2002 Chapter Countdown

1. What is the sum of of the numbe numberr of faces, faces, vertices vertices and edges edges in a triangular prism?

1. ____ ______ ____ ____ ____ ____ __

2. One-third One-third of of a 30-stude 30-student nt class class is absent absent today. today. One-ha One-half lf of those were also absent yesterday. What percent of the class has been absent for two straight days? Express your answer to the nearest whole number.

2. ____ ______ ____ ____ ____ ____ __

2 2 3. Compute: (17 + 10) − (17 − 10) .

3. ____ ______ ____ ____ ____ ____ __

4. Two of Mr. Mr. Bernard Bernards s classes classes took the same test. His class of 20 students had had an average score of 80. 80. His other class of 30 students had an average of 70. What was the average score for all 50 students?

4. ____ ______ ____ ____ ____ ____ __

5. The radius radius of of a circle circle is increased increased by 100%. 100%. By what percent percent is the area of the circle increased?

5. ____ ______ ____ ____ ____ ____ __

6. Compute:

 5 − 

2

5

2 −3

2

 

.

6. ____ ______ ____ ____ ____ ____ __

7. What is the the least least common common multiple multiple of 12, 12, 18 and and 30? 30?

7. ____ ______ ____ ____ ____ ____ __

8. In any given year, the the dates (represented (represented as month/d month/day) ay) 4/4, 4/4, 6/6, 8/8, 10/10 and 12/12 all fall on the same day of the week. June 3, 2020 2020 is a Wednesday. Wednesday. What day of the the week is December 15, 2020?

8. ____ ______ ____ ____ ____ ____ __

9. Taylor Taylor wants to buy buy cases cases to hold hold her 86 compact compact discs. discs. Each case holds 9 discs. How many cases does she she need to buy?

9. ____ ______ ____ ____ ____ ____ __

10. A board whose length length is 84 inches is cut into three pieces in the the ratio 1:2:3. What is the number number of inches in the length length of the shortest piece?

10. _______ ___________ _______ ___

11. How many integers integers can be represented represented as a difference of two distinct members of the set {1, 2, 3}?

11. _______ ___________ _______ ___

12. At what time is the sum sum of the digits which which represent the hours hours and minutes on a 12-hour digital watch the greatest?

12. _______ ___________ _______ ___

13. What is the sum of the coordinates coordinates of the midpoint midpoint of the segment with endpoints (6, 12) and (0, -6)?

13. _______ ___________ _______ ___

©2001 MATHCOUNTS Foundation: 2002 Chapter Countdown Round

14. A refrigerator was originally priced at $250. It was then put on sale for 20% off. What is the number of dollars in the final price of the refrigerator if an additional 15% is taken off of the sale price?

14. ______________

15. What is the sum of all the prime numbers less than 10?

15. ______________

16. Sixteen is 64% of what number?

16. ______________

17. Molly has seven U.S. coins with a total value of 88 cents. She does not have any half-dollars. How many dimes does Molly have?

17. ______________

18. ______________ 18. What is the number of square units in the area of a triangle whose sides are 3, 4 and 5 units? 19. ______________ 19. The point A(-7, 4) is reflected across the x-axis onto point B. Point B is reflected over the y-axis onto point C. What is the sum of the coordinates of point C? 20. If x = 3 and y = 2, then what is the value of

2 x

3

− 3y

6

20. ______________

2

?

21. What is the value of

21. ______________

1 1 1 1 1 × 4 × × 16 × × 64 × × 256 × × 1024 ? 2 8 32 128 512

22. Set A has 16 elements and set B has 37 elements. The union of sets A and B has 43 elements. How many elements are in the intersection of sets A and B?

22. ______________

23. TV screens are described by the lengths of their diagonals. A 19" TV has a rectangular screen with a diagonal length of 19 inches. The screen of a 20" TV is 12 inches tall. How many inches wide is the screen?

23. ______________

24. Jonathan drove at an average rate of 48 miles per hour. How many miles did he travel in 40 minutes?

24. ______________

3

25. For what value of n does as a common fraction.

2× 2

2 n

? Express your answer

25. ______________

26. What part of 15 hours is 15 seconds? Express your answer as a common fraction.

26. ______________

2

2

=2


27. What is the ratio of 1 pound, 4 ounces to 3 pounds, 10 ounces? Express your answer as a common fraction.

27. ______________

28. The cost of the daily school lunch increased from $1.50 to $1.95. What was the percent increase?

28. ______________

29. For class president, Tom received 50% of the votes, John received 30% of the votes and Alana received the remaining 88 votes. How many votes did Tom receive?

29. ______________

30. Compute: (2 + 12 + 22 + 32) + (8 + 18 + 28 + 38).

30. ______________

31. The average of nine consecutive integers is 13. What is the sum of the least and greatest of these integers?

31. ______________

32. If the sides of a triangle are tripled, then the new area is what percent of the original area?

32. ______________

33. Ervin made 37.5% of the shots he took during his basketball game. If he took exactly 40 shots during the game, how many shots did he make?

33. ______________

34. The numbers 1 through 999, inclusive, are printed on a piece of paper. How many digits are printed on the paper?

34. ______________

35. How many pairs of prime numbers have a sum of 40?

35. ______________

36. What is the sum of the first 6 positive odd integers?

36. ______________

37. What is the greatest real number that is at least as large as its square?

37. ______________

38. The Catch The Spirit group is conducting a raffle. Each ticket costs $2, and the total expenses are $500. What is the minimum number of tickets that must be sold to yield a profit of $2000?

