MATHCOUNTS 2009 : CHAPTER CAOUNTDOWN (PART 4)
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Muhammad Yusuf
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You can trade 7 beeps for 3 bops and you can trade 4 bops for 5 dings. How many beeps would you need to be able to trade for 60 dings?
46. What is the area, in square units, of a circle with a circumference of 8π units? Express your answer in terms of π.
47. The sum of the digits of a two-digit positive integer is seven. Subtracting 45 from this integer yields another two-digit integer with the same digits, but in reversed order. What is the original integer?
48. What is the largest integer that is less than the square root of 250?
49. Jordan ran 2 miles in half the time it took Steve to run 3 miles. If it took Steve 24 minutes to run 3 miles, using the same rates, how many minutes would it take Jordan to run 5 miles?
50. Hadley scored 92, 73, 79 and 87 points on the first four tests of the quarter. There is one test remaining. What is the minimum number of points that Hadley must score on the final test in order to have a mean of 80 points for the five tests?
51. A freshly painted circular emblem on a football field is completely covered by the smallest possible square tarp. The tarp covers an area of 196 square feet. In square feet, what is the area of the circular emblem? Express your answer in terms of π.
52. What is the sum of the distinct prime factors of 315?
53. The sum of the numerator and the denominator of a fraction is 216. The fraction is equivalent to 2/7. What is the value of the denominator?
54. What is the sum of the first 10 odd positive integers?
55. A square region with side length 1 foot is covered completely with 2-inch by 2-inch square stickers. How many of the stickers are needed to cover the region exactly without overlap?
56. Two triangles are similar. The ratio of their areas is 1:4. If the height of the smaller triangle is 3 cm, how long is the corresponding height of the larger triangle, in centimeters?
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