are girls?

(A) $\frac{7}{18}$

(B) $\frac{7}{15}$

(C) $\frac{22}{45}$

(D) $\frac{1}{2}$

(E) $\frac{23}{45}$

**AMC 8, 2011, Problem 17**

Let $w, x, y$, and $z$ be whole numbers. If $2^{w} \cdot 3^{x} \cdot 5^{y} \cdot 7^{x}=588$, then what does $2 w+3 x+5 y+7 z$ equal?

(A) $21$

(B) $25$

(C) $27$

(D) $35$

(E) $56$

**AMC 8, 2010, Problem 1**

At Euclid Middle School the mathematics teachers are Mrs. Germain, Mr. Newton, and Mrs. Young. There are $11$ students in Mrs. Germain's class, $8$ students in Mr. Newton's class, and $9$ students in $\mathrm{Mrs}$. Young's class taking the AMC $8$ this year. How many mathematics students at Euclid Middle School are taking the contest?

(A) $26$

(B) $27$

(C) $28$

(D) $29$

(E) $30$

**AMC 8, 2010, Problem 5**

Alice needs to replace a light bulb located 10 centimeters below the ceiling in her kitchen. The ceiling is $2.4$ meters above the floor. Alice is $1.5$ meters tall and can reach 46 centimeters above the top of her head. Standing on a stool, she can just reach the light bulb. What is the height of the stool, in centimeters?

(A) $32$

(B) $34$

(C) $36$

(D) $38$

(E) $40$

**AMC 8, 2010, Problem 7**

Using only pennies, nickels, dimes, and quarters, what is the smallest number of coins Freddie would need so he could pay any amount of money less than a dollar?

(A) $6$

(B) $10$

(C) $15$

(D) $25$

(E) $99$

**AMC 8, 2010, Problem 8**

As Emily is riding her bicycle on a long straight road, she spots Emerson skating in the same direction $1 / 2$ mile in front of her. After she passes him, she can see him in her rear mirror until he is $1 / 2$ mile behind her. Emily rides at a constant rate of $12$ miles per hour, and Emerson skates at a constant rate of $8$ miles per hour. For how many minutes can Emily see Emerson?

(A) $6$

(B) $8$

(C) $12$

(D) $15$

(E) $16$

**AMC 8, 2010, Problem 9**

Ryan got $80 \%$ of the problems correct on a 25-problem test, $90 \%$ on a 40-problem test, and $70 \%$ on a 10-problem test. What percent of all the problems did Ryan answer correctly?

(A) $64$

(B) $75$

(C) $80$

(D) $84$

(E) $86$

**AMC 8, 2010, Problem 10**

Six pepperoni circles will exactly fit across the diameter of a $12$ -inch pizza when placed. If a total of $24$ circles of pepperoni are placed on this pizza without overlap, what fraction of the pizza is covered by pepperoni?

(A) $\frac{1}{2}$

(B) $\frac{2}{3}$

(C) $\frac{3}{4}$

(D) $\frac{5}{6}$

(E) $\frac{7}{8}$

**AMC 8, 2010, Problem 11**

The top of one tree is $16$ feet higher than the top of another tree. The heights of the two trees are in the ratio $3: 4$. In feet, how tall is the taller tree?

(A) $48$

(B) $64$

(C) $80$

(D) $96$

(E) $112$

**AMC 8, 2010, Problem 12**

Of the 500 balls in a large bag, $80 \%$ are red and the rest are blue. How many of the red balls must be removed so that $75 \%$ of the remaining balls are red?

(A) $25$

(B) $50$

(C) $75$

(D) $100$

(E) $150$

**AMC 8, 2010, Problem 13**

The lengths of the sides of a triangle in inches are three consecutive integers. The length of the shortest side is $30 \%$ of the perimeter. What is the length of the longest side?

(A) $7$

(B) $8$

(C) $9$

(D) $10$

(E) $11$

**AMC 8, 2010, Problem 15**

A jar contains 5 different colors of gumdrops. $30 \%$ are blue, $20 \%$ are brown, $15 \%$ are red, $10 \%$ are yellow, and other 30 gumdrops are green. half of the blue gumdrops are replaced with brown gumdrops, how many gumdrops will be brown?

(A) $35$

(B) $36$

(C) $42$

(D) $48$

(E) $64$

**AMC 8, 2010, Problem 16**

A square and a circle have the same area. What is the ratio of the side length of the square to the radius of the circle?

(A) $\frac{\sqrt{\pi}}{2}$

(B) $\sqrt{\pi}$

(C) $\pi$

(D) $2 \pi$

$(\mathbf{E}) \pi^{2}$

**AMC 8, 2010, Problem 24**

What is the correct ordering of the three numbers, $10^{\mathrm{s}}, 5^{12}$, and $2^{24}$ ?

(A) $2^{24}<10^{8}<5^{12}$

(B) $2^{24}<5^{12}<10^{8}$

(C) $5^{12}<2^{24}<10^{8}$

(D) $10^{8}<5^{12}<2^{24}$

(E) $10^{8}<2^{24}<5^{12}$

**AMC 8, 2009, Problem 1**

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?

