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USA AIME 1992 1 Find the sum of all positive rational numbers that are less than 10 and that have denominator 30 when written in lowest terms. 2 A positive integer is called ascending if, in its decimal representation, there are at least two digits and each digit is less than any digit to its right. How many ascending positive integers are there? 3 A tennis player computes her win ratio by dividing the number of matches she has won by the total number of matches she has played. At the start of a weekend, her win ratio is exactly .500. During the weekend, she plays four matches, winning three and losing one. At the end of the weekend, her win ratio is greater than .503. What?s the largest number of matches she could?ve won before the weekend began?

USA AIME 1984 1 Find the value of a2 + a4 + a6 + ? ? ?+ a98 if a1, a2, a3, . . . is an arithmetic progression with common difference 1, and a1 + a2 + a3 + ? ? ?+ a98 = 137. 2 The integer n is the smallest positive multiple of 15 such that every digit of n is either 8 or 0. Compute n15 . 3 A point P is chosen in the interior of 4ABC so that when lines are drawn through P parallel to the sides of 4ABC, the resulting smaller triangles, t1, t2, and t3 in the figure, have areas 4, 9, and 49, respectively. Find the area of 4ABC. A B C t3 t2t1 4 Let S be a list of positive integers - not necessarily distinct - in which the number 68 appears. The average (arithmetic mean) of the numbers in S is 56. However, if 68 is removed, the