Sixth Grade Countdown Round 2002

1. What is the product of all integers from –4 to +6 inclusive?

2. On Tuesday Raymond read the first 30 pages of a 300-page book 2. On Tuesday Raymond read the first 30 pages of a 300-page book. On Wednesday he read 1/3 of the remaining pages. What is the page number of the first page Raymond read on Thursday?

121

By how much is five elevens less than eleven fifties?

495

4. How many integers between 3 and 97 are divisible by 3?

31 (integers)

5. What percent of the first five positive odd numbers are prime?

60 (%)

6. If 5! = 5 x 4 x 3 x 2 x 1 =120. What is the sum of 6! + 6!?

1440

7. What is the second smallest positive integer that is both a perfect square and a perfect cube?

64

8. What percent of 20 is 2.5? Express your answer to the nearest tenth.

12.5 (%)

9. Simplify: 75(89) + 60(25) + 25(29)

8900

10. John has four American coins, none of which has a value greater than 25 cents. What is the number of cents in the difference between the greatest and least amount of money that John could have?

96 (cents)

11. What is 0.5% of 400?

2

12. The sum of two numbers is 24. Their difference is 16 12. The sum of two numbers is 24. Their difference is 16. What is the larger number?

20

13. Jenny walked :of the way home from school in 21 minutes 13. Jenny walked :of the way home from school in 21 minutes. If she continues at the same rate, how many more minutes will it take Jenny to arrive home?

7 (minutes)

14. Two sides of a triangle measure 4 cm and 9 cm 14. Two sides of a triangle measure 4 cm and 9 cm. What is the greatest integer length possible for the third side of the triangle?

12 (cm)

15. The sum of three consecutive odd integers is 75 15. The sum of three consecutive odd integers is 75. What is the least of the three integers?

23

16. How many prime numbers are less than 10?

4 (prime numbers)

17. What is the units digit of 58 ?

5

18. How many positive two-digit numbers are divisible by 23?

43. (x =) 4

19. How many inches are in the perimeter of a square with an edge length of 2 feet?

96 (inches)

20. What fractional part of an hour elapses between 10:40 AM and 11:15 AM?

7/12 (hour)

21. What is the sum of all the positive integers from –3 to +3 inclusive?

6

22. A softball team played 25 games and won 7 more than they lost 22. A softball team played 25 games and won 7 more than they lost. How many games did they win?

16 (games)

23. Moving at a constant rate of 30 miles per hour, how many miles will a vehicle travel in 30 minutes?

15 (miles)

24. What is the median of the following set:   {10, 1, 2, 3, 4, 5, 6, 7, 8, 9}

5.5

25. What fractional part of a foot is 0.75"?

1/16 (foot)

A 20" square pizza with a crust all around the perimeter, is cut into 16 five inch square pieces. How many pieces do not have any crust? 26.

     4 (pieces)

27. How many different prime factors does 24 have?

2 (prime factors)

28. If the first day of February is Tuesday, on what day does the 28th of February fall in the same year?

Monday

29. For what value of x does x4 = 4x ?

(x =) 2 or 4

30. How many two-digit numbers have a units digit of three and an even tens digit?

4 (two-digit numbers)

31. If cashews cost $5.00 per pound, how much would 20 ounces of cashews cost?

$6.25

32. What is the largest integer, less than 193, that is evenly divisible by 8?  

192

33. How many odd positive integers are factors of 24?

      2

34. How many perfect squares are between 10 and 100?

6 (perfect squares)

35. If a and b are positive integers and a2 – b2 = 7, what is the product of a and b?

     12

3 If 8 is the third term of an arithmetic series and 12 is the fifth term of the arithmetic series, what is the first term of the series?  

   4

37. The sum of two prime numbers is 13 37. The sum of two prime numbers is 13. What is the positive difference between the two prime numbers?

9

38. 10% of 200 is what percent of 100?

20 (%)

39. What is the value of f(-1) if f(x) = x3 + 1?

40. Mike gave 3 cookies to each of his classmates 40. Mike gave 3 cookies to each of his classmates. He would need 80 more cookies so that he could give each of his classmates a total of 5 cookies each. How many classmates does Mike have?

40 (classmates)

41. How many of the first five positive integers have reciprocals that are repeating decimals?

      1

42. A number is chosen at random from the set {1, 2} and a second number is chosen from the set {2, 3}. How many different sums are possible?

3 (sums)

What is the greatest integer, x, such that x3 < 100?  

(x =) 4

44. Solve for x:   x + 5 = 82

(x =) 59

45. By what percent is 2 greater than 1?

50 (%)

46. A rectangle has a perimeter of 82" 46. A rectangle has a perimeter of 82". If the length of the rectangle is increased by 4" and the width is increased by 2", what is the new perimeter of the rectangle in inches?

94 (inches)

Simplify: 4 x 4 + 4 – 4 x 4.

4

48. What is the greatest common factor of 16 and 64?

16

49. What is the mean of the first ten odd counting numbers?

10

50. What is the smallest possible whole number that can be multiplied by 20, such that the product will be a perfect square?

5

PowerPoint Presentation by John Watmuff