AMC 8 Problems--2000 美国数学竞赛题.docVIP

Problem 1 Aunt Anna is years old. Caitlin is years younger than Brianna, and Brianna is half as old as Aunt Anna. How old is Caitlin? Problem 2 Which of these numbers is less than its reciprocal? Problem 3 How many whole numbers lie in the interval between and Problem 4 In only of the working adults in Carlin City worked at home. By the at-home work force increased to . In there were approximately working at home, and in there were . The graph that best illustrates this is Problem 5 Each principal of Lincoln High School serves exactly one -year term. What is the maximum number of principals this school could have during an -year period? Problem 6 Figure is a square. Inside this square three smaller squares are drawn with the side lengths as labeled. The area of the shaded L-shaped region is Problem 7 What is the minimum possible product of three different numbers of the set ? Problem 8 Three dice with faces numbered 1 through 6 are stacked as shown. Seven of the eighteen faces are visible, leaving eleven faces hidden (back, bottom, between). The total number of dots NOT visible in this view is Problem 9 Three-digit powers of 2 and 5 are used in this cross-number puzzle. What is the only possible digit for the outlined square? Problem 10 Ara and Shea were once the same height. Since then Shea has grown 20% while Ara has grow half as many inches as Shea. Shea is now 60 inches tall. How tall, in inches, is Ara now? Problem 11 The number 64 has the property that it is divisible by its units digit. How many whole numbers between 10 and 50 have this property? Problem 12 A block wall 100 feet long and 7 feet high will be constructed using blocks that are 1 foot high and either 2 feet long or 1 foot long (no blocks may be cut). The vertical joins in the blocks must be staggered as shown, and the wall must be even on the ends. What is the smallest number of blocks needed to build this wall? Problem 13 In triangle , we have and . If bisects , then Problem 14 Wh