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AMC8 2004

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AMC8 · 2004

Q1
On a map, a 12-centimeter length represents 72 kilometers. How many kilometers does a 17-centimeter length represent?
在地图上，12厘米长度代表72公里。那么17厘米长度代表多少公里？
Q2
How many different four-digit numbers can be formed by rearranging the four digits in 2004?
通过重新排列2004中的四个数字，可以组成多少个不同的四位数？
Q3
Twelve friends met for dinner at Oscar's Overstuffed Oyster House, and each ordered one meal. The portions were so large, there was enough food for 18 people. If they share, how many meals should they have ordered to have just enough food for the 12 of them?
十二个朋友在Oscar's Overstuffed Oyster House聚餐，每人点了一份餐点。份量太大，足够18个人吃。如果他们分享，为12个人刚好够吃，应该点多少份餐点？
Q4
Lance, Sally, Joy and Fred are chosen for the team. In how many ways can the three starters be chosen?
Lance、Sally、Joy和Fred被选入球队。有多少种方法可以选择三个首发？
Q5
The losing team of each game is eliminated from the tournament. If sixteen teams compete, how many games will be played to determine the winner?
每场比赛的失败队伍将被淘汰。如果有十六支队伍参赛，为了决出冠军，将进行多少场比赛？
Q6
After Sally takes 20 shots, she has made 55% of her shots. After she takes 5 more shots, she raises her percentage to 56%. How many of the last 5 shots did she make?
Sally 投了 20 次后，她的命中率为 55%。再投 5 次后，她的命中率提高到 56%。她在最后 5 次投篮中命中了几次？
Q7
An athlete's target heart rate, in beats per minute, is 80% of the theoretical maximum heart rate. The maximum heart rate is found by subtracting the athlete's age, in years, from 220. To the nearest whole number, what is the target heart rate of an athlete who is 26 years old?
运动员的目标心率（每分钟跳动次数）为其理论最大心率的 80%。最大心率等于 220 减去运动员的年龄（年）。对于一名 26 岁的运动员，目标心率取整到最接近的整数是多少？
Q8
Find the number of two-digit positive integers whose digits total 7.
找出两位正整数各位数字之和为 7 的个数。
Q9
The average of the five numbers in a list is 54. The average of the first two numbers is 48. What is the average of the last three numbers?
一个列表中五个数的平均数是 54。前两个数的平均数是 48。后三个数的平均数是多少？
Q10
Handy Aaron helped a neighbor $1 \frac{1}{4}$ hours on Monday, 50 minutes on Tuesday, from 8:20 to 10:45 on Wednesday morning, and a half-hour on Friday. He is paid \$3 per hour. How much did he earn for the week?
Handy Aaron 周一帮助邻居 $1 \frac{1}{4}$ 小时，周二 50 分钟，周三早上从 8:20 到 10:45，周五半小时。他每小时得 3 美元。这周他赚了多少钱？
Q11
The numbers -2, 4, 6, 9 and 12 are rearranged according to these rules: 1. The largest isn't first, but it is in one of the first three places. 2. The smallest isn't last, but it is in one of the last three places. 3. The median isn't first or last. What is the average of the first and last numbers?
数字 -2、4、6、9 和 12 按照以下规则重新排列：1. 最大的数不是第一个，但它在头三个位置之一。2. 最小的数不是最后一个，但它在最后三个位置之一。3. 中位数不是第一个也不是最后一个。第一个和最后一个数字的平均数是多少？
Q12
Niki usually leaves her cell phone on. If her cell phone is on but she is not actually using it, the battery will last for 24 hours. If she is using it constantly, the battery will last for only 3 hours. Since the last recharge, her phone has been on 9 hours, and during that time she has used it for 60 minutes. If she doesn't talk any more but leaves the phone on, how many more hours will the battery last?
Niki 通常保持她的手机开着。如果她的手机开着但她没有实际使用它，电池能持续 24 小时。如果她持续使用它，电池只能持续 3 小时。自上次充电以来，她的手机已经开机 9 小时，在此期间她使用了 60 分钟。如果她不再通话但保持手机开着，电池还能持续多少小时？
Q13
Amy, Bill and Celine are friends with different ages. Exactly one of the following statements is true. I. Bill is the oldest. II. Amy is not the oldest. III. Celine is not the youngest. Rank the friends from the oldest to the youngest.
Amy、Bill 和 Celine 是不同年龄的朋友。以下三个陈述中恰好有一个是真的。I. Bill 是最年长的。II. Amy 不是最年长的。III. Celine 不是最年轻的。将朋友们从最年长到最年轻排名。
Q14
What is the area enclosed by the geoboard quadrilateral below?
