amcdrill | AMC8 AMC10 AMC12 Practice

Q1

Which of the following values is largest?

下列哪个值最大？

(A) $2 + 0 + 1 + 7$ $2 + 0 + 1 + 7$ (B) $2 \times 0 + 1 + 7$ $2 \times 0 + 1 + 7$ (C) $2 + 0 \times 1 + 7$ $2 + 0 \times 1 + 7$ (D) $2 + 0 + 1 \times 7$ $2 + 0 + 1 \times 7$ (E) $2 \times 0 \times 1 \times 7$ $2 \times 0 \times 1 \times 7$

Q2

Alicia, Brenda, and Colby were the candidates in a recent election for student president. The pie chart below shows how the votes were distributed among the three candidates. If Brenda received 36 votes, then how many votes were cast all together?

Alicia、Brenda 和 Colby 是最近学生会长选举的候选人。下方的饼图显示了三位候选人的得票分布。如果 Brenda 获得了 36 票，那么总共投出了多少票？

(A) 70 70 (B) 84 84 (C) 100 100 (D) 106 106 (E) 120 120

Q3

What is the value of the expression ?

求这个表达式的值？

(A) 4 4 (B) $4\sqrt{2}$ $4\sqrt{2}$ (C) 8 8 (D) $8\sqrt{2}$ $8\sqrt{2}$ (E) 16 16

Q4

When 0.000315 is multiplied by 7,928,564 the product is closest to which of the following?

0.000315 乘以 7,928,564 的积最接近下列哪个值？

(A) 210 210 (B) 240 240 (C) 2,100 2,100 (D) 2,400 2,400 (E) 24,000 24,000

Q5

What is the value of the expression $\frac{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8}{1 + 2 + 3 + 4 + 5 + 6 + 7 + 8}$?

求表达式 $\frac{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8}{1 + 2 + 3 + 4 + 5 + 6 + 7 + 8}$ 的值？

(A) 1020 1020 (B) 1120 1120 (C) 1220 1220 (D) 2240 2240 (E) 3360 3360

Q6

If the degree measures of the angles of a triangle are in the ratio 3 : 3 : 4, what is the degree measure of the largest angle of the triangle?

如果一个三角形的角度度数比例为 3 : 3 : 4，那么该三角形最大角度的度数是多少？

(A) 18 18 (B) 36 36 (C) 60 60 (D) 72 72 (E) 90 90

Q7

Let Z be a 6-digit positive integer, such as 123,123, whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must be a factor of Z?

设 Z 是一个 6 位正整数，例如 123123，其前三位数字与后三位数字顺序相同。以下哪个数一定是 Z 的因数？

(A) 11 11 (B) 19 19 (C) 101 101 (D) 111 111 (E) 1111 1111

Q8

Malcolm wants to visit Isabella after school today and knows the street where she lives but doesn't know her house number. She tells him, "My house number has two digits, and exactly three of the following four statements about it are true." (1) It is prime. (2) It is even. (3) It is divisible by 7. (4) One of its digits is 9. This information allows Malcolm to determine Isabella's house number. What is its units digit?

马尔科姆放学后想去拜访伊莎贝拉，他知道她住的街道但不知道她的门牌号。她告诉他：“我的门牌号是两位数，且以下四个陈述中恰好有三个是真的。” (1) 它是质数。 (2) 它是偶数。 (3) 它能被 7 整除。 (4) 它有一个数字是 9。这个信息让马尔科姆能确定伊莎贝拉的门牌号。它的个位数字是多少？

(A) 4 4 (B) 6 6 (C) 7 7 (D) 8 8 (E) 9 9

Q9

All of Marcy's marbles are blue, red, green, or yellow. One third of her marbles are blue, one fourth of them are red, and six of them are green. What is the smallest number of yellow marbles that Marcy could have?

马西所有的弹珠是蓝色、红色、绿色或黄色。她有三分之一的弹珠是蓝色，四分之一是红色，有 6 个是绿色。马西可能拥有的黄色弹珠最少是多少？

(A) 1 1 (B) 2 2 (C) 3 3 (D) 4 4 (E) 5 5

Q10

A box contains five cards, numbered 1, 2, 3, 4, and 5. Three cards are selected randomly without replacement from the box. What is the probability that 4 is the largest value selected?

