2022年AMC8试题解析.docx

41212(C) 55522What is the sum of the two smallest prime factors of 250?(A) 2 (B) 5 (C) 7 (D) 10 (E) 12A 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) 36Chandler wants to buy a $500 dollar 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(B)(A)(E)USAAMC 82022Theresa’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?(A) 9 (B) 10 (C) 11 (D) 12 (E) 13Six-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?250200or150Nm100u50asRaaLM3(D) 5345This file was downloaded from the AoPS Math Olympiad Resources Page Page 1 :// artofproblemsolving / 678910USAAMC 82022paper 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) 28The 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 2022 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) 80The 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) 36In 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 .A 3 B3EC6D(A) 3 (B) 4.5 (C) 6 (D) 9 (E) 18To 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?1 22 34(A) 1 (B) 2 (C) 3 (D) 4 (E) cannot be determinedFor 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 . (A) 13 (B) 20 (C) 24 (D) 28 (E) 30This file was downloaded from the AoPS Math Olympiad Resources Page Page 2 :// artofproblemsolving / 1112USAAMC 82022Tiles 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?I8II6933472BAIII7IV2CD151960(A) I (B) II (C) III (D) IV (E) cannot be determinedA unit hexagon is composed of a regular haxagon of side length 1 and its 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?This file was downloaded from the AoPS Math Olympiad Resources Page Page 3 :// artofproblemsolving / 13141516USAAMC 82022(A) 1 : 1 (B) 6 : 5 (C) 3 : 2 (D) 2 : 1 (E) 3 : 1Sets A and B, shown in the venn diagram, have the same number of elements. Thier union has 2022 elements and their intersection has 1001 elements. Find the number of elements in A.A B1001(A) 503 (B) 1006 (C) 1504 (D) 1507 (E) 1510The base of isosceles ABC is 24 and its area is 60. What is the length of one of the congruent sides?(A) 5 (B) 8 (C) 13 (D) 14 (E) 18Let a, b and c be numbers with 0 < a < b < c. Which of the following is impossible?(A) a + c < b (B) a · b < c (C) a + b < c (D) a · c < bc(E) b = aAmanda Reckonwith draws five circles with radii 1, 2, 3, 4 and 5. Then for e。