Competition · AMC preparation · step 4 of 4

AMC 8 2007: 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 2007 #1 grade 6+ arithmetic
Theresa's parents have agreed to buy her tickets to see her favorite band if she spends an average of 10 hours per week…
AMC 8 2007 #2 grade 6+ rate-ratio
650 students were surveyed about their pasta preferences. The choices were lasagna, manicotti, ravioli and spaghetti. Th…
AMC 8 2007 #3 grade 4+ number-theory
What is the sum of the two smallest prime factors of 250?
AMC 8 2007 #4 grade 4+ counting
A haunted house has six windows. In how many ways can Georgie the Ghost enter the house by one window and leave by a dif…
AMC 8 2007 #5 grade 6+ arithmetic
Chandler wants to buy a 500 dollar mountain bike. For his birthday, his grandparents send him 50 dollars, his aunt sends…
AMC 8 2007 #6 grade 6+ rate-ratio
The average cost of a long-distance call in the USA in 1985 was 41 cents per minute, and the average cost of a long-dist…
AMC 8 2007 #7 grade 6+ arithmetic
The average age of 5 people in a room is 30 years. An 18-year-old person leaves the room. What is the average age of the…
AMC 8 2007 #8 grade 6+ geometry-2d
In trapezoid ABCD, AD is perpendicular to DC, AD = AB = 3, and DC = 6. In addition, E is on DC, and BE is parallel to AD…
AMC 8 2007 #9 grade 4+ logic
To complete the grid below, each of the digits 1 through 4 must occur once in each row and once in each column. What num…
AMC 8 2007 #10 grade 5+ number-theory
For any positive integer n, define n to be the sum of the positive factors of n. For example, 6 = 1 + 2 + 3 + 6 = 12. Fi…
AMC 8 2007 #11 grade 4+ logic
Tiles I, II, III and IV are translated so one tile coincides with each of the rectangles A, B, C and D. In the final arr…
AMC 8 2007 #12 grade 6+ geometry-2d
A unit hexagram is composed of a regular hexagon of side length 1 and its 6 equilateral triangular extensions, as shown…
AMC 8 2007 #13 grade 4+ counting
Sets A and B, shown in the Venn diagram, have the same number of elements. Their union has 2007 elements and their inter…
AMC 8 2007 #14 grade 8+ geometry-2d
The base of isosceles △ ABC is 24 and its area is 60. What is the length of one of the congruent sides?
AMC 8 2007 #15 grade 6+ logic
Let a, b and c be numbers with 0 < a < b < c. Which of the following is impossible?
AMC 8 2007 #16 grade 8+ geometry-2d
Amanda Reckonwith draws five circles with radii 1, 2, 3, 4 and 5. Then for each circle she plots the point (C,A), where…
AMC 8 2007 #17 grade 6+ rate-ratio
A mixture of 30 liters of paint is 25% red tint, 30% yellow tint and 45% water. Five liters of yellow tint are added to…
AMC 8 2007 #18 grade 5+ number-theory
The product of the two 99-digit numbers 303,030,303,...,030,303 and 505,050,505,...,050,505 has thousands digit A and un…
AMC 8 2007 #19 grade 6+ number-theory
Pick two consecutive positive integers whose sum is less than 100. Square both of those integers and then find the diffe…
AMC 8 2007 #20 grade 6+ algebra
Before the district play, the Unicorns had won 45% of their basketball games. During district play, they won six more ga…
AMC 8 2007 #21 grade 7+ probability
Two cards are dealt from a deck of four red cards labeled A, B, C, D and four green cards labeled A, B, C, D. A winning…
AMC 8 2007 #22 grade 6+ geometry-2d
A lemming sits at a corner of a square with side length 10 meters. The lemming runs 6.2 meters along a diagonal toward t…
AMC 8 2007 #23 grade 6+ geometry-2d
What is the area of the shaded pinwheel shown in the 5 × 5 grid?
AMC 8 2007 #24 grade 7+ probability
A bag contains four pieces of paper, each labeled with one of the digits 1, 2, 3 or 4, with no repeats. Three of these p…
AMC 8 2007 #25 grade 7+ probability, geometry-2d
On the dart board shown in the figure below, the outer circle has radius 6 and the inner circle has radius 3. Three radi…

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