一个盒子里有五张卡片，编号 1、2、3、4 和 5。从盒子里不放回地随机抽取三张卡片。4 是所抽最大值的概率是多少？

(A) $\frac{1}{10}$ $\frac{1}{10}$ (B) $\frac{1}{5}$ $\frac{1}{5}$ (C) $\frac{3}{10}$ $\frac{3}{10}$ (D) $\frac{2}{5}$ $\frac{2}{5}$ (E) $\frac{1}{2}$ $\frac{1}{2}$

Q11

A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is 37, how many tiles cover the floor?

一个正方形地板上铺满了相同大小的正方形瓷砖。位于两条对角线上的瓷砖总数为37，问地板上有多少块瓷砖？

(A) 148 148 (B) 324 324 (C) 361 361 (D) 1296 1296 (E) 1369 1369

Q12

The smallest positive whole number greater than 1 that leaves a remainder of 1 when divided by 4, 5, and 6 lies between which of the following pairs of numbers?

大于1的最小的正整数，除以4、5、6时余数均为1，它位于下列哪一对数的之间？

(A) 2 and 19 2 和 19 (B) 20 and 39 20 和 39 (C) 40 and 59 40 和 59 (D) 60 and 79 60 和 79 (E) 80 and 124 80 和 124

Q13

Peter, Emma, and Kyler played chess with each other. Peter won 4 games and lost 2 games. Emma won 3 games and lost 3 games. If Kyler lost 3 games, how many games did he win?

Peter、Emma和Kyler互相下棋对弈。Peter赢了4局，输了2局。Emma赢了3局，输了3局。如果Kyler输了3局，他赢了多少局？

(A) 0 0 (B) 1 1 (C) 2 2 (D) 3 3 (E) 4 4

Q14

Chloe and Zoe are both students in Ms. Demeanor's math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to only 80% of the problems she solved alone, but overall 88% of her answers were correct. Zoe had correct answers to 90% of the problems she solved alone. What was Zoe's overall percentage of correct answers?

Chloe和Zoe都是Ms. Demeanor数学课的学生。昨晚她们各自独立完成了作业的一半，然后一起完成了另一半。Chloe独立完成的题目正确率为80%，但总体正确率为88%。Zoe独立完成的题目正确率为90%。Zoe的总体正确率是多少？

(A) 89 89 (B) 92 92 (C) 93 93 (D) 96 96 (E) 98 98

Q15

In the arrangement of letters and numerals below, by how many different paths can you spell AMC8? Beginning at the A in the middle, a path allows only moves from one letter to an adjacent (above, below, left, or right, but not diagonal) letter. One example of such a path is traced in the picture.

在下面的字母和数字排列中，有多少条不同的路径可以拼出AMC8？从中间的A开始，路径只能移动到相邻的（上下左右，但不包括对角线）字母。图中描画了一条这样的路径示例。

(A) 8 8 (B) 9 9 (C) 12 12 (D) 24 24 (E) 36 36

Q16

In the figure shown below, choose point D on side BC so that $\triangle ACD$ and $\triangle ABD$ have equal perimeters. What is the area of $\triangle ABD$?

如下图所示，在边BC上选择点D，使得$ riangle ACD$和$ riangle ABD$的周长相等。$ riangle ABD$的面积是多少？

(A) $\frac{3}{4}$ $\frac{3}{4}$ (B) $\frac{3}{2}$ $\frac{3}{2}$ (C) 2 2 (D) $\frac{12}{5}$ $\frac{12}{5}$ (E) $\frac{5}{2}$ $\frac{5}{2}$

Q17

Starting with some gold coins and some empty treasure chests, I tried to put 9 gold coins in each treasure chest, but that left 2 treasure chests empty. So instead I put 6 gold coins in each treasure chest, but then I had 3 gold coins left over. How many gold coins did I have?

起始有一些金币和一些空宝箱，我试图每个宝箱放入9枚金币，但剩下2个宝箱为空。所以我改为每个宝箱放入6枚金币，但剩下3枚金币。问我有多少金币？

(A) 9 9 (B) 27 27 (C) 45 45 (D) 63 63 (E) 81 81

Q18

In the non-convex quadrilateral ABCD shown below, $\angle BCD$ is a right angle, AB = 12, BC = 4, CD = 3, and AD = 13. What is the area of quadrilateral ABCD?

如下所示的非凸四边形ABCD中，$\angle BCD$为直角，AB = 12，BC = 4，CD = 3，AD = 13。四边形ABCD的面积是多少？

(A) 12 12 (B) 24 24 (C) 26 26 (D) 30 30 (E) 36 36

Q19

For any positive integer M, the notation M! denotes the product of the integers 1 through M. What is the highest power n of 5 for which $5^n$ is a factor of the sum 98! + 99! + 100!?

