¶ 1999 AMC8 Problems and Solutions
Problem Set Workbook
Access the downloadable workbook for 1999 AMC8 problems here.
Discussion Forum
Engage in discussion about the 1999 AMC8 math contest by visiting Random Math 1999 AMC8 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 1999 AMC8 problems, please refer below:
Problem 1: . To make this statement true, the question mark between the and the should be replaced by
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Problem 2: What is the degree measure of the smaller angle formed by the hands of a clock at o'clock?
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Problem 3: Which triplet of numbers has a sum NOT equal to
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Problem 4: The diagram shows the miles traveled by bikers Alberto and Bjorn. After four hours about how many more miles has Alberto biked then Bjorn?
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Problem 5: A rectangular garden feet long and feet wide is enclosed by a fence. To make the garden larger, while using the same fence, its shape is changed to a square. By how many square feet does this enlarge the garden?
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Problem 6: Bo, Coe, Flo, Jo, and Moe have different amounts of money. Neither Jo nor Bo has as much money as Flo. Both Bo and Coe have more than Moe. Jo has more than Moe, but less than Bo. Who has the least amount of money?
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Problem 7: The third exit on a highway is located at milepost and the tenth exit is at milepost . There is a service center on the highway located three-fourths of the way from the third exit to the tenth exit. At what milepost would you expect to find this service center?
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Problem 8: Six squares are colored, front and back, . They are hinged together as shown, then folded to form a cube. The face opposite the white face is
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Problem 9: Three flower beds overlap as shown. Bed has plants, bed has plants, and bed has plants. Beds and share plants, while beds and share . The total number of plants is
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Problem 10: A complete cycle of a traffic light takes seconds. During each cycle the light is green for seconds, yellow for seconds, and red for seconds. At a randomly chosen time, what is the probability that the light will NOT be green?
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Problem 11: Each of the five numbers , and is placed in one of the five squares so that the sum of the three numbers in the horizontal row equals the sum of the three numbers in the vertical column. The largest possible value for the horizontal or vertical sum is
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Problem 12: The ratio of the number of games won to the number of games lost(no ties) by the Middle School Middies is . To the nearest whole percent, what percent of its games did the team lose?
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Problem 13: The average age of the members of a computer science camp is years. There are girls, boys, and adults. If the average age of the girls is and the average age of the boys is , what is the average age of the adults?
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Problem 14: In trapezoid , the side and are equal. The perimeter of is
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Problem 15: Bicycle license plates in Flatville each contain three letters. The first is chosen from the set , the second from , and the third from .
When Flatville needed more license plates, they added two new letters. The new letters may both be added to one set or one letter may be added to one set and one to another set. What is the largest possible number of license plates than can be made by adding two letters?
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Problem 16: Tori's mathematics test had problems: arithmetic, algebra, and geometry problems. Although she answered of the arithmetic, of the algebra, and of the geometry problems correctly, she did not pass the test because she got less than of the problems right. How many more questions would she have needed to answer correctly to earn a passing grade?
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Problem 17: At Central Middle School the students who take the meet in the evening to talk about problems and eat an average of two cookies apiece. Walter and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe, which makes a pan of cookies, list these items:
cups of flour, eggs, tablespoons butter, cups sugar, and package of chocolate drops. They will make only full recipes, not partial recipe.
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Walter can buy eggs by the half-dozen. How many half-dozens should be buy to make enough cookies? (Some eggs and some cookies may be left over.)
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Problem 18: At Central Middle School the students who take the meet in the evening to talk about problems and eat an average of two cookies apiece. Walter and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe, which makes a pan of cookies, list these items:
cups of flour, eggs, tablespoons butter, cups sugar, and package of chocolate drops. They will make only full recipes, not partial recipe.
They learn that a big concert is scheduled for the same night and attendance will be down . How many recipes of cookies should they make for their smaller party?
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Problem 19: At Central Middle School the students who take the meet in the evening to talk about problems and eat an average of two cookies apiece. Walter and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe, which makes a pan of cookies, list these items:
cups of flour, eggs, tablespoons butter, cups sugar, and package of chocolate drops. They will make only full recipes, not partial recipe.
The drummer gets sick. The concert is cancelled. Walter and Gretel must make enough pans of cookies to supply cookies. There are tablespoons in a stick of butter. How many sticks of butter will be needed? (Some butter may be left over, of course.)
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Problem 20: Figure is called a "stack map." The numbers tell how many cubes are stacked in each position. Fig. shows these cubes, and Fig. shows the view of the stacked cubes as seen from the front.
Which of the following is the front view for the stack map in Fig.
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Problem 21: The degree measure of angle is
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Problem 22: In a far-off land three fish can be traded for two loaves of bread and a loaf of bread can be traded for four bags of rice. How many bags of rice is one fish worth?
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Problem 23: Square has sides of length . Segments and divide the square's area into three equal part. How long is segment
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Problem 24: When is divided by , the remainder is
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Problem 25: Points , and are midpoints of the sides of right triangle . Points are midpoints of the sides of triangle , etc. If the dividing and shading process is done times(the first three are shown) and , then the total area of the shaded triangles is nearest
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The problems on this page are the property of the MAA's American Mathematics Competitions