1. MATHCOUNTS
2002 School Competition
Countdown Round

2. 1. What is the value of ?

3. Answer: 21,000

4. 2. What is the value obtained by dividing the number of square inches in a square yard by the number of square inches in a square foot?

5. Answer: 9

6. 3. What is the number of square inches in the area of a rectangular tablecloth that measures 4 feet by 5 feet?

7. Answer: 2880 (square inches)

8. 4. What is the value of ?

9. Answer: 140

10. 5. How many different positive integers can be represented as a difference of two distinct members of the set {1, 2, 3, 4, 5, 6} ?

11. Answer: 5 (integers)

12. 6. How many hours will it take Katina to drive 495 miles at 45 miles per hour?

13. Answer: 11 (hours)

14. 7. Ten students stand on a circle
7. Ten students stand on a circle. No two adjacent students have brown hair. What is the maximum number of these students that could have brown hair?

15. Answer: 5 (students)

16. 8. The bill for dinner was $63
8. The bill for dinner was $63. Joanna agreed to pay of the bill, since she had dessert. How many dollars should Joanna pay?

17. Answer: 35 (dollars)

18. 9. John’s diet requires him to eat, at most, 30 grams of carbohydrates at snack time. If he selects chips with 24 grams of carbohydrates per ounce, how many ounces of chips may he eat at snack time? Express your answer as a decimal to the nearest hundredth.

19. Answer: (ounces)

20. 10. What single percent discount from the original price is equivalent to a 40% discount on an item already on sale at a 20% discount from the original price?

21. Answer: 52 (percent)

22. 11. The volume of a cone is given by the formula V = Bh, where B is the area of the base and h is the height. The area of the base of a cone is 30 square units, and its height is 6.5 units. What is the number of cubic units in its volume?

23. Answer: 65 (cubic units)

24. 12. If 25% of n is 18, what is 125% of n?

25. Answer: 90

26. 13. If 3x = 8y, 12y = 7z and kz = 72x, then what is the value of k ?

27. Answer: 112

28. 14. Ashley’s old dresser has nine drawers
14. Ashley’s old dresser has nine drawers. Six of the drawers each have a volume of 2 ft3, and three drawers each have a volume of 1 ft3. Her new dresser has the same total volume in five equal-sized drawers. What is the volume in cubic feet of each drawer of her new dresser?

29. Answer: 3 (cubic feet)

30. 15. Bryan has some 3¢ stamps and some 4¢ stamps
15. Bryan has some 3¢ stamps and some 4¢ stamps. What is the least number of stamps he can combine so the value of the stamps is 33¢?

31. Answer: 9 (stamps)

32. 16. If a * b = 2a + 3b for all a and b, then what is the value of 4 * 3?

33. Answer: 17

34. 17. How many degrees are in the complement of a 54° angle?

35. Answer: 36 (degrees)

36. 18. The sum of two numbers is 352. One number is three times the other
18. The sum of two numbers is 352. One number is three times the other. What is the value of the smaller number?

37. Answer: 88

38. 19. A couple plans to have three children
19. A couple plans to have three children. The birth of a boy or girl is equally likely. What is the probability that all three children will be the same sex? Express your answer as a common fraction.

39. Answer:

40. 20. What is the positive difference, in inches, between the greatest cabin height and the least cabin height of the following business jets? Business Jet Cabin Height Learjet 31A feet, 5 inches Learjet feet, 8 inches Cessna Citation V 4 feet, 7 inches Gulfstream V 6 feet, 2 inches

41. Answer: 21 (inches)

42. 21. Charles Schultz drew 18,000 comic strips over a 50-year period
21. Charles Schultz drew 18,000 comic strips over a 50-year period. What is the mean number of comic strips he drew each year?

43. Answer: 360 (comic strips)

44. 22. The mean of ten numbers is 7. 2
22. The mean of ten numbers is When an 11th number is added to the set, the mean becomes 5. What is the th number?

45. Answer: -17

46. 23. Each row of the Misty Moon Amphitheater has 30 seats
23. Each row of the Misty Moon Amphitheater has 30 seats Rows 12 through 22 are reserved for a special group. How many seats are reserved for this group?

47. Answer: 330 (seats)

48. 24. A circular pizza of diameter 12 inches is cut into 4 pieces of equal area. What is the number of square inches in the area of each piece? Express your answer in terms of .

49. Answer: 9 (square inches)

50. 25. On a survey, students must give exactly one of the answers provided to each of these three questions: a) Were you born before 1990? (Yes/No) b) What is your favorite color? (Red / Green / Blue / Other) c) Do you play a musical instrument? (Yes / No) How many different answer combinations are possible?

51. Answer: 16 (combinations)

52. 26. What is the remainder when the sum of the first five primes is divided by the sixth prime?

