Competition · AMC preparation · step 4 of 4

AMC 10 2004A: all 25 problems

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

AMC 10 2004A #1 grade 4+ arithmetic
You and five friends need to raise 1500 dollars in donations for a charity, dividing the fundraising equally. How many d…
AMC 10 2004A #2 grade 7+ arithmetic
For any three real numbers a, b, and c, with b≠ c, the operation otimes is defined by: otimes(a,b,c)=a/(b-c) What is oti…
AMC 10 2004A #3 grade 6+ arithmetic
Alicia earns 20 dollars per hour, of which 1.45% is deducted to pay local taxes. How many cents per hour of Alicia's wag…
AMC 10 2004A #4 grade 7+ algebra
What is the value of x if |x-1|=|x-2|?
AMC 10 2004A #5 grade 7+ probability
A set of three points is randomly chosen from the grid shown. Each three point set has the same probability of being cho…
AMC 10 2004A #6 grade 4+ arithmetic
Bertha has 6 daughters and no sons. Some of her daughters have 6 daughters, and the rest have none. Bertha has a total o…
AMC 10 2004A #7 grade 4+ geometry-3d
A grocer stacks oranges in a pyramid-like stack whose rectangular base is 5 oranges by 8 oranges. Each orange above the…
AMC 10 2004A #8 grade 4+ arithmetic
A game is played with tokens according to the following rule. In each round, the player with the most tokens gives one t…
AMC 10 2004A #9 grade 6+ geometry-2d
In the overlapping triangles △ABC and △ABE sharing common side AB, ∠EAB and ∠ABC are right angles, AB=4, BC=6, AE=8, and…
AMC 10 2004A #10 grade 7+ probability
Coin A is flipped three times and coin B is flipped four times. What is the probability that the number of heads obtaine…
AMC 10 2004A #11 grade 8+ geometry-3d
A company sells peanut butter in cylindrical jars. Marketing research suggests that using wider jars will increase sales…
AMC 10 2004A #12 grade 7+ counting
Henry's Hamburger Haven offers its hamburgers with the following condiments: ketchup, mustard, mayonnaise, tomato, lettu…
AMC 10 2004A #13 grade 4+ arithmetic
At a party, each man danced with exactly three women and each woman danced with exactly two men. Twelve men attended the…
AMC 10 2004A #14 grade 8+ arithmetic
The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is 20 cents. If she had one more qua…
AMC 10 2004A #15 grade 7+ algebra
Given that -4≤ x≤-2 and 2≤ y≤4, what is the largest possible value of (x+y)/x?
AMC 10 2004A #16 grade 3+ geometry-2d
The 5× 5 grid shown contains a collection of squares with sizes from 1× 1 to 5× 5. How many of these squares contain the…
AMC 10 2004A #17 grade 7+ rate-ratio
Brenda and Sally run in opposite directions on a circular track, starting at diametrically opposite points. They first m…
AMC 10 2004A #18 grade 8+ algebra
A sequence of three real numbers forms an arithmetic progression with a first term of 9. If 2 is added to the second ter…
AMC 10 2004A #19 grade 7+ geometry-2d
A white cylindrical silo has a diameter of 30 feet and a height of 80 feet. A red stripe with a horizontal width of 3 fe…
AMC 10 2004A #20 grade 8+ geometry-2d
Points E and F are located on square ABCD so that △ BEF is equilateral. What is the ratio of the area of △ DEF to that o…
AMC 10 2004A #21 grade 8+ geometry-2d
Two distinct lines pass through the center of three concentric circles of radii 3, 2, and 1. The area of the shaded regi…
AMC 10 2004A #22 grade 8+ geometry-2d
Square ABCD has side length 2. A semicircle with diameter AB is constructed inside the square, and the tangent to the se…
AMC 10 2004A #23 grade 8+ geometry-2d
Circles A, B and C are externally tangent to each other, and internally tangent to circle D. Circles B and C are congrue…
AMC 10 2004A #24 grade 8+ arithmetic
Let f be a function with the following properties: (i) f(1) = 1, and (ii) f(2n) = n · f(n) for any positive integer n. W…
AMC 10 2004A #25 grade 8+ geometry-3d
Three mutually tangent spheres of radius 1 rest on a horizontal plane. A sphere of radius 2 rests on them. What is the d…

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