对于任意正整数M，记M!为1到M的乘积。求5的最高幂次n，使得$5^n$整除98! + 99! + 100!之和？

(A) 23 23 (B) 24 24 (C) 25 25 (D) 26 26 (E) 27 27

Q20

An integer between 1000 and 9999, inclusive, is chosen at random. What is the probability that it is an odd integer whose digits are all distinct?

随机选取一个1000到9999（包含端点）的整数。求其为奇数且各位数字均不同的概率？

(A) $\dfrac{14}{75}$ $\dfrac{14}{75}$ (B) $\dfrac{56}{225}$ $\dfrac{56}{225}$ (C) $\dfrac{107}{400}$ $\dfrac{107}{400}$ (D) $\dfrac{7}{25}$ $\dfrac{7}{25}$ (E) $\dfrac{9}{25}$ $\dfrac{9}{25}$

Q21

Suppose a, b, and c are nonzero real numbers, and a + b + c = 0. What are the possible value(s) for $\dfrac{a}{|a|} + \dfrac{b}{|b|} + \dfrac{c}{|c|} + \dfrac{abc}{|abc|}$?

假设 a、b 和 c 是非零实数，且 a + b + c = 0。那么 $\dfrac{a}{|a|} + \dfrac{b}{|b|} + \dfrac{c}{|c|} + \dfrac{abc}{|abc|}$ 的可能值是多少？

(A) 0 0 (B) 1 and –1 1 和 –1 (C) 2 and –2 2 和 –2 (D) 0, 2, and –2 0、2 和 –2 (E) 0, 1, and –1 0、1 和 –1

Q22

In the right triangle ABC, AC = 12, BC = 5, and angle C is a right angle. A semicircle is inscribed in the triangle as shown. What is the radius of the semicircle?

在直角三角形 ABC 中，AC = 12，BC = 5，∠C 为直角。如图所示，一个半圆内接于三角形中。求该半圆的半径。

(A) $\dfrac{7}{6}$ $\dfrac{7}{6}$ (B) $\dfrac{13}{5}$ $\dfrac{13}{5}$ (C) $\dfrac{59}{18}$ $\dfrac{59}{18}$ (D) $\dfrac{10}{3}$ $\dfrac{10}{3}$ (E) $\dfrac{60}{13}$ $\dfrac{60}{13}$

Q23

Each day for four days, Linda traveled for one hour at a speed that resulted in her traveling one mile in an integer number of minutes. Each day after the first, her speed decreased so that the number of minutes to travel one mile increased by 5 minutes over the preceding day. Each of the four days, her distance traveled was also an integer number of miles. What was the total number of miles for the four trips?

连续四天，每天琳达以某种速度旅行一小时，使得她每英里旅行的时间是整数分钟。从第二天起，她的每英里旅行时间比前一天增加 5 分钟。每天她旅行的距离也是整数英里。四次旅行的总英里数是多少？

(A) 10 10 (B) 15 15 (C) 25 25 (D) 50 50 (E) 82 82

Q24

Mrs. Sanders has three grandchildren who call her regularly. One calls her every three days, one calls her every four days, and one calls her every five days. All three called her on December 31. On how many days during the next year did she not receive a phone call from any of her grandchildren?

桑德斯太太有三个孙辈定期给她打电话。一个每 3 天打一次，一个每 4 天打一次，一个每 5 天打一次。他们三人都于 12 月 31 日给她打了电话。接下来一年中，有多少天她没有接到任何孙辈的电话？

(A) 78 78 (B) 80 80 (C) 144 144 (D) 146 146 (E) 152 152

Q25

In the figure shown, US and UT are line segments each of length 2, and m$\angle$TUS = 60°. Arcs TR and SR are each one-sixth of a circle with radius 2. What is the area of the region shown?

如图所示，线段 US 和 UT 各长 2，∠TUS = 60°。弧 TR 和弧 SR 各为半径为 2 的圆的六分之一。求图示区域的面积。

(A) $3\sqrt{3} + \pi$ $3\sqrt{3} + \pi$ (B) $4\sqrt{3} - 4\pi/3$ $4\sqrt{3} - 4\pi/3$ (C) $2\sqrt{3}$ $2\sqrt{3}$ (D) $4\sqrt{3} - 2\pi/3$ $4\sqrt{3} - 2\pi/3$ (E) $4 + 4\pi/3$ $4 + 4\pi/3$

AMC8 2017