amcdrill | AMC8 AMC10 AMC12 Practice

Q1

Theresa's parents have agreed to buy her tickets to see her favorite band if she spends an average of 10 hours per week helping around the house for 6 weeks. For the first 5 weeks she helps around the house for 8, 11, 7, 12 and 10 hours. How many hours must she work during the final week to earn the tickets?

Theresa的父母同意如果她在6周内每周平均帮助家里做10小时家务，就给她买去看她最喜欢的乐队的门票。前5周她帮助家里的时间分别是8、11、7、12和10小时。最后一周她必须工作多少小时才能拿到门票？

(A) 9 9 (B) 10 10 (C) 11 11 (D) 12 12 (E) 13 13

Q2

Six-hundred fifty students were surveyed about their pasta preferences. The choices were lasagna, manicotti, ravioli and spaghetti. The results of the survey are displayed in the bar graph. What is the ratio of the number of students who preferred spaghetti to the number of students who preferred manicotti?

有650名学生接受了关于意面偏好的调查。选择有lasagna、manicotti、ravioli和spaghetti。调查结果显示在条形图中。喜欢spaghetti的学生人数与喜欢manicotti的学生人数之比是多少？

(A) 2/5 $\frac{2}{5}$ (B) 1/2 $\frac{1}{2}$ (C) 5/4 $\frac{5}{4}$ (D) 5/3 $\frac{5}{3}$ (E) 5/2 $\frac{5}{2}$

Q3

What is the sum of the two smallest prime factors of 250?

250的两个最小质因数的和是多少？

(A) 2 2 (B) 5 5 (C) 7 7 (D) 10 10 (E) 12 12

Q4

A haunted house has six windows. In how many ways can Georgie the Ghost enter the house by one window and leave by a different window?

一个鬼屋有六个窗户。Georgie the Ghost可以通过一个窗户进入房子并从另一个不同窗户离开，有多少种方式？

(A) 12 12 (B) 15 15 (C) 18 18 (D) 30 30 (E) 36 36

Q5

Chandler wants to buy a \$500 mountain bike. For his birthday, his grandparents send him \$50, his aunt sends him \$35 and his cousin gives him \$15. He earns \$16 per week for his paper route. He will use all of his birthday money and all of the money he earns from his paper route. In how many weeks will he be able to buy the mountain bike?

Chandler想买一辆500美元的山地车。他的生日时，祖父母给了他50美元，姑姑给了他35美元，表亲给了他15美元。他每周做报纸递送赚16美元。他将使用所有的生日钱和报纸递送赚的钱。需要多少周他才能买得起山地车？

(A) 24 24 (B) 25 25 (C) 26 26 (D) 27 27 (E) 28 28

Q6

The average cost of a long-distance call in the USA in 1985 was 41 cents per minute, and the average cost of a long-distance call in the USA in 2005 was 7 cents per minute. Find the approximate percent decrease in the cost per minute of a long-distance call.

1985年美国长途电话的平均费用是每分钟41美分，2005年是每分钟7美分。求长途电话每分钟费用的大致百分比减少量。

(A) 7 7 (B) 17 17 (C) 34 34 (D) 41 41 (E) 80 80

Q7

The average age of 5 people in a room is 30 years. An 18-year-old person leaves the room. What is the average age of the four remaining people?

房间里有5个人，平均年龄30岁。一个18岁的人离开了房间。剩下4人的平均年龄是多少？

(A) 25 25 (B) 26 26 (C) 29 29 (D) 33 33 (E) 36 36

Q8

In trapezoid ABCD, $\overline{AD}$ is perpendicular to $\overline{DC}$, $AD = AB = 3$, and $DC = 6$. In addition, $E$ is on $\overline{DC}$, and $BE$ is parallel to $\overline{AD}$. Find the area of $\triangle BEC$.

梯形ABCD中，$\overline{AD}$ 与 $\overline{DC}$ 垂直，$AD = AB = 3$，$DC = 6$。此外，$E$ 在 $\overline{DC}$ 上，$BE$ 平行于 $\overline{AD}$。求 $\triangle BEC$ 的面积。

(A) 3 3 (B) 4.5 4.5 (C) 6 6 (D) 9 9 (E) 18 18

Q9

To complete the grid below, each of the digits 1 through 4 must occur once in each row and once in each column. What number will occupy the lower right-hand square?

