MATHCOUNTS 2008 Sixth Grade Competition Countdown Round 1

1. Simplify: 2. 0 + 0. 228. Express your answer as a decimal to

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

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

6. A jar contains only nickels, dimes and quarters. There is at least one

7. Starting on January 1, 2008 what month will it be when exactly 26%

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

10. Find the mean of all the whole numbers from 1 to 20 inclusive.

11. The average of four numbers is 15. The average of three of the

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

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

14. What is the units digit of the product of all the integers from

15. It costs 2. 5 cents to copy a page. How many pages can

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

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

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

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

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

22. What is the sum of the reciprocals of the distinct factors of 4?

23. Which of the following are divisible by 7 but not by 3: A.

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

25. How many positive factors does 30 have?

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

27. What is the number of square inches in the area of a tablecloth

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

29. What is the remainder when the sum of the first five primes is

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

31. Together, Larry and Lenny have $35. Larry has two-fifths of Lenny’s amount. How

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

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

34. The formula for the volume of a sphere is 4/3( r 3) where

35. If f(x) = x 3 + 1, what is f(1) – f(0)?

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

37. There are 400 students in the eighth grade. 37. 5% are girls. How

38. The area of a certain circle is 100 square inches. If the diameter

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

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

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

43. What is the maximum number of nickels that you can exchange for $20.

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

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

46. The area of a triangle is 600 square feet. If the length of

48. What is the difference in ml between 1. 5 L and 757 ml?

49. Tom ate 12 cookies in 5 minutes. Eating at the same rate, how

50. How many minutes are between 11: 00 A. M. and 2: 20 P.

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MATHCOUNTS 2008 Sixth Grade Competition Countdown Round

1. Simplify: 2. 0 + 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. 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. Express your answer as a decimal to the nearest tenth.

Answer: 10. 5

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. How many pages can you copy for $10?

Answer: 400 (pages)

16. Express in simplest form: 4, 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? 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. 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. 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? Express your answer as a common fraction.

Answer: 21/10

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. 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( r 3) 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?