Competition · AMC preparation · step 4 of 4

AMC 8 2004: all 25 problems

Each problem has a solution worked from first principles and the first grade (by CCSS standards) that can solve it.

AMC 8 2004 #1 grade 6+ arithmetic
On a map, a 12-centimeter length represents 72 kilometers. How many kilometers does a 17-centimeter length represent?
AMC 8 2004 #2 grade 3+ counting
How many different four-digit numbers can be formed by rearranging the four digits in 2004?
AMC 8 2004 #3 grade 6+ arithmetic
Twelve friends met for dinner at Oscar's Overstuffed Oyster House, and each ordered one meal. The portions were so large…
AMC 8 2004 #4 grade 3+ counting
Ms. Hamilton’s eighth-grade class wants to participate in the annual three-person-team basketball tournament. Lance, Sal…
AMC 8 2004 #5 grade 3+ counting
Ms. Hamilton's eighth-grade class wants to participate in the annual three-person-team basketball tournament. The losing…
AMC 8 2004 #6 grade 6+ arithmetic
After Sally takes 20 shots, she has made 55% of her shots. After she takes 5 more shots, she raises her percentage to 56…
AMC 8 2004 #7 grade 6+ rate-ratio
An athlete's target heart rate, in beats per minute, is 80% of the theoretical maximum heart rate. The maximum heart rat…
AMC 8 2004 #8 grade 6+ counting
Find the number of two-digit positive integers whose digits total 7.
AMC 8 2004 #9 grade 6+ arithmetic
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…
AMC 8 2004 #10 grade 5+ arithmetic
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…
AMC 8 2004 #11 grade 6+ counting
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…
AMC 8 2004 #12 grade 6+ rate-ratio
Niki usually leaves her cell phone on. If her cell phone is on but she is not actually using it, the battery will last f…
AMC 8 2004 #13 counting
Amy, Bill and Celine are friends with different ages. Exactly one of the following statements is true. I. Bill is the ol…
AMC 8 2004 #14 grade 6+ geometry-2d
What is the area enclosed by the geoboard quadrilateral below?
AMC 8 2004 #15 grade 4+ counting
Thirteen black and six white hexagonal tiles were used to create the figure below. If a new figure is created by attachi…
AMC 8 2004 #16 grade 5+ rate-ratio
Two 600 mL pitchers contain orange juice. One pitcher is 1/3 full and the other pitcher is 2/5 full. Water is added to f…
AMC 8 2004 #17 grade 4+ counting
Three friends have a total of 6 identical pencils, and each one has at least one pencil. In how many ways can this happe…
AMC 8 2004 #18 grade 3+ counting
Five friends compete in a dart-throwing contest. Each one has two darts to throw at the same circular target, and each i…
AMC 8 2004 #19 grade 6+ number-theory
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 su…
AMC 8 2004 #20 grade 5+ arithmetic
Two-thirds of the people in a room are seated in three-fourths of the chairs. The rest of the people are standing. If th…
AMC 8 2004 #21 grade 7+ probability
Spinners A and B are spun. On each spinner, the arrow is equally likely to land on each number. What is the probability…
AMC 8 2004 #22 grade 7+ probability
At a party there are only single women and married men with their wives. The probability that a randomly selected woman…
AMC 8 2004 #23 grade 8+ rate-ratio
Tess runs counterclockwise around rectangular block JKLM. She lives at corner J. Which graph could represent her straigh…
AMC 8 2004 #24 grade 8+ geometry-2d
In the figure, ABCD is a rectangle and EFGH is a parallelogram. Using the measurements given in the figure, what is the…
AMC 8 2004 #25 grade 8+ geometry-2d
Two 4 × 4 squares intersect at right angles, bisecting their intersecting sides, as shown. The circle's diameter is the…

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