MATHCOUNTS Countdown Round

1. Half of 12 is equal to what number?

Answer: 6

2. What is the smallest positive integer that can be added to 100 to make a multiple of 3?

Answer: 2

3. Five U.S. coins are worth a total of 35 cents. How many of the coins are dimes?

Answer: 2 coins

4. How much more than 42 is 33?

Answer: 11

5. What is the greatest common factor of 40 and 48?

Answer: 8

6. What is the sum of the number of faces and edges of a triangular prism?

Answer: 14

7. The value of eight nickels and six dimes is the same as four nickels and how many dimes?

Answer: 8 dimes

8. Fred has 2 yellow, 2 red and 2 green tokens. One red token is equal to 9 green tokens. One yellow token is equal to 3 green tokens. Fred converts all of his tokens to green tokens. How many green tokens does he have?

Answer: 26 tokens

9. If the last two digits of 9567 were interchanged, how much larger would the new number be?

Answer: 9

10. The average of five numbers is 10. Four of the numbers are 10, 10, 10 and 9. What is the value of the fifth number?

Answer: 11

11. In the figure shown, polygons ABCD, CDEF and DEGH are squares. The length of segment FG is 10 cm. How many square centimeters are in the area of hexagon ABFGHD?

F E G

C

B A

DH

Answer: 75 square centimeters

12. How many positive integers are less than 10?

Answer: 31 integers

13. In training, Petra runs of a mile in 60 seconds. At this rate, how many seconds does it take Petra to complete a run of 1 mile?

16

Answer: 360 seconds

14. What is the remainder when 4697 is divided by 9?

Answer: 8

15. How many more boxes are needed if 70 ornaments are packaged in boxes that each hold 5 ornaments rather than boxes that each hold 7 ornaments?

Answer: 4 boxes

16. What reduced fraction is equivalent to 25%?

Answer: 14

22. The area of a square is 49 square centimeters. How many centimeters are in the length of a side of the square?

Answer: 7 centimeters

17. At which of the following stores is the average cost per pencil the least? Store A: 17 pencils for $1.70 Store B: 7 pencils for $1.40 Store C: 5 pencils for $0.85

Answer: Store A

18. In any month with a “Friday the 13th,” what day of the week is the first day of the same month?

Answer: Sunday

19. Each side of pentagon ABCDE has length less than or equal to 7 units, AB = 5 units and BC = 4 units. How many units are in the greatest possible perimeter of ABCDE?

Answer: 30 units

20. Two figures each have a perimeter of 80 feet. One is a square and one is a rectangle with dimensions of 10 feet by 30 feet. What is the positive difference in the number of square feet of their areas?

Answer: 100 square feet

21. What is the greatest integer

less than ? 17

4

Answer: 5

22. Using two distinct members of the set {0, 1, 2, 3}, how many different sums can be found?

Answer: 5 sums

23. How many integers between 20 and 90 are perfect squares?

Answer: 5 integers

24. What is the greatest two-digit multiple of 4?

Answer: 96

25. Joshua’s restaurant bill is $10. To calculate the tip, he calculates 15% of the value of the bill and then rounds up to the nearest dollar. What was the amount of his tip?

Answer: 2 dollars

26. What is the sum: –4 + –3 + –2 + ... + 3 + 4 + 5 + 6?

Answer: 11

27. The ratio of x to 10 is equal to the ratio of 12 to 30. What is the value of x?

Answer: 4

28. What is the units digit of the product of the first four positive integers?

Answer: 4

29. Evaluate (x + y)(x – y) when x = 15 and y = 5.

Answer: 200

30. How many degrees are in each interior angle of an equilateral triangle?

Answer: 60 degrees

31. If 75 seeds are planted and 25 of the seeds are germinating, what is the ratio of seeds germinating to seeds planted? Express your answer as a reduced fraction.

Answer:13

32. The scale of a backpacker’s map is “1 cm on the map = 240 meters on the ground.” How many kilometers long is a hike that measures 10 cm on the map? Express your answer as a decimal to the nearest tenth.

Answer: 2.4 kilometers

33. Mississippi was one of the 10 states to lose a Congressional seat based on the 2000 Census. What percent of the 50 states did not lose a Congressional seat?

