2007 AMC amc8 真题 答案 详解

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中英双语真题

2007 AMC8
Problem 1
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?
如果特蕾莎平均每周花10个小时在家里帮忙，一共帮忙6周，那么她的父母就同意给她买票去看她最喜欢的乐队。在最初的5周里，她在家里帮忙了8，11，7，12和10个小时。最后一周她必须工作多少小时才能挣到票？
(A) 9 (B) 10 (C) 11 (D) 12 (E) 13

Problem 2
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?
调查了650个学生对意大利面的偏好。可供选择的食品有烤宽面条、意大利通心面、水饺和意大利细面条。调查结果显示在下面条形图中。喜欢意大利细面条的学生人数与喜欢意大利通心面的学生人数的比值是多少？
(A) (\frac{2}{5}) (B) (\frac{1}{2}) (C) (\frac{5}{4}) (D) (\frac{5}{3}) (E) (\frac{5}{2})

英文真题

Compiled on: January 1, 2021 AMC8 2007 Problems Page 62 of 109 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 for the final week to earn the tickets? A) 9 B) 10 C) 11 D) 12 E) 13 Q2. 650 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? A) ( \frac{2}{5} ) B) ( \frac{1}{2} ) C) ( \frac{5}{4} ) D) ( \frac{5}{3} ) E) ( \frac{5}{2} ) Q3. What is the sum of the two smallest prime factors of 250? A) 2 B) 5 C) 7 D) 10 E) 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? A) 12 B) 15 C) 18 D) 30 E) 36 Q5. Chandler wants to buy a 500 dollar mountain bike. For his birthday, his grandparents send him 50 dollars, his aunt sends him 35 dollars and his cousin gives him 15 dollars. He earns 16 dollars 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? A) 24 B) 25 C) 26 D) 27 E) 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. A) 7 B) 17 C) 34 D) 41 E) 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? A) 25 B) 26 C) 29 D) 33 E) 36 Q8. In trapezoid ABCD, AD is perpendicular to DC, AD = AB = 3, and DC = 6. In addition, E is on DC, and BE is parallel to AD. Find the area of △BEC.

真题文字详解(英文)

Problem 1 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 for the final week to earn the tickets?
(A) 9 (B) 10 (C) 11 (D) 12 (E) 13

Solution 1 Let ( x ) be the number of hours she must work for the final week. We are looking for the average, so
[ \frac{8 + 11 + 7 + 12 + 10 + x}{6} = 10 ]
Solving gives:
[ \frac{48 + x}{6} = 10 ]
[ 48 + x = 60 ]
[ x = 12 ]
So, the answer is (D) 12

Solution 2 Use average deviation:
The average is 10 hour per day. If work 8 hours then it is 2 hours short; if work 11 hours then there is 1 hour surplus, the last day need to cancel out the collective deviation from the previous 5 days.
So we got
[ -2 + 1 - 3 + 2 + 0 = -2 ]
The last day need to have +2 deviation to cancel out the -2 collective deviation to get 10 as average value, so (D) 12.

Problem 2 650 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?

真题文字详解(中英双语)

Problem 1 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 for the final week to earn the tickets?
(A) 9 (B) 10 (C) 11 (D) 12 (E) 13

Solution 1 Let ( x ) be the number of hours she must work for the final week. We are looking for the average, so
[ \frac{8 + 11 + 7 + 12 + 10 + x}{6} = 10 ]
Solving gives:
[ \frac{48 + x}{6} = 10 ]
[ 48 + x = 60 ]
[ x = 12 ]
So, the answer is (D) 12.

Solution 2 Use average deviation:
The average is 10 hour per day. If work 8 hours then it is 2 hours short; if work 11 hours then there is 1 hour surplus, the last day need to cancel out the collective deviation from the previous 5 days.
So we got
[ -2 + 1 - 3 + 2 + 0 = -2 ]
The last day need to have +2 deviation to cancel out the -2 collective deviation to get 10 as average value, so (D) 12.

Problem 2 650 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?