《2005年美国数学竞赛-AMC_12》.pdfVIP

USA AMC 12 2005 A 1 Two is 10% of x and 20% of y . What is x − y? A. 1 B. 2 C. 5 D. 10 E. 20 2 The equations 2x + 7 = 3 and bx − 10 = −2 have the same solution. What is the value of b? A. -8 B. -4 C. -2 D. 4 E. 8 3 A rectangle with a diagonal length of x is twice as long as it is wide. What is the area of the rectangle? 1 2 2 2 1 2 2 3 2 A. x B. x C. x D. x E. x 4 5 2 2 4 A store normally sells windows at $100 each. This week the store is offering one free window for each purchase of four. Dave needs seven windows and Doug needs eight windows. How much will they save if they purchase the windows together than rather separately? A. 100 B. 200 C. 300 D. 400 E. 500 5 The average (mean) of 20 numbers is 30, and the average of 30 other numbers is 20. What is the average of all 50 numbers? A. 23 B. 24 C. 25 D. 26 E. 27 6 Josh and Mike live 13 miles apart. Yesterday, Josh started to ride his bicycle toward Mike’s house. A little later Mike started to ride his bicycle toward Josh’s house. When they met, Josh had ridden for twice the length of time as Mike and at four-fifths of Mike’s rate. How many miles had Mike ridden when they met? A. 4 B. 5 C. 6 D. 7 E. 8 7 Square EF GH is inside the square ABCD so that each side of EF GH can be extended to pass through a vertex of ABCD. Square ABCD has side length √50 and BE = 1. What is the area of the inner square EF GH ? A. 25 B. 32 C. 36 D. 40 E. 42 8 Let A, M , and C be digits with (100A + 10M + C)(A + M + C) = 2005 What is A? A. 1 B. 2 C. 3 D. 4 E. 5 This file was downloaded from the AoPS − MathL