下面几何板上的四边形围成的面积是多少？
stem
Q15
Thirteen black and six white hexagonal tiles were used to create the figure below. If a new figure is created by attaching a border of white tiles with the same size and shape as the others, what will be the difference between the total number of white tiles and the total number of black tiles in the new figure?
使用 13 块黑色和 6 块白色六边形瓷砖创建了下面的图形。如果通过附加一层与其它相同大小和形状的白色瓷砖边框创建新图形，新图形中白色瓷砖总数与黑色瓷砖总数的差是多少？
stem
Q16
Two 600 ml pitchers contain orange juice. One pitcher is $\frac{1}{3}$ full and the other pitcher is $\frac{2}{3}$ full. Water is added to fill each pitcher completely, then both pitchers are poured into one large container. What fraction of the mixture in the large container is orange juice?
有两个600毫升的橙汁罐。一个罐子装有\frac{1}{3}的橙汁，另一个装有\frac{2}{3}的橙汁。向每个罐子中加水直到装满，然后将两个罐子倒入一个大容器中。大容器中的混合物中有多少分数是橙汁？
Q17
Three friends have a total of 6 identical pencils, and each one has at least one pencil. In how many ways can this happen?
三个朋友总共有6支相同的铅笔，每人至少有一支。这种情况有多少种分配方式？
Q18
Five friends compete in a dart-throwing contest. Each one has two darts to throw at the same circular target, and each individual's score is the sum of the scores in the target regions that are hit. The scores for the target regions are the whole numbers 1 through 10. Each throw hits the target in a region with a different value. The scores are: Alice 16 points, Ben 4 points, Cindy 7 points, Dave 11 points, and Ellen 17 points. Who hits the region worth 6 points?
五个朋友参加飞镖投掷比赛。每人投两支飞镖击中同一个圆形靶，每个人的得分是击中靶区得分的总和。靶区得分为1到10的整数。每支飞镖击中的区域得分不同。得分分别是：Alice 16分，Ben 4分，Cindy 7分，Dave 11分，Ellen 17分。谁击中了6分的区域？
Q19
A whole number larger than 2 leaves a remainder of 2 when divided by each of the numbers 3, 4, 5 and 6. The smallest such number lies between which two numbers?
一个大于2的整数，除以3、4、5、6各数时余数均为2。最小这样的数在哪两个数之间？
Q20
Two-thirds of the people in a room are seated in three-fourths of the chairs. The rest of the people are standing. If there are 6 empty chairs, how many people are in the room?
房间里的人中有三分之二坐在四分之三的椅子上。其余人站着。如果有6把空椅子，房间里有多少人？
Q21
Spinners A and B are spun. On each spinner, the arrow is equally likely to land on each number. What is the probability that the product of the two spinners' numbers is even?
转盘 A 和 B 同时旋转。每个转盘上的箭头等可能地落在每个数字上。两个转盘数字的乘积为偶数的概率是多少？
stem
Q22
At a party there are only single women and married men with their wives. The probability that a randomly selected woman is single is $\frac{2}{5}$. What fraction of the people in the room are married men?
在一个派对上，只有单身女性和带着妻子的已婚男性。随机选择的女性是单身的概率为 $\frac{2}{5}$。房间里的人中有多少分数是已婚男性？
Q23
Tess runs counterclockwise around rectangular block JKLM. She lives at corner J. Which graph could represent her straight-line distance from home?
Tess 逆时针绕矩形街区 JKLM 跑步。她住在角 J。哪张图可能表示她与家的直线距离？
stem
Q24
In the figure, $ABCD$ is a rectangle and $EFGH$ is a parallelogram. Using the measurements given in the figure, what is the length $d$ of the segment that is perpendicular to $\overline{HE}$ and $\overline{FG}$?
在图中，$ABCD$ 是矩形，$EFGH$ 是平行四边形。使用图中给出的测量值，垂直于 $\overline{HE}$ 和 $\overline{FG}$ 的线段 $d$ 的长度是多少？
stem
Q25
Two $4 \times 4$ squares intersect at right angles, bisecting their intersecting sides, as shown. The circle's diameter is the segment between the two points of intersection. What is the area of the shaded region created by removing the circle from the squares?
两个 $4 \times 4$ 正方形垂直相交，平分它们的相交边，如图所示。圆的直径是两个交点之间的线段。从正方形中移除圆后形成的阴影区域的面积是多少？
stem
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