要完成下面的网格，每个数字1到4必须在每行和每列中各出现一次。右下角的方格应该是多少？

(A) 1 1 (B) 2 2 (C) 3 3 (D) 4 4 (E) cannot be determined 无法确定

Q10

For any positive integer $n$, define $n$ to be the sum of the positive factors of $n$. For example, $6 = 1 + 2 + 3 + 6 = 12$. Find $11$.

对于任意正整数 $n$，定义 $\sigma(n)$ 为 $n$ 的所有正因数的和。例如，$\sigma(6) = 1 + 2 + 3 + 6 = 12$。求 $\sigma(11)$。

(A) 13 13 (B) 20 20 (C) 24 24 (D) 28 28 (E) 30 30

Q11

Tiles I, II, III and IV are translated so one tile coincides with each of the rectangles A, B, C and D. In the final arrangement, the two numbers on any side common to two adjacent tiles must be the same. Which of the tiles is translated to Rectangle C?

瓦片 I、II、III 和 IV 被平移，使得每个瓦片与矩形 A、B、C 和 D 中的一个重合。在最终排列中，任何两个相邻瓦片共用的边的两个数字必须相同。哪块瓦片被平移到矩形 C？

(A) I I (B) II II (C) III III (D) IV IV (E) cannot be determined 无法确定

Q12

A unit hexagram is composed of a regular hexagon of side length 1 and its 6 equilateral triangular extensions, as shown in the diagram. What is the ratio of the area of the extensions to the area of the original hexagon?

一个单位六芒星由边长为 1 的正六边形及其 6 个等边三角形扩展组成，如图所示。扩展部分的面积与原始六边形面积的比率为多少？

(A) 1:1 1:1 (B) 6:5 6:5 (C) 3:2 3:2 (D) 2:1 2:1 (E) 3:1 3:1

Q13

Sets A and B, shown in the Venn diagram, have the same number of elements. Their union has 2007 elements and their intersection has 1001 elements. Find the number of elements in A.

集合 A 和 B 如维恩图所示，具有相同数量的元素。它们的并集有 2007 个元素，交集有 1001 个元素。求集合 A 中的元素个数。

(A) 503 503 (B) 1006 1006 (C) 1504 1504 (D) 1507 1507 (E) 1510 1510

Q14

The base of isosceles △ABC is 24 and its area is 60. What is the length of one of the congruent sides?

等腰三角形 △ABC 的底边长为 24，其面积为 60。求一对全等边的长度。

(A) 5 5 (B) 8 8 (C) 13 13 (D) 14 14 (E) 18 18

Q15

Let a, b and c be numbers with 0 < a < b < c. Which of the following is impossible?

设 a、b 和 c 是满足 0 < a < b < c 的数。以下哪个是不可能的？

(A) a + c < b a + c < b (B) a · b < c a × b < c (C) a + b < c a + b < c (D) a · c < b a × c < b (E) b/c = a b/c = a

Q16

Amanda Reckonwith draws five circles with radii 1, 2, 3, 4 and 5. Then for each circle she plots the point (C, A), where C is its circumference and A is its area. Which of the following could be her graph?

Amanda Reckonwith 画了五个半径分别为 1、2、3、4 和 5 的圆。然后对于每个圆，她绘制点 (C, A)，其中 C 是其周长，A 是其面积。以下哪一个可能是她的图像？

(A)

(B)

(C)

(D)

(E)

Q17

A mixture of 30 liters of paint is 25% red tint, 30% yellow tint and 45% water. Five liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture?

一种 30 升的油漆混合物含有 25% 红色颜料、30% 黄色颜料和 45% 水。在原混合物中加入 5 升黄色颜料。新混合物中黄色颜料的百分比是多少？

(A) 25 25 (B) 35 35 (C) 40 40 (D) 45 45 (E) 50 50

Q18

The product of the two 99-digit numbers 303,030,303, ..., 030,303 and 505,050,505, ..., 050,505 has thousands digit A and units digit B. What is the sum of A and B?

两个 99 位数 303,030,303, ..., 030,303 和 505,050,505, ..., 050,505 的乘积，千位数字为 A，个位数字为 B。A 和 B 的和是多少？

(A) 3 3 (B) 5 5 (C) 6 6 (D) 8 8 (E) 10 10

Q19

Pick two consecutive positive integers whose sum is less than 100. Square both of those integers and then find the difference of the squares. Which of the following could be the difference?

