MATHCOUNTS 2009 : CHAPTER CAOUNTDOWN (PART 5)
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Muhammad Yusuf
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57. Wilma has 3 red pens, 3 blue pens, 4 black pens and 5 green pens in her school bag. If she randomly selects one pen from her bag, what is the probability that she selects a green pen? Express your answer as a common fraction.
58. How many positive integers, x, satisfy x − 4 < 3?
59. Zachary paid for a $1 burger with 32 coins and received no change. Each coin was either a penny or a nickel. What was the number of nickels Zachary used?
60. The sum of three consecutive one-digit, positive, odd integers is one-seventh of the product of the same three integers. What is the middle integer when the three integers are listed in ascending order?
61. A regular hexagon is divided into six congruent equilateral triangles. If the perimeter of one of the triangles is 39 inches, what is the perimeter of the regular hexagon, in inches?
62. Kyle has five tires but only uses four at a time on his car. He has rotated the five tires on his car so that each tire has been on the car for the same number of miles. If the car has been driven 90,000 miles, for how many miles was each of the five tires on the car?
63. Each of the digits 3, 4, 6, 7, 8 and 9 is used once and only once to form a six-digit integer. What is the largest six-digit multiple of 4 that can be formed?
64. How many cubic feet are in three cubic yards?
65. In the six-digit integer 3A6,792, what is the largest digit A so that the six-digit integer will be divisible by 3?
66. A regular polygon has exterior angles each measuring 15 degrees. How many sides does the polygon have?
67. If A = 1/4 and B = -1/2, what is the absolute value of the difference between 18A and 18B? Express your answer as a decimal to the nearest tenth.
68. In a spelling bee 50% of the students were eliminated after the first round. Only 1/3 of the remaining students were still in the contest after the second round. If 24 students were still in the contest after the second round, how many students began the contest?
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