Arithmetic
How Many Ways?
Math
About AMC
100
On a map, a 12-centimeter length represents 72 kilometers. How many kilometers does a 17-centimeter length represent?
102 kilometers
100
Twelve friends met for dinner at Oscar's Overstuffed Oyster House, and each ordered one meal. The portions were so large, there was enough food for 18 people. If they shared, how many meals should they have ordered to have just enough food for the 12 of them?
8
100
Ms. Hamilton’s eighth-grade class wants to participate in the annual three-person-team basketball tournament. Lance, Sally, Joy, and Fred are chosen for the team. In how many ways can the three starters be chosen?
4
100
What does AMC stand for?
American Mathematics Competition
200
After Sally takes 20 shots, she has made 55% of her shots. After she takes 5 more shots, she raises her percentage to 56%. How many of the last 5 shots did she make?
3 shots
200
Three friends have a total of 6 identical pencils, and each one has at least one pencil. In how many ways can this happen?
10
200
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?
What is 58?
200
Who is eligible in participating AMC 8?
Students with a passion for problem-solving who are in grade 8 or below and under 14.5 years of age on the day of the competition.
300
The numbers -2, 4, 6, 9 and 12 are rearranged according to these rules:
1. The largest isn’t first, but it is in one of the first three places.
2. The smallest isn’t last, but it is in one of the last three places.
3. The median isn’t first or last.
What is the average of the first and last numbers?
6.5
300
Amy, Bill and Celine are friends with different ages. Exactly one of the following statements is true.
I. Bill is the oldest. II. Amy is not the oldest. III. Celine is not the youngest.
Rank the friends from the oldest to the youngest.
What is Amy, Celine, Bill?
300
The Little Twelve Basketball Conference has two divisions, with six teams in each division. Each team plays each of the other teams in its own division twice and every team in the other division once. How many conference games are scheduled?
What is 96?
300
What is the format of AMC 8 and how long is the test?
25 MCQ questions, 40 minutes
400
Find the number of two-digit positive integers whose digits total 7.
7
400
Five friends compete in a dart-throwing contest. Each one has two darts to throw at the same circular target, and each individual's score is the sum of the scores in the target regions that are hit. The scores for the target regions are the whole numbers 1 through 10. Each throw hits the target in a region with a different value. The scores are: Alice 16 points, Ben 4 points, Cindy 7 points, Dave 11 points, and Ellen 17 points. Who hits the region worth 6 points?
Who is Alice?
400
A whole number larger than 2 leaves a remainder of 2 when divided by each of the numbers 3, 4, 5, and 6. The smallest such number is...
62.
400
List 5 topics covered in AMC 8.
counting and probability, estimation, proportional reasoning, elementary geometry including the Pythagorean Theorem, spatial visualization, reading and interpreting graphs and tables, linear or quadratic functions and equations, coordinate geometry, and other topics traditionally covered in a beginning algebra course.
500
Two-thirds of the people in a room are seated in three-fourths of the chairs. The rest of the people are standing. If there are 6 empty chairs, how many people are in the room?
27
500
Name the 5 friends of the show "Friends".
Phoebe, Joey, Monica, Chandler, Rachel, and Ross
500
Handy Aaron helped a neighbor 1 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?
What is 15?
500
Who is qualified for The American Invitational Mathematics Examination (AIME)?
For AMC 10, invitations are issued to at least the top 2.5% of all scorers. For AMC 12, invitations are issued to at least the top 5% of all scorers.