38. ______________

39. What is the sum of the reciprocals of all the positive divisors of 8? Express your answer as a mixed number.

39. ______________

40. If 220 − 219

=2

40. ______________

41. Solve for n:

4

x

2

n

, what is the value of x ? ⋅5

2

9

2

=

41. ______________

10,000 .

42. Of the following numbers, what is the sum of the two smallest, to the nearest thousandth: 0.15 0.42 0.063 0.1657 ?

42. ______________


43. How many solutions does the equation

3 x

=x

3 have?

43. ______________

44. If n!5! = 6!, then what is value of n ?

44. ______________

45. If a * b = a b + ba, for all positive integer values of a and b, then what is the value of 4 * 3?

45. ______________

46. Each bounce of a ball goes 43 as high as the previous bounce. The second bounce was 24 inches high. What was the height, in inches, of the first bounce?

46. ______________

47. The perimeter of an isosceles triangle is 36 cm, and the altitude to its base is 12 cm. What is the number of square centimeters in the area of the triangle?

47. ______________

48. There are 30 equally-weighted questions on Mr. Davens math final. If a student must score 68% or greater to pass, what is the minimum number of questions that must be answered correctly to pass?

48. ______________

49. A pizza parlor offers six toppings. What is the greatest number of four-topping pizzas that can be made such that no two pizzas have the same topping combination?

49. ______________

50. Jacob bought a CD for $15 and sold it for $20. He then bought it back for $25 and sold it again for $28. How many dollars profit did he make?

50. ______________

51. What is 150% of 0.84, to the nearest hundredth?

51. ______________

52. Given

x y

=

2 3

and

y z

=

3 2

, what is the value of

x

?

z

52. ______________

53. What is the greatest odd integer that is a factor of 5! ?

53. ______________

54. What is the number of centimeters in the diameter of a circle whose area is 100 π cm2?

54. ______________

55. Compute: 55 × 1212 − 15 × 1212 .

55. ______________

56. One leg of a right triangle is increased by 10%, and the other leg is decreased by 10%. By what percent does the area of the triangle decrease?

56. ______________


57. Data can be entered at the rate of 150 pieces of information in 15 minutes. At this rate, how many pieces of information can be entered in 1 21 hours?

57. ______________

58. A suitcase lock has 3 dials with the digits 0, 1, 2,..., 9 on each. How many different settings are possible if all three digits have to be different?

58. ______________

59. Ralph can do one-third of a job in two-thirds of an hour. At this rate, how many hours will it take him to finish the entire job?

59. ______________

60. Compute: 6 ÷ 6 − 6 + 6 × 6 .

60. ______________

> 6 and n is a positive integer. What is the 61. It is known that 200 n largest possible value for n?

61. ______________

62. Fifty cards, numbered 1- 50, are placed in a box. One card is randomly selected. What is the probability that the number on the card is prime and is a multiple of 7? Express your answer as a common fraction.

62. ______________

63. Tylers quiz scores in Math Investigations were 5, 7, 9, 10, 13, 19 and 21. Determine the ratio of the median of his scores to the arithmetic mean of his scores. Express your answer as a common fraction.

63. ______________

64. A discount card offers $5 off for any purchase from $50 to $99.99, and $15 off any purchase of $100 or more. What is the maximum percent discount that can be obtained using this card?

64. ______________

65. A rectangle has perimeter 26 inches and integer length sides, in inches. What is the number of square inches in the greatest possible area?

65. ______________

66. What is 1/2 of 1/3 of 1/5 of 60?

66. ______________ 3

67. Compute and express as a common fraction:

4 4 5

+

+

1 5 1

.

67. ______________

2

68. During a 24-hour period, 1440 cars pass through a toll booth. What is the mean number of cars that pass through per minute?

68. ______________

69. What is the greatest common factor of 68 and 92?

69. ______________


70. The angle measures of the three angles of a triangle are in the ratio 1:3:6. What is the number of degrees in the measure of the largest angle?

70. ______________

71. What is the least common multiple of 1, 2, 3, 4, 5, 6, 7 and 8?

71. ______________

72. Express as a common fraction:

5

4 9

.

72. ______________

73. The number 115 can be written as 12q + r where q and r are integers and 0 ≤ r < 12 . What is the value of q - r ?

73. ______________

74. How many seconds are in 1 41 hours?

74. ______________

75. If Mike drinks eight 8-ounce glasses of water each day during 2002, how many gallons of water will he consume? (A gallon is 128 ounces.) Express your answer as a decimal to the nearest tenth.

75. ______________

76. Two opposite sides of a square are each increased by 40%, while the other two sides are each decreased by 30%. The perimeter of the original square is increased by what percent?

76. ______________

77. A book of tickets for 30 games of a local universitys baseball team sold for $120, and a book of tickets for 7 games of the same universitys football team sold for $161. By how many dollars did the average cost of one football game ticket exceed that of one baseball game ticket?

77. ______________

78. A portion of a number line is divided into 4 equal parts, as shown. What is the value of p, to the nearest ten-thousandth?

78. ______________

0.2304

79.

p

0.4304

Hamburgers Cheeseburgers Mr. Jones Needs: 15 12 1 Meal Deal includes: 2 2

Fries 25 3

Sodas 30 4

79. ______________

What is the least number of Meal Deals that Mr. Jones must purchase to get all of the food and beverage that he needs? 2

80. A rectangle has an area of 36 m2 and a width of meters. 3 What is the number of meters in the length of the rectangle?

80. ______________


2002 Chapter Countdown

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