Answer: 80 percent

34. Let y = 2 + 3x. How much greater is y when x = 3 than when x = 2?

Answer: 3

35. Ben flips a fair nickel two times. What is the probability that Ben flips a Head and then a Tail? Express your answer as a reduced fraction.

Answer:14

36. Mary jogs 12 miles in 2 hours. On average, how many minutes does it take her to jog one mile?

Answer: 10 minutes

37. With one skein of wool yarn, Sharon can knit 3 inches of a scarf that is 9 inches wide. What is the least whole number of skeins with which she can knit a scarf that is 6 inches wide and 27 inches long?

Answer: 6 skeins

38. Two positive integers have a sum of 28 and are in the ratio 3:4. What is the least of these two integers?

Answer: 12

39. Marie owns 11 department stores. Each store has 12 shelves for towels. What is the total number of shelves for towels?

Answer: 132 shelves

40. When 5 is subtracted from three times a particular number, the result is 13. What is the number?

3 × 5 = 13

Answer: 6

41. The Battling Hummingbirds have won 40% of their first 60 games. If they win their next 12 games in a row, what percent of all of their games will they have won?

Answer: 50 percent

42. In box A, there are four more pennies than in box B. The total number of pennies in boxes A and B is 34. What is the number of pennies in box A?

Answer: 19 pennies

43. What is the sum of the first five positive odd integers?

Answer: 25

44. What number is one hundred less than one thousand thirty-three?

Answer: 933

45. Katrina can bicycle 50 miles in four hours. At the same speed, how many miles does she bicycle in six hours?

Answer: 75 miles

46. What is the least positive integer that has exactly three distinct factors?

Answer: 4

47. The total value of 90 pennies, 20 dimes and 12 quarters is what percent of the value of a ten-dollar bill?

Answer: 59 percent

48. Solve for x: 18 x = 10 + x.

Answer: 4

49. What is the number of degrees in the measure of angle ABD in square ABCD?

A B

D C

Answer: 45 degrees

50. What is the units digit of 64?

Answer: 6

51. Triangle ABC is isosceles with angle B congruent to angle C. The measure of angle C is four times the measure of angle A. What is the number of degrees in the measure of angle B?

Answer: 80 degrees

52. What integer is closest

to ?100

7

Answer: 14

53. What is the largest three-digit multiple of 2?

Answer: 998

54. The Carters had a 10-foot by 10-foot patio built at a cost of $2200. How many dollars per square foot did the patio cost to build?

Answer: 22 dollars per sq ft

55. What is the decimal

equivalent of ? Express

your answer to the nearest

hundredth.

114

Answer: 2.75

56. The ratio of the measures of two complementary angles is 2:1. What is the measure, in degrees, of the larger angle?

Answer: 60 degrees

57. From a one-meter piece of yarn, Chris cuts a 31.5 cm piece and a 35.5 cm piece. In centimeters, how much yarn is left?

Answer: 33 centimeters

58. Simplify:

7 103 + 5 1024101 + 7100

Answer: 7467

59. A stair-step exercise machine indicates that Leon burns 180 calories in 12 minutes. At the same rate, how many calories would Leon burn in a 4-minute workout?

Answer: 60 calories

60. If y = x2 1, what is the value of y when x =

Answer: 0

61. Four friends are in line for movie tickets. Rick is somewhere behind Tom, but ahead of Mark. James and Tom are separated by one person. Who is last in line?

Answer: Mark

62. Steven is making a scale drawing of his living room. He is using a scale of 1/4 in = 1 ft. In the drawing, how many inches will represent the length of a 6-foot long couch? Express your answer as a decimal to the nearest tenth.

Answer: 1.5 inches

63. The ages, in years, of the eight people in the math club are: 12, 12, 12, 12, 13, 13, 14, 14. What is the mode of the ages?

Answer: 12 years

64. What is the greatest prime factor of 10!?

Answer: 7

65. Rebecca remembered the first 6 digits of a friend’s 7-digit phone number. If she randomly selects a digit to fill the last digit she can’t remember, what is the probability she will dial the correct number? Express your answer as a common fraction.

