Competition · AMC preparation · step 4 of 4

AMC 8 1999: 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 1999 #1 grade 6+ arithmetic
(6?3) + 4 - (2 - 1) = 5. To make this statement true, the question mark between the 6 and the 3 should be replaced by
AMC 8 1999 #2 grade 4+ geometry-2d
What is the degree measure of the smaller angle formed by the hands of a clock at 10 o'clock?
AMC 8 1999 #3 grade 7+ arithmetic
Which triplet of numbers has a sum NOT equal to 1?
AMC 8 1999 #4 grade 5+ rate-ratio
The diagram shows the miles traveled by bikers Alberto and Bjorn. After four hours, about how many more miles has Albert…
AMC 8 1999 #5 grade 4+ geometry-2d
A rectangular garden 60 feet long and 20 feet wide is enclosed by a fence. To make the garden larger, while using the sa…
AMC 8 1999 #6 grade 1+ logic
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 h…
AMC 8 1999 #7 grade 4+ arithmetic
The third exit on a highway is located at milepost 40 and the tenth exit is at milepost 160. There is a service center o…
AMC 8 1999 #8 grade 6+ geometry-3d
Six squares are colored, front and back, (R = red, B = blue, O = orange, Y = yellow, G = green, and W = white). They are…
AMC 8 1999 #9 grade 4+ counting
Three flower beds overlap as shown. Bed A has 500 plants, bed B has 450 plants, and bed C has 350 plants. Beds A and B s…
AMC 8 1999 #10 grade 7+ probability
A complete cycle of a traffic light takes 60 seconds. During each cycle the light is green for 25 seconds, yellow for 5…
AMC 8 1999 #11 grade 6+ arithmetic
Each of the five numbers 1, 4, 7, 10, and 13 is placed in one of the five squares so that the sum of the three numbers i…
AMC 8 1999 #12 grade 6+ rate-ratio
The ratio of the number of games won to the number of games lost (no ties) by the Middle School Middies is 11/4. To the…
AMC 8 1999 #13 grade 6+ arithmetic
The average age of the 40 members of a computer science camp is 17 years. There are 20 girls, 15 boys, and 5 adults. If…
AMC 8 1999 #14 grade 8+ geometry-2d
In trapezoid ABCD, the sides AB and CD are equal. The perimeter of ABCD is
AMC 8 1999 #15 grade 5+ counting
Bicycle license plates in Flatville each contain three letters. The first is chosen from the set {C,H,L,P,R}, the second…
AMC 8 1999 #16 grade 6+ rate-ratio
Tori's mathematics test had 75 problems: 10 arithmetic, 30 algebra, and 35 geometry problems. Although she answered 70%…
AMC 8 1999 #17 grade 5+ rate-ratio
At Central Middle School the 108 students who take the AMC 8 meet in the evening to talk about problems and eat an avera…
AMC 8 1999 #18 grade 6+ rate-ratio
At Central Middle School the 108 students who take the AMC8 meet in the evening to talk about problems and eat an averag…
AMC 8 1999 #19 grade 6+ rate-ratio
At Central Middle School, the 108 students who take the AMC 8 meet in the evening to talk about food and eat an average…
AMC 8 1999 #20 grade 6+ geometry-3d
Figure 1 is called a "stack map." The numbers tell how many cubes are stacked in each position. Fig. 2 shows these cubes…
AMC 8 1999 #21 grade 7+ geometry-2d
The degree measure of angle A is
AMC 8 1999 #22 grade 6+ rate-ratio
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 ri…
AMC 8 1999 #23 grade 8+ geometry-2d
Square ABCD has sides of length 3. Segments CM and CN divide the square's area into three equal parts. How long is segme…
AMC 8 1999 #24 grade 5+ number-theory
When 1999²⁰⁰⁰ is divided by 5, the remainder is
AMC 8 1999 #25 grade 8+ geometry-2d
Points B, D, and J are midpoints of the sides of right triangle ACG. Points K, E, I are midpoints of the sides of triang…

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