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AMC8 1999

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AMC8 · 1999

Q1
$(6 \ ? \ 3) + 4 - (2 - 1) = 5$. To make this statement true, the question mark between the 6 and the 3 should be replaced by
$(6 \ ? \ 3) + 4 - (2 - 1) = 5$。要使这个等式成立，6 和 3 之间的问号应该替换为
Q2
What is the degree measure of the smaller angle formed by the hands of a clock at 10 o'clock?
10点钟时，钟表指针形成的较小角度的度数是多少？
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Q3
Which triplet of numbers has a sum NOT equal to 1?
哪个数字三元组的和不等于1？
Q4
The diagram shows the miles traveled by bikers Alberto and Bjorn. After four hours about how many more miles has Alberto biked than Bjorn?
图表显示了自行车手Alberto和Bjorn行驶的英里数。四小时后，Alberto比Bjorn多骑了大约多少英里？
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Q5
A rectangular garden 50 feet long and 10 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?
一个长50英尺、宽10英尺的矩形花园被栅栏围住。为了使花园更大，同时使用相同的栅栏，将其形状改为正方形。这个变化使花园扩大了多少平方英尺？
Q6
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?
Bo、Coe、Flo、Jo 和 Moe 有不同数量的钱。Jo 和 Bo 都没有 Flo 多钱。Bo 和 Coe 都比 Moe 多钱。Jo 比 Moe 多，但比 Bo 少。谁的钱最少？
Q7
The third exit on a highway is located at milepost 40 and the tenth exit is at milepost 160. 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?
高速公路上的第三个出口位于 40 英里桩，十个出口位于 160 英里桩。服务中心的位于从第三个出口到第十个出口的三分之四处。你期望在哪个英里桩找到这个服务中心？
Q8
Six squares are colored, front and back, (R=red, B=blue, O=orange, Y=yellow, G=green, and W=white). They are hinged together as shown, then folded to form a cube. The face opposite the white face is
六个正方形被涂色，正反面（R=红，B=蓝，O=橙，Y=黄，G=绿，W=白）。它们如图所示铰接在一起，然后折叠成一个立方体。与白面相对的面是
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Q9
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 share 50 plants, while beds A and C share 100. The total number of plants is
三个花坛如图所示重叠。A 花坛有 500 株植物，B 花坛有 450 株，C 花坛有 350 株。A 和 B 共享 50 株植物，A 和 C 共享 100 株。总植物数是
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Q10
A complete cycle of a traffic light takes 60 seconds. During each cycle the light is green for 25 seconds, yellow for 5 seconds, and red for 30 seconds. At a randomly chosen time, what is the probability that the light will NOT be green?
一个完整的交通灯周期需要 60 秒。每个周期灯绿灯 25 秒，黄灯 5 秒，红灯 30 秒。在随机选择的时刻，灯不是绿灯的概率是多少？
Q11
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 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
将五个数字1、4、7、10和13各放入五个方格中，使得水平行三个数字的和等于垂直列三个数字的和。水平或垂直和的最大可能值为
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Q12
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 nearest whole percent, what percent of its games did the team lose?
中学生Middies队的胜场数与负场数（无平局）的比为11/4。该队负场的百分比（四舍五入到最接近的整百分比）是多少？
Q13
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 the average age of the girls is 15 and the average age of the boys is 16, what is the average age of the adults?
一个计算机科学夏令营有40名成员，平均年龄17岁。其中20名女孩、15名男孩和5名成人。女孩平均年龄15岁，男孩平均年龄16岁，成人平均年龄是多少？
Q14
In trapezoid ABCD, the sides AB and CD are equal. The perimeter of ABCD is
梯形ABCD中，边AB和CD相等。ABCD的周长是
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Q15
Bicycle license plates in Flatville each contain three letters. The first is chosen from the set ${C,H,L,P,R}$, the second from ${A,I,O}$, and the third from ${D,M,N,T}$. 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 ADDITIONAL license plates that can be made by adding two letters?
