Competition · AMC preparation · step 4 of 4

AMC 10 2004B: 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 2004B #1 grade 4+ arithmetic
Each row of the Misty Moon Amphitheater has 33 seats. Rows 12 through 22 are reserved for a youth club. How many seats a…
AMC 10 2004B #2 grade 3+ arithmetic
How many two-digit positive integers have at least one 7 as a digit?
AMC 10 2004B #3 grade 4+ arithmetic
At each basketball practice last week, Jenny made twice as many free throws as she made at the previous practice. At her…
AMC 10 2004B #4 grade 6+ number-theory
A standard six-sided die is rolled, and P is the product of the five numbers that are visible. What is the largest numbe…
AMC 10 2004B #5 grade 6+ algebra
In the expression c· a^b-d, the values of a, b, c, and d are 0, 1, 2, and 3, although not necessarily in that order. Wha…
AMC 10 2004B #6 grade 8+ number-theory
Which of the following numbers is a perfect square?
AMC 10 2004B #7 grade 7+ arithmetic
On a trip from the United States to Canada, Isabella took d U.S. dollars. At the border she exchanged them all, receivin…
AMC 10 2004B #8 grade 8+ geometry-2d
Minneapolis-St. Paul International Airport is 8 miles southwest of downtown St. Paul and 10 miles southeast of downtown…
AMC 10 2004B #9 grade 7+ geometry-2d
A square has sides of length 10, and a circle centered at one of its vertices has radius 10. What is the area of the uni…
AMC 10 2004B #10 grade 4+ arithmetic
A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row abov…
AMC 10 2004B #11 grade 7+ probability
Two eight-sided dice each have faces numbered 1 through 8. When the dice are rolled, each face has an equal probability…
AMC 10 2004B #12 grade 8+ geometry-2d
An annulus is the region between two concentric circles. The concentric circles in the figure have radii b and c, with b…
AMC 10 2004B #13 grade 6+ arithmetic
In the United States, coins have the following thicknesses: penny, 1.55 mm; nickel, 1.95 mm; dime, 1.35 mm; quarter, 1.7…
AMC 10 2004B #14 grade 6+ rate-ratio
A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag un…
AMC 10 2004B #15 grade 4+ arithmetic
Patty has 20 coins consisting of nickels and dimes. If her nickels were dimes and her dimes were nickels, she would have…
AMC 10 2004B #16 grade 8+ geometry-2d
Three circles of radius 1 are externally tangent to each other and internally tangent to a larger circle. What is the ra…
AMC 10 2004B #17 grade 6+ arithmetic
The two digits in Jack's age are the same as the digits in Bill's age, but in reverse order. In five years Jack will be…
AMC 10 2004B #18 grade 8+ geometry-2d
In the right triangle △ ACE, we have AC=12, CE=16, and EA=20. Points B, D, and F are located on AC, CE, and EA, respecti…
AMC 10 2004B #19 grade 6+ arithmetic
In the sequence 2001, 2002, 2003, … , each term after the third is found by subtracting the previous term from the sum o…
AMC 10 2004B #20 grade 7+ geometry-2d
In △ ABC points D and E lie on BC and AC, respectively. If AD and BE intersect at T so that AT/DT=3 and BT/ET=4, what is…
AMC 10 2004B #21 grade 6+ arithmetic
Let 1; 4; 7; … and 9; 16; 23; … be two arithmetic progressions. The set S is the union of the first 2004 terms of each s…
AMC 10 2004B #22 grade 8+ geometry-2d
A triangle with sides of 5, 12, and 13 has both an inscribed and a circumscribed circle. What is the distance between th…
AMC 10 2004B #23 grade 7+ geometry-3d
Each face of a cube is painted either red or blue, each with probability 1/2. The color of each face is determined indep…
AMC 10 2004B #24 grade 8+ geometry-2d
In triangle ABC we have AB=7, AC=8, BC=9. Point D is on the circumscribed circle of the triangle so that AD bisects angl…
AMC 10 2004B #25 grade 8+ geometry-2d
A circle of radius 1 is internally tangent to two circles of radius 2 at points A and B, where AB is a diameter of the s…

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