ΒΆ 2017 AMC8 Problems and Solutions
Problem Set Workbook
Access the downloadable workbook for 2017 AMC8 problems here.
Discussion Forum
Engage in discussion about the 2017 AMC8 math contest by visiting Random Math 2017 AMC8 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2017 AMC8 problems, please refer below:
Problem 1: Which of the following values is largest?
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Problem 2: Alicia, Brenda, and Colby were the candidates in a recent election for student president. The pie chart below shows how the votes were distributed among the three candidates. If Brenda received votes, then how many votes were cast all together?
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Problem 3: What is the value of the expression
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Problem 4: When is multiplied by the product is closest to which of the following?
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Problem 5: What is the value of the expression
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Problem 6: If the degree measures of the angles of a triangle are in the ratio , what is the degree measure of the largest angle of the triangle?
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Problem 7: Let be a -digit positive integer, such as , whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must be a factor of
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Problem 8: Malcolm wants to visit Isabella after school today and knows the street where she lives but doesn't know her house number. She tells him, "My house number has two digits, and exactly three of the following four statements about it are true."
It is prime.
It is even.
It is divisible by .
One of its digits is .
This information allows Malcolm to determine Isabella's house number. What is its units digit?
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Problem 9: All of Marcy's marbles are blue, red, green, or yellow. One third of her marbles are blue, one fourth of them are red, and six of them are green. What is the smallest number of yellow marbles that Marcy could have?
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Problem 10: A box contains five cards, numbered , and . Three cards are selected randomly without replacement from the box. What is the probability that is the largest value selected?
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Problem 11: A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is , how many tiles cover the floor?
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Problem 12: The smallest positive integer greater than that leaves a remainder of when divided by , and lies between which of the following pairs of numbers?
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Problem 13: Peter, Emma, and Kyler played chess with each other. Peter won games and lost games. Emma won games and lost games. If Kyler lost games, how many games did he win?
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Problem 14: Chloe and Zoe are both students in Ms. Demeanor's math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to only of the problems she solved alone, but overall of her answers were correct. Zoe had correct answers to of the problems she solved alone. What was Zoe's overall percentage of correct answers?
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Problem 15: In the arrangement of letters and numerals below, by how many different paths can one spell Beginning at the in the middle, a path allows only moves from one letter to an adjacent (above, below, left, or right, but not diagonal) letter. One example of such a path is traced in the picture.
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Problem 16: In the figure shown below, choose point on side so that and have equal perimeters. What is the area of
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Problem 17: Starting with some gold coins and some empty treasure chests, I tried to put gold coins in each treasure chest, but that left treasure chests empty. So instead I put gold coins in each treasure chest, but then I had gold coins left over. How many gold coins did I have?
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Problem 18: In the non-convex quadrilateral shown below, is a right angle, , and .
What is the area of quadrilateral
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Problem 19: For any positive integer , the notation denotes the product of the integers through . What is the largest integer for which is a factor of the sum
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Problem 20: An integer between and , inclusive, is chosen at random. What is the probability that it is an odd integer whose digits are all distinct?
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Problem 21: Suppose , and are nonzero real numbers, and . What are the possible value(s) for
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Problem 22: In the right triangle , and angle is a right angle. A semicircle is inscribed in the triangle as shown. What is the radius of the semicircle?
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Problem 23: Each day for four days, Linda traveled for one hour at a speed that resulted in her traveling one mile in an integer number of minutes. Each day after the first, her speed decreased so that the number of minutes to travel one mile increased by minutes over the preceding day. Each of the four days, her distance traveled was also an integer number of miles. What was the total number of miles for the four trips?
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Problem 24: Mrs. Sanders has three grandchildren, who call her regularly. One calls her every three days, one calls her every four days, and one calls her every five days. All three called her on December , . On how many days during the next year did she not receive a phone call from any of her grandchildren?
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Problem 25: In the figure shown, and are line segments each of length , and . Arcs and are each one-sixth of a circle with radius . What is the area of the region shown?
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The problems on this page are the property of the MAA's American Mathematics Competitions