Flatville的自行车车牌每个包含三个字母。第一位从集合${C,H,L,P,R}$选，第二位从${A,I,O}$选，第三位从${D,M,N,T}$选。为了需要更多车牌，他们添加了两个新字母。新字母可都加到一个集合，或各加到一个集合。添加两个字母能制造的最大可能新增车牌数是多少？
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Q16
Tori's mathematics test had 75 problems: 10 arithmetic, 30 algebra, and 35 geometry problems. Although she answered 70% of the arithmetic, 40% of the algebra, and 60% of the geometry problems correctly, she did not pass the test because she got less than 60% of the problems right. How many more questions would she have needed to answer correctly to earn a 60% passing grade?
Tori 的数学测试共有 75 道题：10 道算术题，30 道代数题，35 道几何题。虽然她在算术题中答对了 70%，代数题中答对了 40%，几何题中答对了 60%，但她没有通过测试，因为她答对的题目不到 60%。她还需要多答对多少题才能达到 60% 的及格分数？
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Q17
Walter can buy eggs by the half-dozen. How many half-dozens should he buy to make enough cookies? (Some eggs and some cookies may be left over.) [Context: 108 students eat avg 2 cookies each, recipe 15 cookies/pan, 2 eggs/recipe]
Walter 可以按半打购买鸡蛋。他需要买多少半打鸡蛋才能做足够的饼干？（可能会有一些鸡蛋和饼干剩余。）[背景：108 名学生平均每人吃 2 块饼干，配方每盘 15 块饼干，每配方 2 个鸡蛋]
Q18
They learn that a big concert is scheduled for the same night and attendance will be down 25%. How many recipes of cookies should they make for their smaller party? [same context]
他们得知当晚有大型音乐会，出席人数将减少 25%。他们为人数减少的派对应该做多少配方的饼干？[相同背景]
Q19
The drummer gets sick. The concert is cancelled. Walter and Gretel must make enough pans of cookies to supply 216 cookies. There are 8 tablespoons in a stick of butter. How many sticks of butter will be needed? (Some butter may be left over, of course.) [recipe: 3 tbsp butter]
鼓手生病了。音乐会取消了。Walter 和 Gretel 必须做足够的饼干盘来提供 216 块饼干。一根黄油棒有 8 汤匙。需要多少根黄油棒？（当然可能会有一些黄油剩余。）[配方：3 汤匙黄油]
Q20
Figure 1 is called a "stack map." The numbers tell how many cubes are stacked in each position. Fig. 2 shows these cubes, and Fig. 3 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. 4?
图 1 称为“堆叠图”。数字表示每个位置堆叠的立方体数量。图 2 显示这些立方体，图 3 显示从前面看到的堆叠立方体的视图。以下哪项是图 4 的堆叠图的前视图？
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Q21
The degree measure of angle A is
角 A 的度量是
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Q22
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?
在一个遥远的国家，三条鱼可以换两块面包，一块面包可以换四袋米。一条鱼值多少袋米？
Q23
Square ABCD has sides of length 3. Segments CM and CN divide the square's area into three equal parts. How long is segment CM?
正方形 ABCD 边长为 3。线段 CM 和 CN 将正方形的面积分为三等分。线段 CM 长多少？
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Q24
When $1999^{2000}$ is divided by 5, the remainder is
$1999^{2000}$ 除以 5 的余数是
Q25
Points B, D, and J are midpoints of the sides of right triangle ACG. Points K, E, I are midpoints of the sides of triangle JDG, etc. If the dividing and shading process is done 100 times (the first three are shown) and AC = CG = 6, then the total area of the shaded triangles is nearest
点 B、D 和 J 是直角三角形 ACG 边的中点。点 K、E、I 是三角形 JDG 边的中点，等等。如果划分和着色过程进行 100 次（显示前三次），且 AC = CG = 6，则着色三角形的总面积最接近
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