53. Answer: 2

54. 27. What is the positive difference between one-million and seventy-two thousand?

55. Answer: 928,000

56. 28. The value of 400,000 squared can be written as 1. 6 10n
28. The value of 400,000 squared can be written as n. What is the value of n ?

57. Answer: 11

58. 29. On five consecutive days, the low temperatures in Sioux City, SD were 2, -9, 9, 7 and -4, measured in degrees Celsius. How many degrees Celsius was the mean of these low temperatures?

59. Answer: 1 (degree Celsius)

60. 30. What is the greatest possible quotient using two distinct numbers from the set { 0.2, 0.5, 0.8, 3.2 }?

61. Answer: 16

62. 31. How many eighths are in ?

63. Answer: 46 (eighths)

64. 32. Compute:

65. Answer: 9996

66. 33. The table below represents the male population of students attending Walker Middle School. One boy is selected at random from the male students. What is the probability that he is in seventh grade? Express your answer as a common fraction th Grade 8th Grade 9th Grade Males

67. Answer:

68. 34. Marcia has a total of 65 game pieces worth 89 points
34. Marcia has a total of game pieces worth 89 points. Each game piece is worth one or two points. How many one-point game pieces does she have?

69. Answer: 41 (one-point game pieces)

70. 35. The sum of three numbers is 90. One of the numbers is 22
35. The sum of three numbers is 90. One of the numbers is 22. What is the arithmetic mean of the other two numbers?

71. Answer: 34

72. 36. For what value of n does 38 = 9n?

73. Answer: 4

74. 37. The longest side of a right triangle is 5 meters, and the shortest side is 3 meters. What is the area of the triangle in square meters?

75. Answer: 6 (square meters)

76. 38. What integer x satisfies ?

77. Answer: 2

78. 39. Compute:

79. Answer: 11

80. 40. What percent of a 48-minute basketball game is over if the time remaining is one-third the time played?

81. Answer: 75 (percent)

82. 41. If carpet costs $18 per square yard, how many dollars will it cost to completely carpet a foot by 18 foot rectangular floor?

83. Answer: 540 (dollars)

84. 42. Alexa has a mixture consisting of 8 ounces of red jelly beans and 13 ounces of green jelly beans. What is the minimum number of ounces of white jelly beans she must buy so that, when added to the old mixture, her new mixture is an integer number of pounds?

85. Answer: 11 (ounces)

86. 43. April 1, 2002 is a Monday. What day is April 23, 2002?

87. Answer: Tuesday

88. 44. The area of a triangle is 600 ft2
44. The area of a triangle is ft2. If the length of the base is 30 feet, then what is the number of feet in the altitude?

89. Answer: 40 (feet)

90. 45. For what positive integer n is n2 = 26?

91. Answer: 8

92. 46. In parallelogram ABCD, angle B measures 110°
46. In parallelogram ABCD, angle B measures 110°. What is the number of degrees in the measure of angle C?

93. Answer: 70 (degrees)

94. 47. Together, Larry and Lenny have $35
47. Together, Larry and Lenny have $35. Larry has two-fifths of Lenny’s amount. How many more dollars than Larry does Lenny have?

95. Answer: 15 (dollars)

96. 48. An airplane travels at 360 kilometers per hour
48. An airplane travels at kilometers per hour. How many meters does it travel in one second?

97. Answer: 100 (meters)

98. 49. For what value of n does 0.0000048 = 4.8 10n ?

99. Answer: -6

100. 50. How many degrees is the measure of the supplement of an angle whose complement measures 50°?

101. Answer: 140 (degrees)

102. 51. By how much does 3. 5 exceed its reciprocal
51. By how much does 3.5 exceed its reciprocal? Express your answer as a common fraction.

103. Answer:

104. 52. What is of 200?

105. Answer: 1

106. 53. A rectangular sheet of paper with dimensions 9 inches by inches is cut into n identical notecards, each of which is inches by 2.6 inches. What is the maximum value of n ?

107. Answer: 15

108. 54. What is the ratio of to ? Express your answer as a common fraction.

109. Answer:

110. 55. What is the value of ? Express your answer as a decimal to the nearest tenth.

111. Answer: 1.3

112. 56. How many square feet are in a square yard?

113. Answer: 9 (square feet)

114. 57. What is the number of square units in the area of a triangle whose sides are 9, 12 and 15 units?

115. Answer: 54 (square units)

116. 58. If and , then what is the value of ?

117. Answer: 240

118. 59. What is the least number of 2 cm 5 cm rectangular tiles that will completely cover a cm 35 cm rectangle?

119. Answer: 105 (tiles)

120. 60. Two percent of half a number is 5. What is the number?

121. Answer: 500