Competition · AMC preparation · step 4 of 4

AMC 8 2001: 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 2001 #1 grade 4+ arithmetic, rate-ratio
Casey's shop class is making a golf trophy. He has to paint 300 dimples on a golf ball. If it takes him 2 seconds to pai…
AMC 8 2001 #2 grade 4+ arithmetic, number-theory
I'm thinking of two whole numbers. Their product is 24 and their sum is 11. What is the larger number?
AMC 8 2001 #3 grade 6+ arithmetic
Granny Smith has $63. Elberta has $2 more than Anjou and Anjou has one-third as much as Granny Smith. How many dollars d…
AMC 8 2001 #4 grade 4+ number-theory, arithmetic
The digits 1, 2, 3, 4 and 9 are each used once to form the smallest possible even five-digit number. The digit in the te…
AMC 8 2001 #5 grade 6+ rate-ratio, arithmetic
On a dark and stormy night Snoopy suddenly saw a flash of lightning. Ten seconds later he heard the sound of thunder. Th…
AMC 8 2001 #6 grade 4+ arithmetic, pattern
Six trees are equally spaced along one side of a straight road. The distance from the first tree to the fourth is 60 fee…
AMC 8 2001 #7 grade 6+ geometry-2d
To promote her school's annual Kite Olympics, Genevieve makes a small kite and a large kite for a bulletin board display…
AMC 8 2001 #8 grade 5+ geometry-2d, rate-ratio
To promote her school's annual Kite Olympics, Genevieve makes a small kite and a large kite for a bulletin board display…
AMC 8 2001 #9 grade 7+ geometry-2d
To promote her school's annual Kite Olympics, Genevieve makes a small kite and a large kite for a bulletin board display…
AMC 8 2001 #10 grade 6+ arithmetic, rate-ratio
A collector offers to buy state quarters for 2000% of their face value. At that rate how much will Bryden get for his fo…
AMC 8 2001 #11 grade 6+ geometry-2d
Points A, B, C and D have these coordinates: A(3,2), B(3,-2), C(-3,-2) and D(-3, 0). The area of quadrilateral ABCD is
AMC 8 2001 #12 grade 6+ arithmetic, algebra
If aotimes b = (a + b)/(a - b), then (6otimes 4)otimes 3 =
AMC 8 2001 #13 grade 6+ arithmetic, rate-ratio
Of the 36 students in Richelle's class, 12 prefer chocolate pie, 8 prefer apple, and 6 prefer blueberry. Half of the rem…
AMC 8 2001 #14 grade 4+ counting
Tyler has entered a buffet line in which he chooses one kind of meat, two different vegetables and one dessert. If the o…
AMC 8 2001 #15 grade 6+ rate-ratio, algebra
Homer began peeling a pile of 44 potatoes at the rate of 3 potatoes per minute. Four minutes later Christen joined him a…
AMC 8 2001 #16 grade 4+ geometry-2d, rate-ratio
A square piece of paper, 4 inches on a side, is folded in half vertically. Both layers are then cut in half parallel to…
AMC 8 2001 #17 grade 6+ rate-ratio, pattern
For the game show Who Wants To Be A Millionaire?, the dollar values of each question are shown in the following table (w…
AMC 8 2001 #18 grade 7+ probability, counting
Two dice are thrown. What is the probability that the product of the two numbers is a multiple of 5?
AMC 8 2001 #19 grade 6+ rate-ratio
Car M traveled at a constant speed for a given time. This is shown by the dashed line. Car N traveled at twice the speed…
AMC 8 2001 #20 grade 6+ logic
Kaleana shows her test score to Quay, Marty and Shana, but the others keep theirs hidden. Quay thinks, "At least two of…
AMC 8 2001 #21 grade 6+ arithmetic, number-theory
The mean of a set of five different positive integers is 15. The median is 18. The maximum possible value of the largest…
AMC 8 2001 #22 grade 6+ number-theory, arithmetic
On a twenty-question test, each correct answer is worth 5 points, each unanswered question is worth 1 point and each inc…
AMC 8 2001 #23 grade 8+ geometry-2d, counting
Points R, S and T are vertices of an equilateral triangle, and points X, Y and Z are midpoints of its sides. How many no…
AMC 8 2001 #24 grade 6+ counting, logic
Each half of this figure is composed of 3 red triangles, 5 blue triangles and 8 white triangles. When the upper half is…
AMC 8 2001 #25 grade 5+ number-theory
There are 24 four-digit whole numbers that use each of the four digits 2, 4, 5 and 7 exactly once. Only one of these fou…

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