amcdrill | AMC8 AMC10 AMC12 Practice

Q1

Which of the following is the largest?

以下哪个最大？

(A) $\frac{1}{3}$ $\frac{1}{3}$ (B) $\frac{1}{4}$ $\frac{1}{4}$ (C) $\frac{3}{8}$ $\frac{3}{8}$ (D) $\frac{5}{12}$ $\frac{5}{12}$ (E) $\frac{7}{24}$ $\frac{7}{24}$

Q2

$\frac{1}{10} + \frac{2}{10} + \frac{3}{10} + \frac{4}{10} + \frac{5}{10} + \frac{6}{10} + \frac{7}{10} + \frac{8}{10} + \frac{9}{10} + \frac{55}{10} =$

(A) $\frac{1}{4}$ $\frac{1}{4}$ (B) 6.4 6.4 (C) 9 9 (D) 10 10 (E) 11 11

Q3

Each day Maria must work 8 hours. This does not include the 45 minutes she takes for lunch. If she begins working at 7:25 AM and takes her lunch break at noon, then her working day will end at

Maria 每天必须工作 8 小时。这不包括她午餐的 45 分钟。如果她早上 7:25 开始工作，并在中午休息午餐，那么她的工作日将结束于

(A) 3:40 PM 下午3:40 (B) 3:55 PM 下午3:55 (C) 4:10 PM 下午4:10 (D) 4:25 PM 下午4:25 (E) 4:40 PM 下午4:40

Q4

Which of the following represents the result when the figure shown at the right is rotated clockwise 120° about its center?

将右图顺时针绕其中心旋转 120° 后，哪个选项表示结果？

(A)

(B)

(C)

(D)

(E)

Q5

Given that 1 mile = 8 furlongs and 1 furlong = 40 rods, the number of rods in one mile is

已知 1 英里 = 8 弗隆，1 弗隆 = 40 杆，则 1 英里有多少杆？

(A) 5 5 (B) 320 320 (C) 660 660 (D) 1760 1760 (E) 5280 5280

Q6

The unit's digit (one's digit) of the product of any six consecutive positive whole numbers is

任意六个连续正整数的乘积的个位数（个位）是

(A) 0 0 (B) 2 2 (C) 4 4 (D) 6 6 (E) 8 8

Q7

If $\angle A = 60^\circ$, $\angle E = 40^\circ$ and $\angle C = 30^\circ$, then $\angle BDC =$

如果 $\angle A = 60^\circ$，$\angle E = 40^\circ$ 且 $\angle C = 30^\circ$，则 $\angle BDC =$

(A) 40° 40° (B) 50° 50° (C) 60° 60° (D) 70° 70° (E) 80° 80°

Q8

For how many three-digit whole numbers does the sum of the digits equal 25?

三位数中有多少个各位数字之和等于25？

(A) 2 2 (B) 4 4 (C) 6 6 (D) 8 8 (E) 10 10

Q9

A shopper buys a $100 coat on sale for 20% off. An additional $5 is taken off the sale price by using a discount coupon. A sales tax of 8% is paid on the final selling price. The total amount the shopper pays for the coat is

一位顾客以20%折扣购买一件原价100美元的外套，使用折扣券额外减去5美元销售价。最终售价需缴纳8%的销售税。顾客为这件外套支付的总金额是

(A) $81.00 81.00美元 (B) $81.40 81.40美元 (C) $82.00 82.00美元 (D) $82.08 82.08美元 (E) $82.40 82.40美元

Q10

For how many positive integer values of N (N > 0) is the expression $\frac{36}{N+2}$ an integer?

对于多少个正整数 N（N > 0），表达式 $\frac{36}{N+2}$ 是整数？

(A) 7 7 (B) 8 8 (C) 9 9 (D) 10 10 (E) 12 12

Q11

Last summer 100 students attended basketball camp. Of those attending, 52 were boys and 48 were girls. Also, 40 students were from Jones Middle School and 60 were from Clay Middle School. Twenty of the girls were from Jones Middle School. How many of the boys were from Clay Middle School?