Answer:1

10

66. Fifty percent of what number is 12?

Answer: 24

67. What is the number of square centimeters in the area of a circle with radius 4 cm? Express your answer is terms of

Answer: 16square centimeters

68. A candy company puts 21 candies in each bag. There are only red and blue candies in each bag. For every 2 red candies in a bag there are 5 blue candies. How many red candies are in each bag?

Answer: 6 candies

69. What is the value of 52 32?

Answer: 16

70. How many triangles of any size are in this figure?

Answer: 5 triangles

71. What is 150% of 26?

Answer: 39

72. In how many ways can a pair of students be selected from a group of four students?

Answer: 6 ways

73. In the formula d = rt, what is the value of r if d = 60 and t = 4?

Answer: 15

74. On average, each American consumes 286 eggs per year. What is the number of years it would take, at this rate, for an American to eat 2000 eggs? Express your answer to the nearest whole number.

Answer: 7 years

75. Of the 80 students at camp, 40% of them are male. How many female students are at camp?

Answer: 48 female students

76. One fair standard six-sided die is rolled. What is the probability of rolling a number greater than 4? Express your answer as a reduced fraction.

Answer:13

77. What is the positive difference between 32 and 23?

Answer: 1

78. Jane turns 15 in the year 2008. In what year was she born?

Answer: 1993

79. A printer prints 17 pages per minute. How many minutes will it take to print 200 pages? Express your answer to the nearest whole number.

Answer: 12 minutes

80. Jenna is at a fair with 4 friends. They all want to ride the roller coaster, but only 3 people can fit in a car. How many different groups of 3 can the 5 of them make?

Answer: 10 groups

81. What is the value of the following expression:

10 – 9 + 8 – 7 + … + 4 – 3 + 2 – 1?

Answer: 5

82. A three-digit integer will be chosen at random from all possible positive three-digit integers. What is the probability that the number’s units digit will be less than 5? Express your answer as a common fraction.

Answer: 12

83. If + 5 = 18, what is the

value of +   ?

Answer: 26

84. How many factors does 20 have?

Answer: 6 factors

85. Kaya ate 60 cookies over a 5-minute period. On average, how many cookies did she eat each minute?

Answer: 12 cookies

86. What is the average of 3, 4, 5 and 8?

Answer: 5

87. If two different numbers are chosen from the set {0, 4, 6, 20}, and the smaller number is subtracted from the larger number, what is the smallest possible result?

Answer: 2

88. The area of a circle is 49 square units. What is the radius of the circle, in units?

Answer: 7 units

89. What is the least common multiple of 3, 5 and 6?

Answer: 30

90. If 3 × + 5 = 29, what number must be placed in the square?

Answer: 8

91. A hot air balloon is 10 feet off the ground now and is rising at a constant rate of 2 feet per second. What is the height of the balloon, in feet, after 25 more seconds?

Answer: 60 feet

92. What fraction of 2 feet is 3 inches? Express your answer as a reduced fraction.

Answer:18

93. The three-digit integer 63_ is a multiple of 3. What is the greatest possible digit that can be placed in the blank?

Answer: 9

94. The probability that Asha

will lose the game is . What is

the probability Asha will not lose the game? Express your answer as a reduced fraction.

49

Answer:59

95. What is the value of 5!?

Answer: 120

96. Robert reads 90 pages per hour. How many 270-page books can he read in six hours?

Answer: 2 books

97. Pencils come in a package holding 10 pencils. Rina’s teacher bought 23 packages of pencils. How many pencils did she buy?

Answer: 230 pencils

3085

A

B

C

98. On a protractor, ray BA goes through the 85-degree mark and ray BC goes through the 30-degree mark. What is the measure, in degrees, of angle ABC?

Answer: 55 degrees

99. What is the sum of the first five positive even integers?

Answer: 30

100. Two sides of an isosceles triangle are 15 cm and 10 cm. What is the greatest possible perimeter of this triangle, in centimeters?

Answer: 40 centimeters

101. What is the sum of the greatest possible three-digit integer and the greatest possible two-digit integer?

Answer: 1098

102. What is the ratio of one interior angle of an equilateral triangle to one interior angle of a square? Express your answer as a reduced fraction.

Answer: 23

103. What is the greatest possible three-digit number that is divisible by 3 and divisible by 6?

Answer: 996

104. How many obtuse interior angles are in an obtuse triangle?

Answer: 1 angle