2012 AMC amc12b 真题 答案 详解

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中英双语真题

2012 AMC12B

Problem 1

Each third-grade classroom at Pearl Creek Elementary has 18 students and 2 pet rabbits. How many more students than rabbits are there in all 4 of the third-grade classrooms?

Pearl Creek 小学的每一个三年级教室都有 18 个学生和 2 只宠物兔，问四个三年级教室的学生总数比宠物兔总数多出多少个？

(A) 48 (B) 56 (C) 64 (D) 72 (E) 80

Problem 2

A circle of radius 5 is inscribed in a rectangle as shown. The ratio of the length of the rectangle to its width is 2:1. What is the area of the rectangle?

如图所示，一个半径为 5 的圆和一个矩形内切，矩形的长和宽之比为 2:1，问矩形的面积是多少？

(A) 50 (B) 100 (C) 125 (D) 150 (E) 200

Problem 3

For a science project, Sammy observed a chipmunk and squirrel stashing acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The squirrel hid 4 acorns in each of the holes it dug. They each hid the same number of acorns, although the squirrel needed 4 fewer holes. How many acorns did the chipmunk hide?

为了完成一项科学作业，Sammy 观察花栗鼠和松鼠在洞里藏橡果的情况。花栗鼠在它所挖的每个洞里藏 3 颗橡果，而松鼠在它所挖的每个洞里藏 4 颗橡果，它们藏的橡果的总数一样多，但是松鼠所需要的洞比花栗鼠的少 4 个，问花栗鼠藏了多少颗橡果？

(A) 30 (B) 36 (C) 42 (D) 48 (E) 54

英文真题

2012 AMC 12B Problems Problem 1 Each third-grade classroom at Pearl Creek Elementary has 18 students and 2 pet rabbits. How many more students than rabbits are there in all 4 of the third-grade classrooms? (A) 48 (B) 56 (C) 64 (D) 72 (E) 80 Problem 2 A circle of radius 5 is inscribed in a rectangle as shown. The ratio of the length of the rectangle to its width is 2:1. What is the area of the rectangle? (A) 50 (B) 100 (C) 125 (D) 150 (E) 200 Problem 3 For a science project, Sammy observed a chipmunk and squirrel stashing acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The squirrel hid 4 acorns in each of the holes it dug. They each hid the same number of acorns, although the squirrel needed 4 fewer holes. How many acorns did the chipmunk hide? (A) 30 (B) 36 (C) 42 (D) 48 (E) 54 Problem 4 Suppose that the euro is worth $1.30 dollars. If Diana has $500 dollars and Etienne has 400 euros, by what percent is the value of Etienne's money greater than the value of Diana's money? (A) 2 (B) 4 (C) 6.5 (D) 8 (E) 13 Problem 5 Two integers have a sum of 26. When two more integers are added to the first two, the sum is 41. Finally, when two more integers are added to the sum of the previous 4 integers, the sum is 57. What is the minimum number of even integers among the 6 integers? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 Problem 6 In order to estimate the value of x - y where x and y are real numbers with x > y > 0, Xiaoli rounded x up by a small amount, rounded y down by the same amount, and then subtracted her rounded values. Which of the following statements is necessarily correct? (A) Her estimate is larger than x - y (B) Her estimate is smaller than x - y (C) Her estimate equals x - y (D) Her estimate equals y - x (E) Her estimate is 0 Problem 7 Small lights are hung on a string 6 inches apart in the order red, red, green, green, green, red, red, green, green, and so continuing this pattern of 2 red lights followed by 3 green lights. How many feet separate the 3rd red light and the 21st red light? Note: 1 foot is equal to 12 inches.

