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AMC8 2008

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AMC8 · 2008

Q1
Susan had $50$ to spend at the carnival. She spent $12$ on food and twice as much on rides. How many dollars did she have left to spend?
Susan 在嘉年华上有 $50$ 美元可以花。她花了 $12$ 买食物，在游乐设施上花了这两倍的钱。她还剩下多少美元可以花？
Q2
The ten-letter code BEST OF LUCK represents the ten digits $0-9$, in order. What $4$-digit number is represented by the code word CLUE?
十个字母的密码 BEST OF LUCK 代表数字 $0-9$，按顺序对应。密码单词 CLUE 表示的四位数是？
Q3
If February is a month that contains Friday the $13$th, what day of the week is February $1$?
如果二月包含星期五的 $13$ 号，那么二月 $1$ 号是星期几？
Q4
In the figure, the outer equilateral triangle has area $16$, the inner equilateral triangle has area $1$, and the three trapezoids are congruent. What is the area of one of the trapezoids?
在图中，外层等边三角形的面积是 $16$，内层等边三角形的面积是 $1$，三个梯形全等。其中一个梯形的面积是多少？
stem
Q5
Barney Schwinn notices that the odometer on his bicycle reads $1441$, a palindrome, because it reads the same forward and backward. After riding $4$ more hours that day and $6$ the next, he notices that the odometer shows another palindrome, $1661$. What was his average speed in miles per hour?
Barney Schwinn 注意到他的自行车里程表显示 $1441$，这是一个回文数，因为正读反读都一样。那天他又骑了 $4$ 小时，第二天骑了 $6$ 小时后，他注意到里程表又显示另一个回文数 $1661$。他的平均速度是多少英里每小时？
Q6
In the figure, what is the ratio of the area of the gray squares to the area of the white squares?
在图中，灰色正方形的面积与白色正方形的面积之比是多少？
stem
Q7
If $\frac{3}{5} = \frac{M}{45} = \frac{60}{N}$, what is $M + N$?
如果 $\frac{3}{5} = \frac{M}{45} = \frac{60}{N}$，那么 $M + N$ 是多少？
Q8
Candy sales of the Boosters Club for January through April are shown. What were the average sales per month in dollars?
助推俱乐部一月至四月的糖果销售额如图所示。每月平均销售额（美元）是多少？
stem
Q9
In $2005$ Tycoon Tammy invested $\$100$ for two years. During the first year her investment suffered a $15\%$ loss, but during the second year the remaining investment showed a $20\%$ gain. Over the two-year period, what was the change in Tammy's investment?
2005 年，Tycoon Tammy 投资了 $\$100$ 两年。第一年她的投资损失了 $15\%$，但第二年剩余投资获得了 $20\%$ 的收益。在两年期间，Tammy 的投资变化是多少？
Q10
The average age of the $6$ people in Room A is $40$. The average age of the $4$ people in Room B is $25$. If the two groups are combined, what is the average age of all the people?
A 室 $6$ 人的平均年龄是 $40$。B 室 $4$ 人的平均年龄是 $25$。如果将两组人合并，所有人的平均年龄是多少？
Q11
Each of the $39$ students in the eighth grade at Lincoln Middle School has one dog or one cat or both a dog and a cat. Twenty students have a dog and $26$ students have a cat. How many students have both a dog and a cat?
林肯中学八年级的39名学生每人都有狗或猫或既有狗又有猫。有20名学生有狗，26名学生有猫。有多少名学生既有狗又有猫？
Q12
A ball is dropped from a height of $3$ meters. On its first bounce it rises to a height of $2$ meters. It keeps falling and bouncing to $\frac{2}{3}$ of the height it reached in the previous bounce. On which bounce will it not rise to a height of $0.5$ meters?
一个球从3米高处落下。第一次弹起时升到2米高。它不断落下和弹起，每次弹起高度是前一次的$\frac{2}{3}$。在第几次弹起时它不会升到0.5米高？
stem
Q13
Mr. Harman needs to know the combined weight in pounds of three boxes he wants to mail. However, the only available scale is not accurate for weights less than $100$ pounds or more than $150$ pounds. So the boxes are weighed in pairs in every possible way. The results are $122$, $125$ and $127$ pounds. What is the combined weight in pounds of the three boxes?
哈曼先生需要知道他要邮寄的三个盒子的总重量（磅）。但是，可用的秤不准确，无法称量小于100磅或大于150磅的重量。因此，盒子以每种可能的方式成对称重。结果分别是122、125和127磅。三个盒子的总重量是多少磅？
Q14
Three As, three Bs and three Cs are placed in the nine spaces so that each row and column contain one of each letter. If A is placed in the upper left corner, how many arrangements are possible?
