2008 Sixth Grade Competition Countdown Round MATHCOUNTS  2008 Sixth Grade Competition Countdown Round

1. Simplify: 2.0 + 0.2 + 0.22 + 0.228. Express your answer as a decimal to the nearest tenth.

Answer: 2.6

2. What is the greatest common factor of 30, 50 and 90?

Answer: 10

3. Simplify: 12(½ + ⅓) + 5.

Answer: 15

4. What is ½% of 200?

Answer: 1

5. By how much does the sum of the squares of 3 and 4 exceed the product of 3 and 4?

Answer: 13

6. A jar contains only nickels, dimes and quarters 6. A jar contains only nickels, dimes and quarters. There is at least one of each type of coin in the jar. If the total value of the coins in the jar equals 60 cents, how many quarters are in the jar?

Answer: 1 (quarter)

7. Starting on January 1, 2008 what month will it be when exactly 26% of the year has passed?

Answer: April

8. Compute: (-10)(5)(9) + (20)(25).

Answer: 50

9. What are the last thirteen digits of the expansion of 100!?

Answer: 0

10. Find the mean of all the whole numbers from 1 to 20 inclusive 10. Find the mean of all the whole numbers from 1 to 20 inclusive. Express your answer as a decimal to the nearest tenth.

Answer: 10.5

11. The average of four numbers is 15 11. The average of four numbers is 15. The average of three of the numbers is 19. What is the fourth number?

Answer: 3

12. What is the least common multiple of 10 and 105?

Answer: 210

13. What is the greatest integer less than -43/4?

Answer: -11

14. What is the units digit of the product of all the integers from 1 to 8?

Answer: 0

15. It costs 2. 5 cents to copy a page 15. It costs 2.5 cents to copy a page. How many pages can you copy for $10?

Answer: 400 (pages)

16. Express in simplest form: 4,000,000  5,000.

Answer: 800

17. What is the remainder when you divide 433,333 by 3?

Answer: 1

18. The cube of what number is closest to 500?

Answer: 8

19. What is the sum of the least positive 3-digit number and the largest positive 4-digit number?

Answer: 10,099

20. What is the units digit of 67?

Answer: 6

21. What is the arithmetic mean of all the positive one-digit multiples of 2?

Answer: 5

22. What is the sum of the reciprocals of the distinct factors of 4 22. What is the sum of the reciprocals of the distinct factors of 4? Express your answer as a mixed number?

Answer: 1¾

23. Which of the following are divisible by 7 but not by 3:. A. 105. B 23. Which of the following are divisible by 7 but not by 3: A. 105 B. 420 C. 112 D. 84

Answer: C (112)

24. What is the greatest prime factor of 6!?

Answer: 5

25. How many positive factors does 30 have?

Answer: 8 (factors)

26. Two sides of an isosceles triangle are 15 cm and 10 cm 26. 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 (cm)

27. What is the number of square inches in the area of a tablecloth that measures 2 feet by 5 feet?

Answer: 1,440 (sq. in.)

28. If 25% of n is 10, what is 125% of n?

Answer: 50

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

Answer: 2

30. By how much does 2. 5 exceed its reciprocal 30. By how much does 2.5 exceed its reciprocal? Express your answer as a common fraction.

Answer: 21/10

31. Together, Larry and Lenny have $35 31. Together, Larry and Lenny have $35. Larry has two-fifths of Lenny’s amount. How many more dollars than Larry does Lenny have?

Answer: 15 (dollars)

32. When 5 is subtracted from three times a number, the result is 7 32. When 5 is subtracted from three times a number, the result is 7. What is the number?

Answer: 4

33. What percent of the integers from 1 to 100 inclusive are divisible by 3?

Answer: 33 (%)

34. The formula for the volume of a sphere is 4/3(r3) where r is the radius of the sphere. If the radius of the sphere is 3 inches, what is the volume of the sphere in terms of  cubic inches?

Answer: 36 (cu. in.)

35. If f(x) = x3 + 1, what is f(1) – f(0)?

Answer: 1

36. Twenty-seven minutes is what percent of an hour?

Answer: 45 (%)

37. There are 400 students in the eighth grade. 37. 5% are girls 37. There are 400 students in the eighth grade. 37.5% are girls. How many boys are in the eighth grade?

Answer: 250 (boys)

38. The area of a certain circle is 100 square inches 38. The area of a certain circle is 100 square inches. If the diameter of the circle is doubled, what is the area of the new circle in square inches?

Answer: 400 (sq. in.)

39. How many multiples of 13 are between 100 and 200?

Answer: 8

40. By how much does the tenth smallest positive even integer exceed the ninth smallest positive odd integer?

Answer: 3

41. What is the fifth term of the geometric sequence 4, 2, 1, …?

Answer: ¼ or 0.25

42. What percent of 5 is ¼?

Answer: 5 (%)

43. What is the maximum number of nickels that you can exchange for $20.10?

Answer: 402 (nickels)

44. What is forty-four times the cube root of eight?

Answer: 88

45. Four percent of half a number is 10. What is the number?

Answer: 500

46. The area of a triangle is 600 square feet 46. The area of a triangle is 600 square feet. If the length of the base is 30 feet, then what is the number of feet in the altitude?

Answer: 40 (feet)

47. 1¼ is 25% of what number?

Answer: 5

48. What is the difference in ml between 1.5L and 757ml?

Answer: 743 (ml)

49. Tom ate 12 cookies in 5 minutes 49. Tom ate 12 cookies in 5 minutes. Eating at the same rate, how many cookies would he eat in an hour?

Answer: 144 (cookies)

50. How many minutes are between 11:00 A. M. and 2:20 P. M 50. How many minutes are between 11:00 A.M. and 2:20 P.M. on the same day?

Answer: 200 (minutes)