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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 88 · 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.The average of 7 numbers is 49. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 49 (b) 97 (c) 7 (d) 55
  2. 2.What is the average of all the whole numbers from 42 to 74? (a) 32 (b) 58 (c) 16 (d) 59
  3. 3.A batter has an average of 35 runs in 7 matches. How many runs are needed in the next match to raise the average to 37? (a) 37 (b) 39 (c) 16 (d) 51
  4. 4.The average of 6 numbers is 13. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 30 (b) 38 (c) 21 (d) 13
  5. 5.What is the average of 40, 26, 39, 36, 20 and 1? (a) 28 (b) 27 (c) 29 (d) 26
  6. 6.What is the average of 16, 26, 16, 15 and 77? (a) 29 (b) 32 (c) 31 (d) 30
  7. 7.What is the average of 20, 32, 8 and 20? (a) 19 (b) 20 (c) 21 (d) 22
  8. 8.What is the average of 56, 55, 51, 56, 49 and 105? (a) 62 (b) 61 (c) 64 (d) 63
  9. 9.What is the average of all the whole numbers from 35 to 43? (a) 40 (b) 8 (c) 39 (d) 4
  10. 10.A batter has an average of 23 runs in 9 matches. How many runs are needed in the next match to raise the average to 29? (a) 35 (b) 83 (c) 29 (d) 60
  11. 11.The average of 6 numbers is 33. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 33 (b) 14 (c) 70 (d) 13
  12. 12.What is the average of 35, 26, 22, 23, 41 and 57? (a) 36 (b) 35 (c) 33 (d) 34
  13. 13.What is the average of all the whole numbers from 54 to 92? (a) 74 (b) 73 (c) 38 (d) 19
  14. 14.The average of 6 numbers is 47. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 23 (b) 22 (c) 47 (d) 99
  15. 15.What is the average of all the whole numbers from 44 to 50? (a) 3 (b) 48 (c) 47 (d) 6
  16. 16.What is the average of all the whole numbers from 57 to 67? (a) 10 (b) 62 (c) 5 (d) 63
  17. 17.What is the average of 65, 61, 47 and 75? (a) 62 (b) 64 (c) 61 (d) 63
  18. 18.What is the average of 56, 37, 54 and 29? (a) 46 (b) 45 (c) 43 (d) 44
  19. 19.The average of 6 numbers is 39. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 15 (b) 14 (c) 39 (d) 83
  20. 20.What is the average of all the whole numbers from 36 to 70? (a) 53 (b) 34 (c) 54 (d) 17
  21. 21.What is the average of all the whole numbers from 49 to 87? (a) 19 (b) 68 (c) 38 (d) 69
  22. 22.A batter has an average of 25 runs in 6 matches. How many runs are needed in the next match to raise the average to 30? (a) 60 (b) 30 (c) 61 (d) 35
  23. 23.What is the average of 42, 55, 64, 38 and 56? (a) 52 (b) 50 (c) 53 (d) 51
  24. 24.What is the average of all the whole numbers from 60 to 82? (a) 71 (b) 72 (c) 22 (d) 11
  25. 25.What is the average of 30, 38, 49 and 51? (a) 43 (b) 42 (c) 41 (d) 56
  26. 26.The average of 4 numbers is 42. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 48 (b) 42 (c) 82 (d) 8
  27. 27.The average of 4 numbers is 22. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 28 (b) 22 (c) 42 (d) 8
  28. 28.A batter has an average of 24 runs in 3 matches. How many runs are needed in the next match to raise the average to 27? (a) 12 (b) 36 (c) 27 (d) 30
  29. 29.The average of 5 numbers is 47. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 47 (b) 89 (c) 67 (d) 25
  30. 30.What is the average of all the whole numbers from 47 to 85? (a) 67 (b) 38 (c) 66 (d) 19
  31. 31.What is the average of 71, 71, 58, 60 and 25? (a) 59 (b) 57 (c) 58 (d) 56
  32. 32.What is the average of 73, 81, 66, 93, 79 and 88? (a) 79 (b) 81 (c) 80 (d) 96
  33. 33.The average of 5 numbers is 42. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 87 (b) 31 (c) 30 (d) 42
  34. 34.What is the average of all the whole numbers from 60 to 78? (a) 69 (b) 18 (c) 70 (d) 9
  35. 35.A batter has an average of 23 runs in 9 matches. How many runs are needed in the next match to raise the average to 27? (a) 27 (b) 31 (c) 63 (d) 40
  36. 36.What is the average of 72, 50, 77, 67, 50 and 62? (a) 62 (b) 64 (c) 63 (d) 65
  37. 37.What is the average of 52, 43, 46, 30 and 29? (a) 41 (b) 40 (c) 50 (d) 39
  38. 38.The average of 5 numbers is 39. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 43 (b) 77 (c) 39 (d) 5
  39. 39.What is the average of 43, 14, 28 and 31? (a) 30 (b) 31 (c) 28 (d) 29
  40. 40.What is the average of 22, 12, 18, 8, 35 and 25? (a) 20 (b) 19 (c) 21 (d) 24

Answer key

  1. 55
  2. 58
  3. 51
  4. 38
  5. 27
  6. 30
  7. 20
  8. 62
  9. 39
  10. 83
  11. 13
  12. 34
  13. 73
  14. 22
  15. 47
  16. 62
  17. 62
  18. 44
  19. 14
  20. 53
  21. 68
  22. 60
  23. 51
  24. 71
  25. 42
  26. 48
  27. 28
  28. 36
  29. 67
  30. 66
  31. 57
  32. 80
  33. 30
  34. 69
  35. 63
  36. 63
  37. 40
  38. 43
  39. 29
  40. 20

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