在九个空格中放置三个A、三个B和三个C，使得每行和每列包含每个字母各一个。如果A放在左上角，可能的排列有多少种？
stem
Q15
In Theresa's first $8$ basketball games, she scored $7, 4, 3, 6, 8, 3, 1$ and $5$ points. In her ninth game, she scored fewer than $10$ points and her points-per-game average for the nine games was an integer. Similarly in her tenth game, she scored fewer than $10$ points and her points-per-game average for the $10$ games was also an integer. What is the product of the number of points she scored in the ninth and tenth games?
在特蕾莎的前8场篮球比赛中，她得分分别是7、4、3、6、8、3、1和5分。在第九场比赛中，她得分少于10分，且九场比赛的场均得分是整数。同样，在第十场比赛中，她得分少于10分，且十场比赛的场均得分也是整数。第九场和第十场比赛得分的乘积是多少？
stem
Q16
A shape is created by joining seven unit cubes, as shown. What is the ratio of the volume in cubic units to the surface area in square units?
通过连接七个单位立方体形成的形状，如图所示。体积（立方单位）与表面积（平方单位）的比率为多少？
stem
Q17
Ms. Osborne asks each student in her class to draw a rectangle with integer side lengths and a perimeter of $50$ units. All of her students calculate the area of the rectangle they draw. What is the difference between the largest and smallest possible areas of the rectangles?
奥斯本女士让班上的每个学生画一个周长为 $50$ 单位的整数边长矩形。所有学生都计算了自己画的矩形的面积。最大可能面积与最小可能面积的差是多少？
Q18
Two circles that share the same center have radii $10$ meters and $20$ meters. An aardvark runs along the path shown, starting at A and ending at K. How many meters does the aardvark run?
两个同心圆，半径分别为 $10$ 米和 $20$ 米。土豚沿着图示路径从 A 点跑到 K 点。土豚跑了多少米？
stem
Q19
Eight points are spaced at intervals of one unit around a $2\times 2$ square, as shown. Two of the $8$ points are chosen at random. What is the probability that the points are one unit apart?
八个点围绕 $2\times 2$ 正方形以一单位间隔等距放置，如图所示。从 8 个点中随机选择两个点。这两个点相距一单位的概率是多少？
stem
Q20
The students in Mr. Neatkin's class took a penmanship test. Two-thirds of the boys and $\frac{3}{4}$ of the girls passed the test, and an equal number of boys and girls passed the test. What is the minimum possible number of students in the class?
尼特金先生班上的学生参加了一次笔迹测试。男生中有 $\frac{2}{3}$ 和女生中有 $\frac{3}{4}$ 通过了测试，并且通过测试的男生和女生人数相等。班上学生的最小可能人数是多少？
Q21
Jerry cuts a wedge from a $6$-cm cylinder of bologna as shown by the dashed curve. Which answer choice is closest to the volume of his wedge in cubic centimeters?
杰瑞从一个6厘米高的博洛尼亚香肠圆柱体中切下一个楔形块，如虚线所示。哪个选项最接近他的楔形块的体积（立方厘米）？
stem
Q22
For how many positive integer values of $n$ are both $\frac{n}{3}$ and $3n$ three-digit whole numbers?
有且仅有几个正整数 $n$ 使得 $\frac{n}{3}$ 和 $3n$ 都是三位数的整数？
Q23
In square $ABCE$, $AF = 2FE$ and $CD = 2DE$. What is the ratio of the area of $\triangle BFD$ to the area of square $ABCE$?
在正方形 $ABCE$ 中，$AF = 2FE$ 且 $CD = 2DE$。$ riangle BFD$ 的面积与正方形 $ABCE$ 的面积之比是多少？
stem
Q24
Ten tiles numbered $1$ through $10$ are turned face down. One tile is turned up at random, and a die is rolled. What is the probability that the product of the numbers on the tile and the die will be a square?
十块编号为1到10的瓷砖面朝下放置。随机翻开一块瓷砖，并掷一颗骰子。瓷砖和骰子上的数字乘积为完全平方的概率是多少？
Q25
Margie's winning art design is shown. The smallest circle has radius $2$ inches, with each successive circle's radius increasing by $2$ inches. Approximately what percent of the design is black?
玛吉获奖的艺术设计如图所示。最小的圆半径为2英寸，每一个后续圆的半径增加2英寸。设计中大约百分之多少是黑色的？
stem
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