真题文字详解(英文)

Problem 1 The following problem is from both the 2012 AMC 12B #1 and 2012 AMC 10B #1, so both problems redirect to this page. Each third-grade classroom at Pearl Creek Elementary has 18 students and 2 pet rabbits. How many more students than rabbits are there in all 4 of the third-grade classrooms? (A) 48 (B) 56 (C) 64 (D) 72 (E) 80 Solution Solution 1 Multiplying 18 and 2 by 4 we get 72 students and 8 rabbits. We then subtract: 72 - 8 = (C) 64. Solution 2 In each class, there are 18 - 2 = 16 more students than rabbits. So for all classrooms, the difference between students and rabbits is 16 × 4 = (C) 64 Problem 2 A circle of radius 5 is inscribed in a rectangle as shown. The ratio of the length of the rectangle to its width is 2:1. What is the area of the rectangle? (A) 50 (B) 100 (C) 125 (D) 150 (E) 200 Solution If the radius is 5, then the width is 10, hence the length is 20. 10 × 20 = (E) 200. Problem 3 For a science project, Sammy observed a chipmunk and squirrel stashing acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The squirrel hid 4 acorns in each of the holes it dug. They each hid the same number of acorns, although the squirrel needed 4 fewer holes. How many acorns did the chipmunk hide? (A) 30 (B) 36 (C) 42 (D) 48 (E) 54 Solution If x is the number of holes that the chipmunk dug, then 3x = 4(x - 4) so 3x = 4x - 16, and x = 16. The number of acorns hidden by the chipmunk is equal to 3x = (D) 48 Solution 2 Trying answer choices, we see that (D) 48 works. ~Extremelysupercool dude Problem 4 Suppose that the euro is worth 1.3 dollars. If Diana has 500 dollars and Etienne has 400 euros, by what percent is the value of Etienne's money greater that the value of Diana's money? (A) 2 (B) 4 (C) 6.5 (D) 8 (E) 13 Solution The ratio 400 euros/500 dollars can be simplified using conversion factors: 400 euros/500 dollars · 1.3 dollars/1 euro = 520/500 = 1.04 which means the money is greater by (B) 4 percent.

真题文字详解(中英双语)

Problem 1 The following problem is from both the 2012 AMC 12B #1 and 2012 AMC 10B #1, so both problems redirect to this page. 以下题目来自2012年AMC 12B #1和2012年AMC 10B #1，因此这两个问题都重定向到这个页面。 Each third-grade classroom at Pearl Creek Elementary has 18 students and 2 pet rabbits. How many more students than rabbits are there in all 4 of the third-grade classrooms? 珍珠溪小学每个三年级教室有18名学生和2只宠物兔子。所有4个三年级教室里，学生比兔子多多少？ (A) 48 (B) 56 (C) 64 (D) 72 (E) 80 Solution Solution 1 Multiplying 18 and 2 by 4 we get 72 students and 8 rabbits. We then subtract: 72 - 8 = (C) 64. Solution 2 In each class, there are 18 - 2 = 16 more students than rabbits. So for all classrooms, the difference between students and rabbits is 16 × 4 = (C) 64 Problem 2 A circle of radius 5 is inscribed in a rectangle as shown. The ratio of the length of the rectangle to its width is 2:1. What is the area of the rectangle? (A) 50 (B) 100 (C) 125 (D) 150 (E) 200 Solution If the radius is 5, then the width is 10, hence the length is 20. 10 × 20 = (E) 200. Problem 3 For a science project, Sammy observed a chipmunk and squirrel stashing acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The squirrel hid 4 acorns in each of the holes it dug. They each hid the same number of acorns, although the squirrel needed 4 fewer holes. How many acorns did the chipmunk hide? (A) 30 (B) 36 (C) 42 (D) 48 (E) 54 Solution If x is the number of holes that the chipmunk dug, then 3x = 4(x - 4), so 3x = 4x - 16, and x = 16. The number of acorns hidden by the chipmunk is equal to 3x = (D) 48 Solution 2 Trying answer choices, we see that (D) 48 works. ~Extremelysupercool dude Problem 4 Suppose that the euro is worth 1.3 dollars. If Diana has 500 dollars and Etienne has 400 euros, by what percent is the value of Etienne's money greater that the value of Diana's money? (A) 2 (B) 4 (C) 6.5 (D) 8 (E) 13 Solution