(A) $3$

(B) $4$

(C) $7$

(D) $11$

(E) $14$

**AMC 8, 2009, Problem 2**

On average, for every 4 sports cars sold at the local 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?

(A) $7$

(B) $32$

(C) $35$

(D) $49$

(E) $112$

**AMC 8, 2009, Problem 6**

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 wate per minute. How many hours will it take to fill Steve's pool?

(A) $40$

(B) $42$

(C) $44$

(D) $46$

(E) $48$

**AMC 8, 2009, Problem 7**

If $\frac{3}{5}=\frac{M}{45}=\frac{60}{N^{\prime}}$ what is $M+N ?$

(A) $27$ (B) $29$ (C) $45$ (D) $105$ (E) $127$

**AMC 8, 2009, Problem 11**

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?

(A) $1$

(B) $2$

(C) $3$

(D) $4$

(E) $5$

**AMC 8, 2009, Problem 14**

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) $46$

(B) $48$

(C) $50$

(D) $52$

(E) $54$

**AMC 8, 2009, Problem 15**

A recipe that makes 5 servings of hot chocolate requires 2 squares of chocolate, $\frac{1}{4}$ 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 he maintains the same ratio of ingredients, what is the greatest number of servings of hot chocolate he can make?

(A) $5 \frac{1}{8}$

(B) $6 \frac{1}{4}$

(C) $7 \frac{1}{2}$

(D) $8 \frac{3}{4}$

(E) $9 \frac{7}{8}$

**AMC 8, 2009, Problem 21**

Andy and Bethany have a rectangular array of numbers greater than zero with 40 rows and 75 columns. Andy adds the numbers in each row. The average of his 40 sums is $A$. Bethany adds the numbers in each column. The average of her 75 sums is $B$. Using only the answer choices given, What is the value of $\frac{A}{B}$ ?

(A) $\frac{64}{225}$

(B) $\frac{8}{15}$

(C) $1$

(D) $\frac{15}{8}$

(E) $\frac{225}{64}$

**AMC 8, 2009, Problem 23**

On the last day of school, Mrs. Awesome gave jelly beans to her class. She gave each boy as many jelly beans as there were boys in the class. She gave each girl as many jelly beans as there were girls in the class. She brought 400 jelly beans, and when she finished, she had six jelly beans left. There were two more boys than girls in her class. How many students were in her class?

(A) $26$

(B) $28$

(C) $30$

(D) $32$

(E) $34$

**AMC 8, 2007, Problem 18**

The product of the two $99$ -digit numbers $303,030,303, \ldots, 030,303$ and $505,050,505, \ldots, 050,505$ has thousands digit $A$ and units digit $B$. What is the sum of $A$ and $B$ ?

(A) $3$

(B) $5$

(C) $6$

(D) $8$

(E) $10$

**AMC 8, 2007, Problem 19**

Pick two consecutive positive integers whose sum is less than $100 .$ Square both of those integers and then find the difference of the squares. Which of the following could be the difference?

(A) $2$

(B) $64$

(C) $79$

(D) $96$

(E) $131$

**AMC 8, 2004, Problem 9**

The average of the five numbers in a list is $54$ . The average of the first two numbers is $48 .$ What is the average of the last three numbers?

(A) $55$

(B) $56$

(C) $57$

(D) $58$

(E) $59$

**AMC 8, 2004, Problem 10**

Handy Aaron helped a neighbor $1 \frac{1}{4}$ hours on Monday, $50$ minutes on Tuesday, from $8: 20$ to $10: 45$ on Wednesday morning, and a half-hour on Friday. He is paid $\$ 3$ per hour. How much did he earn for the week?

(A) $\$ 8$

(B) $\$ 9$

(C) $\$ 10$

(D) $\$ 12$

(E) $\$ 15$

**AMC 8, 2004, Problem 11**

The numbers $-2,4,6,9$ and $12$ are rearranged according to these rules:

The largest isn't first, but it is in one of the first three places. The smallest isn't last, but it is in one of the last three places. The median isn't first or last.

What is the average of the first and last numbers?

(A) $3.5$

(B) $5$

(C) $6.5$

(D) $7.5$

(E) $8$

**AMC 8, 2004, Problem 12**

Niki usually leaves her cell phone on. If her cell phone is on but she is not actually using it, the battery will last for $24$ hours. If she is using it constantly, the battery will last for only $3$ hours. Since the last recharge, her phone has been on 9 hours, and during that time she has used it for $60$ minutes. If she doesn't talk anymore but leaves the phone on, how many more hours will the battery last?

(A) $7$

(B) $8$

(C) $11$

(D) $14$

(E) $15$

**AMC 8, 2001, Problem 12**

If $a \otimes b=\frac{a+b}{a-b}$, then $(6 \otimes 4) \otimes 3=$

(A) $4$

(B) $13$

(C) $15$

(D) $30$

(E) $72$

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