去年夏天，有100名学生参加篮球夏令营。其中52名男孩，48名女孩。还有40名学生来自琼斯中学，60名来自克雷中学。20名女孩来自琼斯中学。克雷中学的男孩有多少名？

(A) 20 20 (B) 32 32 (C) 40 40 (D) 48 48 (E) 52 52

Q12

Each of the three large squares shown below is the same size. Segments that intersect the sides of the squares intersect at the midpoints of the sides. How do the shaded areas of these squares compare?

下面的三个大正方形大小相同。穿过正方形边的线段都在边的中点相交。这些正方形的阴影面积如何比较？

(A) The shaded area in all three are equal. 三个阴影面积相等。 (B) Only the shaded areas of I and II are equal. 仅I和II阴影面积相等。 (C) Only the shaded areas of I and III are equal. 仅I和III阴影面积相等。 (D) Only the shaded areas of II and III are equal. 仅II和III阴影面积相等。 (E) The shaded areas of I, II and III are all different. I、II、III阴影面积均不同。

Q13

The number halfway between $\frac{1}{6}$ and $\frac{1}{4}$ is

$\frac{1}{6}$ 和 $\frac{1}{4}$ 的中间数是

(A) $\frac{1}{10}$ $\frac{1}{10}$ (B) $\frac{1}{5}$ $\frac{1}{5}$ (C) $\frac{5}{24}$ $\frac{5}{24}$ (D) $\frac{7}{24}$ $\frac{7}{24}$ (E) $\frac{5}{12}$ $\frac{5}{12}$

Q14

Two children at a time can play pairball. For 90 minutes, with only two children playing at one time, five children take turns so that each one plays the same amount of time. The number of minutes each child plays is

每次两个孩子玩配对球。90分钟内，每次只有两个孩子玩，五个孩子轮流玩，每人玩的时间相同。每个孩子玩的分钟数是

(A) 9 9 (B) 10 10 (C) 18 18 (D) 20 20 (E) 36 36

Q15

If this path is to continue in the same pattern: then which sequence of arrows goes from point 425 to point 427?

如果这条路径继续相同的模式：那么从点425到点427的箭头序列是哪一个？

(A)

(B)

(C)

(D)

(E)

Q16

The perimeter of one square is 3 times the perimeter of another square. The area of the larger square is how many times the area of the smaller square?

一个正方形的周长是另一个正方形周长的3倍。那么较大正方形的面积是较小正方形面积的几倍？

(A) 2 2 (B) 3 3 (C) 4 4 (D) 6 6 (E) 9 9

Q17

Pauline Bunyan can shovel snow at the rate of 20 cubic yards for the first hour, 19 cubic yards for the second, 18 for the third, etc., always shoveling one cubic yard less per hour than the previous hour. If her driveway is 4 yards wide, 10 yards long, and covered with snow 3 yards deep, then the number of hours it will take her to shovel it clean is closest to

Pauline Bunyan 第一小时铲雪20立方码，第二小时19立方码，第三小时18立方码，依此类推，每小时比前一小时少铲1立方码。如果她的车道宽4码，长10码，雪深3码，她铲干净需要的时间最接近

(A) 4 4 (B) 5 5 (C) 6 6 (D) 7 7 (E) 12 12

Q18

Mike leaves home and drives slowly east through city traffic. When he reaches the highway he drives east more rapidly until he reaches the shopping mall where he stops. He shops at the mall for an hour. Mike returns home by the same route as he came, driving west rapidly along the highway and then slowly through city traffic. Each graph shows the distance from home on the vertical axis versus the time elapsed since leaving home on the horizontal axis. Which graph is the best representation of Mike's trip?

