Competition · AMC preparation · step 4 of 4

AMC 8 2017: 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 2017 #1 grade 5+ arithmetic
Which of the following values is largest?
AMC 8 2017 #2 grade 6+ rate-ratio
Alicia, Brenda, and Colby were the candidates in a recent election for student president. The pie chart below shows how…
AMC 8 2017 #3 grade 8+ arithmetic
What is the value of the expression √16√8√4?
AMC 8 2017 #4 grade 5+ arithmetic
When 0.000315 is multiplied by 7,928,564 the product is closest to which of the following?
AMC 8 2017 #5 grade 4+ arithmetic
What is the value of the expression (1 · 2 · 3 · 4 · 5 · 6 · 7 · 8)/(1+2+3+4+5+6+7+8)?
AMC 8 2017 #6 grade 8+ geometry-2d, rate-ratio
If the degree measures of the angles of a triangle are in the ratio 3:3:4, what is the degree measure of the largest ang…
AMC 8 2017 #7 grade 4+ number-theory
Let Z be a 6-digit positive integer, such as 247247, whose first three digits are the same as its last three digits take…
AMC 8 2017 #8 grade 4+ number-theory, logic
Malcolm wants to visit Isabella after school today and knows the street where she lives but doesn't know her house numbe…
AMC 8 2017 #9 grade 4+ rate-ratio, number-theory
All of Marcy's marbles are blue, red, green, or yellow. One third of her marbles are blue, one fourth of them are red, a…
AMC 8 2017 #10 grade 7+ probability, counting
A box contains five cards, numbered 1, 2, 3, 4, and 5. Three cards are selected randomly without replacement from the bo…
AMC 8 2017 #11 grade 4+ geometry-2d, pattern
A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals…
AMC 8 2017 #12 grade 4+ number-theory
The smallest positive integer greater than 1 that leaves a remainder of 1 when divided by 4, 5, and 6 lies between which…
AMC 8 2017 #13 grade 2+ logic, arithmetic
Peter, Emma, and Kyler played chess with each other. Peter won 4 games and lost 2 games. Emma won 3 games and lost 3 gam…
AMC 8 2017 #14 grade 6+ rate-ratio, algebra
Chloe and Zoe are both students in Ms. Demeanor's math class. Last night, they each solved half of the problems in their…
AMC 8 2017 #15 grade 4+ counting
In the arrangement of letters and numerals below, by how many different paths can one spell AMC8? Beginning at the A in…
AMC 8 2017 #16 grade 6+ geometry-2d, algebra
In the figure below, choose point D on BC so that △ ACD and △ ABD have equal perimeters. What is the area of △ ABD?
AMC 8 2017 #17 grade 4+ algebra
Starting with some gold coins and some empty treasure chests, I tried to put 9 gold coins in each treasure chest, but th…
AMC 8 2017 #18 grade 8+ geometry-2d
In the non-convex quadrilateral ABCD shown below, ∠ BCD is a right angle, AB=12, BC=4, CD=3, and AD=13. What is the area…
AMC 8 2017 #19 grade 6+ number-theory
For any positive integer M, the notation M! denotes the product of the integers 1 through M. What is the largest integer…
AMC 8 2017 #20 grade 7+ probability, counting
An integer between 1000 and 9999, inclusive, is chosen at random. What is the probability that it is an odd integer whos…
AMC 8 2017 #21 grade 7+ algebra, logic
Suppose a, b, and c are nonzero real numbers, and a+b+c=0. What are the possible value(s) for a/(|a|)+b/(|b|)+c/(|c|)+ab…
AMC 8 2017 #22 grade 8+ geometry-2d, algebra
In the right triangle ABC, AC=12, BC=5, and angle C is a right angle. A semicircle is inscribed in the triangle as shown…
AMC 8 2017 #23 grade 4+ rate-ratio, number-theory
Each day for four days, Linda traveled for one hour at a speed that resulted in her traveling one mile in an integer num…
AMC 8 2017 #24 grade 6+ number-theory, counting
Mrs. Sanders has three grandchildren, who call her regularly. One calls her every three days, one calls her every four d…
AMC 8 2017 #25 grade 8+ geometry-2d
In the figure shown, US and UT are line segments each of length 2, and m∠ TUS = 60°. Arcs overarcTR and overarcSR are ea…

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