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AMC8 1995

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AMC8 · 1995

Q1
Walter has exactly one penny, one nickel, one dime and one quarter in his pocket. What percent of one dollar is in his pocket?
沃尔特口袋里正好有一美分、一枚镍币、一角币和一枚25美分硬币。他口袋里的钱占一美元的百分之多少？
Q2
Jose is 4 years younger than Zack. Zack is 3 years older than Inez. Inez is 15 years old. How old is Jose?
何塞比扎克小4岁。扎克比伊内斯大3岁。伊内斯15岁。何塞多大？
Q3
Which of the following operations has the same effect on a number as multiplying by $\frac{3}{4}$ and then dividing by $\frac{3}{5}$?
下列哪个运算与先乘以 $\frac{3}{4}$ 再除以 $\frac{3}{5}$ 对一个数的效果相同？
Q4
A teacher tells the class, "Think of a number, add 1 to it, and double the result. Give the answer to your partner. Partner, subtract 1 from the number you are given and double the result to get your answer." Ben thinks of 6, and gives his answer to Sue. What should Sue's answer be?
老师对全班说：“想一个数，加1，再将结果加倍。把答案给你的伙伴。伙伴，从你得到的数中减1，再将结果加倍得到你的答案。” 本想的是6，把他的答案给了苏。苏的答案应该是多少？
Q5
Find the smallest whole number that is larger than the sum $$2\frac{1}{2} + 3\frac{1}{3} + 4\frac{1}{4} + 5\frac{1}{5}.$$
求比以下和更大的最小整数 $$2\frac{1}{2} + 3\frac{1}{3} + 4\frac{1}{4} + 5\frac{1}{5}$$。
Q6
Figures I, II and III are squares. The perimeter of I is 12 and the perimeter of II is 24. The perimeter of III is
图形 I、II 和 III 是正方形。I 的周长是 12，II 的周长是 24。III 的周长是
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Q7
At Clover View Junior High, one half of the students go home on the school bus. One fourth go home by automobile. One tenth go home on their bicycles. The rest walk home. What fractional part of the students walk home?
在 Clover View 初中，有一半学生乘坐校车回家。四分之一乘坐汽车回家。十分之一骑自行车回家。其余的学生步行回家。步行回家的学生占总数的几分之几？
Q8
An American traveling in Italy wishes to exchange American money (dollars) for Italian money (lire). If 3000 lire = \$1.60, how many lire will the traveler receive in exchange for \$1.00?
一位在美国旅居意大利的美国人希望将美元兑换成意大利货币（里拉）。如果 3000 里拉 = \$1.60，那么兑换 \$1.00 将得到多少里拉？
Q9
Three congruent circles with centers P, Q and R are tangent to the sides of rectangle ABCD as shown. The circle centered at Q has diameter 4 and passes through points P and R. The area of the rectangle is
三个全等的圆，以 P、Q 和 R 为圆心，如图所示，与矩形 ABCD 的边相切。以 Q 为圆心的圆直径为 4，并经过点 P 和 R。矩形的面积是
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Q10
A jacket and a shirt originally sold for \$80 and \$40, respectively. During a sale Chris bought \$80 jacket at a 40% discount and the \$40 shirt at a 55% discount. The total amount saved was what percent of the total of the original prices?
一件夹克衫和一件衬衫原价分别为 $80$ 和 $40$。在促销期间，Chris 以 40% 折扣买了 $80$ 的夹克衫，并以 55% 折扣买了 $40$ 的衬衫。总节省金额占原总价的百分之几？
Q11
Jane can walk any distance in half the time it takes Hector to walk the same distance. They set off in opposite directions around the outside of the 18-block area as shown. When they meet for the first time, they will be closest to
简可以以海克托走相同距离一半的时间走任何距离。他们朝着相反方向绕着图示的18街区区域外围出发。当他们第一次相遇时，他们将最接近于
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Q12
A lucky year is one in which at least one date, when written in the form month/day/year, has the following property: The product of the month times the day equals the last two digits of the year. For example, 1956 is a lucky year because it has the date 7/8/56 and $7 \times 8 = 56$. Which of the following is NOT a lucky year?