Mike离开家，慢慢向东穿过城市交通。到达高速公路后，他更快地向东开到购物中心，然后停下。他在商场购物1小时。Mike返回家时走同一条路，先快速向西沿高速公路行驶，然后慢慢穿过城市交通。每个图表纵轴表示离家的距离，横轴表示离开家后的经过时间。哪张图是Mike旅程的最佳表示？

(A)

(B)

(C)

(D)

(E)

Q19

Around the outsides of a 4 by 4 square, construct four semi-circles (as shown in the figure) with the four sides of the square as their diameters. Another square, ABCD, has its sides parallel to the corresponding sides of the original square, and each side of ABCD is tangent to one of the semicircle. The area of the square ABCD is

在一个4×4的正方形外侧，用正方形的四条边作为直径，构造四个半圆（如图所示）。另一个正方形ABCD，其边与原正方形对应边平行，ABCD的每条边与一个半圆相切。ABCD正方形的面积是

(A) 16 16 (B) 32 32 (C) 36 36 (D) 48 48 (E) 64 64

Q20

Let W, X, Y and Z be four different digits selected from the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. If the sum $\frac{W}{X} + \frac{Y}{Z}$ is to be as small as possible, then $\frac{W}{X} + \frac{Y}{Z}$ must equal

让W、X、Y和Z是从集合{1, 2, 3, 4, 5, 6, 7, 8, 9}中选的四个不同数字。如果要使 $\frac{W}{X} + \frac{Y}{Z}$ 尽可能小，那么 $\frac{W}{X} + \frac{Y}{Z}$ 必须等于

(A) $\frac{2}{17}$ $\frac{2}{17}$ (B) $\frac{3}{17}$ $\frac{3}{17}$ (C) $\frac{17}{72}$ $\frac{17}{72}$ (D) $\frac{25}{72}$ $\frac{25}{72}$ (E) $\frac{13}{36}$ $\frac{13}{36}$

Q21

A gumball machine contains 9 red, 7 white, and 8 blue gumballs. The least number of gumballs a person must buy to be sure of getting four gumballs of the same color is

一个泡泡糖机里有9个红色的、7个白色的和8个蓝色的泡泡糖。一个人必须买至少多少个泡泡糖才能确保得到四个相同颜色的泡泡糖？

(A) 8 8 (B) 9 9 (C) 10 10 (D) 12 12 (E) 18 18

Q22

The two wheels shown at the right are spun and the two resulting numbers are added. The probability that the sum of the two numbers is even is

右侧所示的两个轮子被转动，得到两个数字相加。两个数字之和为偶数的概率是

(A) $\frac{1}{6}$ $\frac{1}{6}$ (B) $\frac{1}{4}$ $\frac{1}{4}$ (C) $\frac{1}{3}$ $\frac{1}{3}$ (D) $\frac{5}{12}$ $\frac{5}{12}$ (E) $\frac{4}{9}$ $\frac{4}{9}$

Q23

If X, Y and Z are different digits, then the largest possible 3-digit sum for XXX + YX + X has the form

如果X、Y和Z是不同的数字，则XXX + YX + X的最大可能3位和的形式是

(A) XXY XXY (B) XYZ XYZ (C) YYX YYX (D) YYZ YYZ (E) ZZY ZZY

Q24

A 2 by 2 square is divided into four 1 by 1 squares. Each of the small squares is to be painted either green or red. In how many different ways can the painting be accomplished so that no green square shares its top or right side with any red square? There may be as few as zero or as many as four small green squares.

一个2×2的正方形被分成四个1×1的小正方形。每个小正方形要么涂绿色要么涂红色。有多少种不同的涂色方式，使得没有绿色小方形与任何红色小方形共享其顶部或右侧？绿色小方形可以有0个到4个。

(A) 4 4 (B) 6 6 (C) 7 7 (D) 8 8 (E) 16 16

Q25

Find the sum of the digits in the answer to $\frac{9999...99}{94 \text{ nines}} \times \frac{4444...44}{94 \text{ fours}}$ where a string of 94 nines is multiplied by a string of 94 fours.

求 $\frac{9999...99}{94 \text{ nines}} \times \frac{4444...44}{94 \text{ fours}}$ 的答案中各位数字之和，其中94个9的串乘以94个4的串。

(A) 846 846 (B) 855 855 (C) 945 945 (D) 954 954 (E) 1072 1072

AMC8 1994