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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 421 · 40 questions
TalentJR

How to solve it (Think in totals): Average = total ÷ how many; so total = average × how many. A number taken away = old total − new total. Evenly spaced numbers (like 10 to 20): average = (first + last) ÷ 2.

NameDateTime takenScore ___ / 40
  1. 1.What is the average of all the whole numbers from 30 to 68? (a) 50 (b) 19 (c) 49 (d) 38
  2. 2.What is the average of all the whole numbers from 36 to 44? (a) 41 (b) 40 (c) 4 (d) 8
  3. 3.What is the average of all the whole numbers from 18 to 42? (a) 31 (b) 24 (c) 12 (d) 30
  4. 4.What is the average of all the whole numbers from 11 to 23? (a) 17 (b) 12 (c) 6 (d) 18
  5. 5.The average of 4 numbers is 27. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 52 (b) 33 (c) 27 (d) 8
  6. 6.The average of 6 numbers is 36. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 11 (b) 36 (c) 77 (d) 12
  7. 7.What is the average of all the whole numbers from 11 to 29? (a) 18 (b) 20 (c) 21 (d) 9
  8. 8.What is the average of 34, 28, 31, 26 and 16? (a) 29 (b) 27 (c) 26 (d) 28
  9. 9.A batter has an average of 35 runs in 6 matches. How many runs are needed in the next match to raise the average to 37? (a) 14 (b) 37 (c) 39 (d) 49
  10. 10.The average of 5 numbers is 44. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 86 (b) 44 (c) 52 (d) 10
  11. 11.A batter has an average of 29 runs in 6 matches. How many runs are needed in the next match to raise the average to 36? (a) 49 (b) 43 (c) 36 (d) 78
  12. 12.The average of 7 numbers is 45. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 40 (b) 39 (c) 45 (d) 91
  13. 13.A batter has an average of 35 runs in 6 matches. How many runs are needed in the next match to raise the average to 39? (a) 63 (b) 39 (c) 43 (d) 28
  14. 14.What is the average of 36, 23, 19 and 38? (a) 28 (b) 31 (c) 29 (d) 30
  15. 15.What is the average of all the whole numbers from 9 to 17? (a) 14 (b) 4 (c) 13 (d) 8
  16. 16.The average of 4 numbers is 36. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 36 (b) 21 (c) 77 (d) 22
  17. 17.What is the average of all the whole numbers from 25 to 35? (a) 30 (b) 31 (c) 5 (d) 10
  18. 18.What is the average of all the whole numbers from 56 to 68? (a) 62 (b) 12 (c) 6 (d) 63
  19. 19.What is the average of 24, 25, 26, 50, 26 and 83? (a) 40 (b) 39 (c) 38 (d) 41
  20. 20.What is the average of 50, 34, 30, 42 and 29? (a) 38 (b) 37 (c) 39 (d) 36
  21. 21.What is the average of 7, 21, 9 and 47? (a) 21 (b) 20 (c) 28 (d) 22
  22. 22.What is the average of 42, 22, 32, 23, 37 and 6? (a) 28 (b) 27 (c) 26 (d) 29
  23. 23.What is the average of 85, 67, 71 and 57? (a) 69 (b) 72 (c) 71 (d) 70
  24. 24.The average of 7 numbers is 45. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 88 (b) 45 (c) 14 (d) 57
  25. 25.A batter has an average of 51 runs in 5 matches. How many runs are needed in the next match to raise the average to 56? (a) 81 (b) 30 (c) 56 (d) 61
  26. 26.What is the average of 37, 38, 34, 44, 45 and 84? (a) 46 (b) 48 (c) 49 (d) 47
  27. 27.The average of 7 numbers is 48. When one number is taken away, the average of the rest is 50. Which number was taken away? (a) 48 (b) 37 (c) 98 (d) 36
  28. 28.What is the average of all the whole numbers from 37 to 51? (a) 44 (b) 7 (c) 45 (d) 14
  29. 29.What is the average of 52, 45, 49 and 34? (a) 44 (b) 45 (c) 60 (d) 46
  30. 30.What is the average of 16, 29, 29, 36 and 30? (a) 27 (b) 35 (c) 29 (d) 28
  31. 31.What is the average of all the whole numbers from 21 to 39? (a) 31 (b) 18 (c) 9 (d) 30
  32. 32.A batter has an average of 48 runs in 7 matches. How many runs are needed in the next match to raise the average to 55? (a) 104 (b) 55 (c) 62 (d) 56
  33. 33.The average of 6 numbers is 45. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 26 (b) 94 (c) 45 (d) 25
  34. 34.The average of 5 numbers is 48. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 45 (b) 48 (c) 97 (d) 44
  35. 35.A batter has an average of 40 runs in 4 matches. How many runs are needed in the next match to raise the average to 48? (a) 40 (b) 48 (c) 80 (d) 56
  36. 36.What is the average of all the whole numbers from 9 to 29? (a) 20 (b) 10 (c) 18 (d) 19
  37. 37.The average of 7 numbers is 41. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 30 (b) 41 (c) 29 (d) 84
  38. 38.What is the average of all the whole numbers from 43 to 75? (a) 16 (b) 59 (c) 32 (d) 60
  39. 39.The average of 7 numbers is 19. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 21 (b) 37 (c) 35 (d) 19
  40. 40.The average of 8 numbers is 48. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 42 (b) 97 (c) 41 (d) 48

Answer key

  1. 49
  2. 40
  3. 30
  4. 17
  5. 33
  6. 11
  7. 20
  8. 27
  9. 49
  10. 52
  11. 78
  12. 39
  13. 63
  14. 29
  15. 13
  16. 21
  17. 30
  18. 62
  19. 39
  20. 37
  21. 21
  22. 27
  23. 70
  24. 57
  25. 81
  26. 47
  27. 36
  28. 44
  29. 45
  30. 28
  31. 30
  32. 104
  33. 25
  34. 44
  35. 80
  36. 19
  37. 29
  38. 59
  39. 37
  40. 41

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