- 1 - USA AMC 10 2000 1 In the year , the United States will host the International Mathematical Olympiad. Let , , and be distinct positive integers such that the product . What's the largest possible value of the sum ? Solution The sum is the highest if two factors are the lowest. So, and . 2 Solution . 3 Each day, Jenny ate of the jellybeans that were in her jar at the beginning of the day. At the end of the second day, remained. How many jellybeans were in the jar originally? Solution - 2 - 4 Chandra pays an online service provider a fixed monthly fee plus an hourly charge for connect time. Her December bill was , but in January her bill was because she used twice as much connect time as in December. What is the fixxed monthly fee? Solution Let be the fixed fee, and be the amount she pays for the minutes she used in the first month. We want the fixed fee, which is 5 Points and are the midpoints of sides and of . As moves along a line that is parallel to side , how many of the four quantities listed below change? (a) the length of the segment (b) the perimeter of (c) the area of (d) the area of trapezoid - 3 - Solution (a) Clearly does not change, and , so doesn't change either. (b) Obviously, the perimeter changes. (c) The area clearly doesn't change, as both the base and its corresponding height remain the same. (d) The bases and do not change, and neither does the height, so the trapezoid remains the same. Only quantity changes, so the correct answer is . 6 The Fibonacci Sequence starts with two 1s and each term afterwards is the sum of its predecessors. Which one of the ten digits is the last to appear in thet units position of a number in...
