1. 2009 State Competition Countdown Round MATH COUNTS 

2. Please note that videotaping, photographing, reproducing or publishing the following questions or answers is strictly prohibited. A sample question follows that you are allowed to reproduce. MATH COUNTS 

3. A 3-ounce can of tomato sauce costs $1.68. In cents, what is the price per ounce? Sample Question

4. Answer: 56 (cents) Sample Question

5. MATH COUNTS 2009 State Competition Countdown Round 

6. 1. A woman 5-feet tall casts an 8-foot shadow. At the same time of day, the shadow of a tree nearby is 120 feet long. In feet, how tall is the tree?

7. Answer: 75 (feet)

9. Answer: 144 (sq units)

10. 3. How many perfect squares are there between 20 and 150?

11. Answer: 8 (perfect squares)

12. 4. What is the value of the sum –1 + 2 – 3 + 4 – 5 + 6 – 7 …+ 10,000?

13. Answer: 5000

14. 5. A palindrome is an integer that reads the same forward and backward, such as 3663. What percent of the palindromes between 100 and 500 contain at least one 5?

15. Answer: 10 (percent)

16. 6. What is the sum of all of the solutions of the equation ?

17. Answer: 0

18. 7. Five balls are numbered with the integers 1 through 5 and placed in a jar. Three are drawn without replacement. What is the probability that the sum of the three integers on the balls is odd? Express your answer as a common fraction.

19. Answer:

20. 8. If , what is the value of x ? Express your answer as a common fraction.

21. Answer:

22. 9. Labor Day is the first Monday in September. In a year when July 4 falls on Sunday, what date is Labor Day?

23. Answer: (September) 6th

24. 10. What is the area, in square units, of the square with the four vertices at A(0, 0), B(–5, –1), C(–4, –6) and D(1, –5)?

25. Answer: 26 (sq units)

26. 11. Kailin’s favorite restaurant has a special offer on a three-course meal. A meal consists of an appetizer, an entrée and a dessert. The menu features five appetizers, eight entrées and four desserts. How many different three-course meals can be formed with these choices?

27. Answer: 160 (three-course meals)

29. Answer: –2

31. Answer: 50 (percent)

33. Answer: 296

35. Answer: 3 (units)

37. Answer:

39. Answer: 10000 (base 2)

41. Answer: 92 (kilograms)

43. Answer: 384 (sq inches)

45. Answer: 21

47. Answer: (4, 6)

49. Answer: 8 (blue beads)

51. Answer: 135 (degrees)

53. Answer: 14

55. Answer: 52 (units)

57. Answer: 36 (wallops)

59. Answer: 80 (grapes)

61. Answer: 3

63. Answer: 3

65. Answer: 120 (cu feet)

67. Answer: 5 (zebras)

69. Answer: –15

71. Answer: –2009

73. Answer: 37.5 (percent)

75. Answer:

77. Answer: 48

79. Answer: 72

81. Answer:

83. Answer: 7

85. Answer:

87. Answer: 37

89. Answer: 3 (liters)

91. Answer: 100 (sq units)

93. Answer: 677 (people)

95. Answer: 174

97. Answer: –2

99. Answer: 36 (hours)

101. Answer: 18

103. Answer:

105. Answer: 8 π (inches)

107. Answer: 331 (dollars)

109. Answer: 10

111. Answer: 4 (cups)

113. Answer: 4 (perfect squares)

115. Answer: 6 (sets)

117. Answer: 60 (percent)

119. Answer: 14

121. Answer:

123. Answer: 12.5 (percent)

125. Answer: (sq units)

127. Answer:

129. Answer: 52 (sq units)

131. Answer:

133. Answer: 19

135. Answer: 280 (integers)

137. Answer: 225

139. Answer: 18 (integers)

141. Answer: 20

143. Answer:

145. Answer: –1004

147. Answer: 29

149. Answer: 13 (digits)

151. Answer: 2008

153. Answer: –15

155. Answer: 36

157. Answer: 10 (points)

159. Answer: 60

161. Answer: (–2, –9)

163. Answer: 21

165. Answer: 215 (adult tickets)