挑选两个连续的正整数，它们的和小于 100。将这两个整数平方，然后求平方差。以下哪一个可能是该差？

(A) 2 2 (B) 64 64 (C) 79 79 (D) 96 96 (E) 131 131

Q20

Before district play, the Unicorns had won 45% of their basketball games. During district play, they won six more games and lost two, to finish the season having won half their games. How many games did the Unicorns play in all?

在地区赛前，独角兽队篮球比赛胜率为 45%。地区赛中，他们赢了 6 场，输了 2 场，整个赛季胜率为一半。他们总共打了多少场比赛？

(A) 48 48 (B) 50 50 (C) 52 52 (D) 54 54 (E) 60 60

Q21

Two cards are dealt from a deck of four red cards labeled A, B, C, D and four green cards labeled A, B, C, D. A winning pair is two of the same color or two of the same letter. What is the probability of drawing a winning pair?

从一副牌中抽出两张牌，这副牌有四张标有A、B、C、D的红牌和四张标有A、B、C、D的绿牌。获胜对子是两张相同颜色或两张相同字母的牌。抽出获胜对子的概率是多少？

(A) $\frac{2}{7}$ $\frac{2}{7}$ (B) $\frac{3}{8}$ $\frac{3}{8}$ (C) $\frac{1}{2}$ $\frac{1}{2}$ (D) $\frac{4}{7}$ $\frac{4}{7}$ (E) $\frac{5}{8}$ $\frac{5}{8}$

Q22

A lemming sits at a corner of a square with side length 10 meters. The lemming runs 6.2 meters along a diagonal toward the opposite corner. It stops, makes a 90° right turn and runs 2 more meters. A scientist measures the shortest distance between the lemming and each side of the square. What is the average of these four distances in meters?

一只旅鼠坐在边长10米的正方形的角上。它沿着对角线向对角跑了6.2米。然后停下，向右转90°，再跑2米。科学家测量旅鼠到正方形每条边的最近距离。这些四个距离的平均值是多少米？

(A) 2 2 (B) 4.5 4.5 (C) 5 5 (D) 6.2 6.2 (E) 7 7

Q23

What is the area of the shaded pinwheel shown in the 5 × 5 grid?

5×5网格中所示的阴影风车图案的面积是多少？

(A) 4 4 (B) 6 6 (C) 8 8 (D) 10 10 (E) 12 12

Q24

A bag contains four pieces of paper, each labeled with one of the digits 1, 2, 3 or 4, with no repeats. Three of these pieces are drawn, one at a time without replacement, to construct a three-digit number. What is the probability that the three-digit number is a multiple of 3?

一个袋子里有四张纸，每张标有一个数字1、2、3或4，没有重复。从中不放回地抽三张纸，依次构造一个三位数。这个三位数是3的倍数的概率是多少？

(A) $\frac{1}{4}$ $\frac{1}{4}$ (B) $\frac{1}{3}$ $\frac{1}{3}$ (C) $\frac{1}{2}$ $\frac{1}{2}$ (D) $\frac{2}{3}$ $\frac{2}{3}$ (E) $\frac{3}{4}$ $\frac{3}{4}$

Q25

On the dart board shown in the figure, the outer circle has radius 6 and the inner circle has radius 3. Three radii divide each circle into three congruent regions, with point values shown. The probability that a dart will hit a given region is proportional to the area of the region. When two darts hit this board, the score is the sum of the point values in the regions. What is the probability that the score is odd?

图示飞镖盘外圆半径6，内圆半径3。三条半径将每个圆分成三个相等区域，显示分数。飞镖击中某区域的概率与该区域面积成正比。两支飞镖击中该盘，分数为两个区域分数的和。分数为奇数的概率是多少？

(A) $\frac{17}{36}$ $\frac{17}{36}$ (B) $\frac{35}{72}$ $\frac{35}{72}$ (C) $\frac{1}{2}$ $\frac{1}{2}$ (D) $\frac{37}{72}$ $\frac{37}{72}$ (E) $\frac{19}{36}$ $\frac{19}{36}$

AMC8 2007