幸运年是指至少有一个日期，以月/日/年形式书写时，具有如下性质：月份乘以日期等于年份的最后两位数字。例如，1956是幸运年，因为有日期7/8/56且$7 \times 8 = 56$。以下哪个不是幸运年？
Q13
In the figure, ∠A, ∠B and ∠C are right angles. If ∠AEB = 40° and ∠BED = ∠BDE, then ∠CDE =
在图中，∠A、∠B和∠C是直角。如果∠AEB = 40°且∠BED = ∠BDE，则∠CDE =
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Q14
A team won 40 of its first 50 games. How many of the remaining 40 games must this team win so it will won exactly 70% of its games for the season?
一支队伍在前50场比赛中赢了40场。要使该队整个赛季的胜率恰好为70%，它还需在剩余40场比赛中赢多少场？
Q15
What is the 100th digit to the right of the decimal point in the decimal form of 4/37?
4/37的小数形式中，小数点右边的第100位数字是什么？
Q16
Students from three middle schools worked on a summer project. Seven students from Allen School worked for 3 days. Four students from Balboa School worked for 5 days. Five students from Carver School worked for 9 days. The total amount paid for the students' work was \$774. Assuming each student received the same amount for a day's work, how much did the students from Balboa School earn altogether?
来自三所中学的学生参加了一个暑期项目。Allen学校的7名学生工作了3天。Balboa学校的4名学生工作了5天。Carver学校的5名学生工作了9天。学生工作的总报酬为774美元。假设每位学生每天的报酬相同，Balboa学校的学生总共赚了多少钱？
Q17
The table below gives the percent of students in each grade at Annville and Cleona elementary schools: Annville has 100 students and Cleona has 200 students. In the two schools combined, what percent of the students are in grade 6?
下表给出了Annville和Cleona小学各年级学生所占百分比： Annville有100名学生，Cleona有200名学生。在两所学校合计中，六年级学生占总学生的百分之多少？
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Q18
The area of each of the four congruent L-shaped regions of this 100-inch by 100-inch square is 3/16 of the total area. How many inches long is the side of the center square?
这个100英寸×100英寸正方形中有四个全等的L形区域，每个区域的面积是总面积的3/16。中心正方形的边长有多少英寸？
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Q19
The graph shows the distribution of the number of children in the families of the students in Ms. Jordan's English class. The median number of children in the family for this distribution is
图表显示了Jordan老师英语班学生家庭中孩子数量的分布。该分布中家庭孩子数量的中位数是
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Q20
Diana and Apollo each roll a standard die obtaining a number at random from 1 to 6. What is the probability that Diana's number is larger than Apollo's number?
Diana和Apollo各掷一个标准骰子，随机得到1到6的数字。Diana的数字大于Apollo的数字的概率是多少？
Q21
A plastic snap-together cube has a protruding snap on one side and receptacle holes on the other five sides as shown. What is the smallest number of these cubes that can be snapped together so that only receptacle holes are showing?
一种塑料卡扣立方体在一面有一个突出的卡扣，其他五面有插孔，如图所示。要使卡在一起的立方体只露出插孔，需要的最小立方体数量是多少？
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Q22
The number 6545 can be written as a product of a pair of positive two-digit numbers. What is the sum of this pair of numbers?
数字 6545 可以写成一对正的双位数的乘积。这对数的和是多少？
Q23
How many four-digit whole numbers are there such that the leftmost digit is odd, the second digit is even, and all four digits are different?
有多少个四位整数，使得最左边数字是奇数，第二个数字是偶数，并且所有四个数字互不相同？
Q24
In parallelogram ABCD, DE is the altitude to the base AB and DF is the altitude to the base BC. If DC = 12, EB = 4 and DE = 6, then DF =
在平行四边形 ABCD 中，DE 是底边 AB 的高，DF 是底边 BC 的高。若 DC = 12，EB = 4 且 DE = 6，则 DF =
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Q25
Buses from Dallas to Houston leave every hour on the hour. Buses from Houston to Dallas leave every hour on the half hour. The trip from one city to the other takes 5 hours. Assuming the buses travel on the same highway, how many Dallas-bound buses does a Houston-bound bus pass on the highway (not in the station)?
从达拉斯到休斯顿的巴士每整点发车。从休斯顿到达拉斯的巴士每半点发车。从一座城市到另一座城市需要5小时。假设巴士在同一公路上行驶，一辆去休斯顿的巴士在公路上（不在车站）会经过多少辆去达拉斯的巴士？
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