2008 AMC amc8 真题 答案 详解

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中英双语真题

2008 AMC8
Problem 1
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?
苏珊在嘉年华上有50美元可以消费。她在食物上花了12美元，在乘车上了两倍的钱。她还剩多少美元可以花？
(A) 12 (B) 14 (C) 26 (D) 38 (E) 50

Problem 2
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?
十个字母的代码BEST OF LUCK按顺序依次表示0-9这十个数字。代码字CLUE代表的4位数是什么？
(A) 8671 (B) 8672 (C) 9781 (D) 9782 (E) 9872

Problem 3
If February is a month that contains Friday the 13th, what day of the week is February 1?
如果2月13号是周五，那么2月1号是周几？
(A) Sunday (B) Monday (C) Wednesday (D) Thursday (E) Saturday

英文真题

Compiled on: January 1, 2021 AMC8 2008 Problems Page 57 of 109 Q1. Susan had 50 dollars to spend at the carnival. She spent 12 dollars on food and twice as much on rides. How many dollars did she have left to spend? A) 12 B) 14 C) 26 D) 38 E) 50 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? A) 8671 B) 8672 C) 9781 D) 9782 E) 9872 Q3. If February is a month that contains Friday the 13th, what day of the week is February 1? A) Sunday B) Monday C) Wednesday D) Thursday E) Saturday 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? A) 3 B) 4 C) 5 D) 6 E) 7 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? A) 15 B) 16 C) 18 D) 20 E) 22 Q6. In the figure, what is the ratio of the area of the grey squares to the area of the white squares? A) 3:10 B) 3:8 C) 3:7 D) 3:5 E) 1:1 Q7. If (\frac{3}{5} = \frac{M}{45} = \frac{60}{N}), what is (M + N)? A) 27 B) 29 C) 45 D) 105 E) 127 Q8. Candy sales from the Boosters Club from January through April are shown. What were the average sales per month in dollars?

真题文字详解(英文)

Problem 1 Susan had 50 dollars to spend at the carnival. She spent 12 dollars on food and twice as much on rides. How many dollars did she have left to spend?
(A) 12 (B) 14 (C) 26 (D) 38 (E) 50

Solution If Susan spent 12 dollars, then twice that much on rides, then she spent $12 + 12 \times 2 = 36$ dollars in total. We subtract 36 from 50 to get (B) 14.

Problem 2 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?
(A) 8671 (B) 8672 (C) 9781 (D) 9782 (E) 9872

Solution We can derive that C=8, L=6, U=7, and E=1. Therefore, the answer is (A) 8671.

Solution 2 We can easily see that C=8, which makes only (A) 8761 and (B) 8762 possible. Since the only difference between answer choices A and B is the last digit and that the last digit in the code word "CLUE" is E, we can just find that E=1 and that the answer is (A) 8671.

Problem 3 If February is a month that contains Friday the 13th, what day of the week is February 1?
(A) Sunday (B) Monday (C) Wednesday (D) Thursday (E) Saturday

Solution We can go backwards by days, but we can also backwards by weeks. If we go backwards by weeks, we see that February 6 is a Friday. If we now go backwards by days, February 1 is a (A) Sunday.

Solution 2 Since the days of the week repeat every 7 days and $1 - 13 \equiv 2 \pmod{7}$, the day of the week of the day 2 days after February 13 is the same as the day of the week of February 1. Since we know that February 13 is a Friday, the day of the week of the day 2 days after February 13 is a Sunday so we get that February 1 is a (A) Sunday.

Solution 3 We can go back 2 weeks and say that Friday is the -1st of February. Going forward 2 days, we get that February 1st is Sunday. So our answer is (A) Sunday.

Problem 4 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?

真题文字详解(中英双语)

Problem 1

Susan had 50 dollars to spend at the carnival. She spent 12 dollars on food and twice as much on rides. How many dollars did she have left to spend?

苏珊在游乐园有 50 美元可以花。她在食物上花了 12 美元，在游乐设施上花了 twice as much。她剩下多少美元可以花？

(A) 12 (B) 14 (C) 26 (D) 38 (E) 50

Solution

If Susan spent 12 dollars, then twice that much on rides, then she spent $12 + 12 \times 2 = 36$ dollars in total. We subtract 36 from 50 to get (B) 14.

如果苏珊花了 12 美元，然后在游乐设施上花了 twice that much，那么她总共花了 $12 + 12 \times 2 = 36$ 美元。我们从 50 减去 36 得到 (B) 14。

Problem 2

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?

这个十字母代码 BEST OF LUCK 代表了按顺序排列的十个数字 0-9。由代码词 CLUE 表示的四位数是多少？

(A) 8671 (B) 8672 (C) 9781 (D) 9782 (E) 9872

Solution

We can derive that C = 8, L = 6, U = 7, and E = 1. Therefore, the answer is (A) 8671.

我们可以推导出 C = 8, L = 6, U = 7, 和 E = 1。因此，答案是 (A) 8671。

Solution 2

We can easily see that C = 8, which makes only (A) 8761 and (B) 8762 possible. Since the only difference between answer choices A and B is the last digit and that the last digit in the code word "CLUE" is E, we can just find that E = 1 and that the answer is (A) 8671.

我们可以很容易地看出 C = 8，这使得只有 (A) 8761 和 (B) 8762 是可能的。由于答案选项 A 和 B 之间的唯一区别是最后一位数字，并且代码词“CLUE”的最后一位数字是 E，我们可以找到 E = 1，答案是 (A) 8671。

Problem 3

If February is a month that contains Friday the 13th, what day of the week is February 1?

如果二月包含星期五 13 号，那么二月初一是星期几？

(A) Sunday (B) Monday (C) Wednesday (D) Thursday (E) Saturday

Solution