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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 660 · 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 60 to 74? (a) 7 (b) 67 (c) 14 (d) 68
  2. 2.The average of 4 numbers is 15. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 18 (b) 15 (c) 4 (d) 29
  3. 3.A batter has an average of 30 runs in 9 matches. How many runs are needed in the next match to raise the average to 37? (a) 44 (b) 37 (c) 70 (d) 100
  4. 4.What is the average of all the whole numbers from 51 to 89? (a) 19 (b) 70 (c) 71 (d) 38
  5. 5.What is the average of all the whole numbers from 38 to 64? (a) 26 (b) 51 (c) 52 (d) 13
  6. 6.What is the average of all the whole numbers from 23 to 55? (a) 16 (b) 40 (c) 32 (d) 39
  7. 7.The average of 8 numbers is 20. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 6 (b) 42 (c) 20 (d) 7
  8. 8.What is the average of all the whole numbers from 52 to 82? (a) 67 (b) 15 (c) 30 (d) 68
  9. 9.The average of 8 numbers is 34. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 64 (b) 32 (c) 34 (d) 62
  10. 10.What is the average of all the whole numbers from 21 to 33? (a) 28 (b) 12 (c) 27 (d) 6
  11. 11.What is the average of all the whole numbers from 11 to 17? (a) 14 (b) 3 (c) 6 (d) 15
  12. 12.What is the average of 67, 68, 65, 71, 70 and 7? (a) 58 (b) 57 (c) 60 (d) 59
  13. 13.What is the average of 30, 49, 48, 43 and 30? (a) 50 (b) 41 (c) 39 (d) 40
  14. 14.A batter has an average of 26 runs in 3 matches. How many runs are needed in the next match to raise the average to 29? (a) 29 (b) 38 (c) 12 (d) 32
  15. 15.What is the average of all the whole numbers from 35 to 63? (a) 50 (b) 49 (c) 14 (d) 28
  16. 16.What is the average of all the whole numbers from 39 to 45? (a) 43 (b) 42 (c) 3 (d) 6
  17. 17.What is the average of all the whole numbers from 49 to 73? (a) 12 (b) 61 (c) 62 (d) 24
  18. 18.What is the average of all the whole numbers from 51 to 57? (a) 3 (b) 54 (c) 55 (d) 6
  19. 19.The average of 4 numbers is 17. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 9 (b) 8 (c) 37 (d) 17
  20. 20.What is the average of 78, 70, 77, 73, 57 and 53? (a) 70 (b) 67 (c) 68 (d) 69
  21. 21.What is the average of 34, 44, 42, 51, 54 and 69? (a) 48 (b) 49 (c) 51 (d) 50
  22. 22.The average of 4 numbers is 32. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 62 (b) 32 (c) 8 (d) 38
  23. 23.The average of 4 numbers is 28. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 34 (b) 28 (c) 54 (d) 8
  24. 24.The average of 4 numbers is 48. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 48 (b) 12 (c) 57 (d) 93
  25. 25.What is the average of 39, 42, 20, 16, 28 and 41? (a) 30 (b) 32 (c) 33 (d) 31
  26. 26.The average of 8 numbers is 30. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 30 (b) 16 (c) 44 (d) 58
  27. 27.What is the average of 72, 71, 78, 78, 73 and 12? (a) 63 (b) 66 (c) 64 (d) 65
  28. 28.What is the average of 73, 75, 62 and 86? (a) 75 (b) 73 (c) 76 (d) 74
  29. 29.The average of 6 numbers is 38. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 38 (b) 14 (c) 81 (d) 13
  30. 30.The average of 7 numbers is 41. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 41 (b) 12 (c) 87 (d) 11
  31. 31.The average of 5 numbers is 47. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 99 (b) 47 (c) 28 (d) 27
  32. 32.The average of 6 numbers is 32. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 32 (b) 7 (c) 69 (d) 8
  33. 33.What is the average of all the whole numbers from 38 to 46? (a) 43 (b) 4 (c) 8 (d) 42
  34. 34.What is the average of all the whole numbers from 56 to 62? (a) 6 (b) 3 (c) 59 (d) 60
  35. 35.What is the average of all the whole numbers from 31 to 43? (a) 37 (b) 6 (c) 38 (d) 12
  36. 36.What is the average of 33, 52, 34, 54, 40 and 27? (a) 48 (b) 39 (c) 41 (d) 40
  37. 37.What is the average of all the whole numbers from 49 to 55? (a) 53 (b) 3 (c) 6 (d) 52
  38. 38.The average of 7 numbers is 18. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 35 (b) 18 (c) 31 (d) 48
  39. 39.What is the average of 61, 49, 39, 50 and 41? (a) 47 (b) 48 (c) 49 (d) 60
  40. 40.What is the average of 46, 48, 46 and 48? (a) 48 (b) 47 (c) 46 (d) 49

Answer key

  1. 67
  2. 18
  3. 100
  4. 70
  5. 51
  6. 39
  7. 6
  8. 67
  9. 62
  10. 27
  11. 14
  12. 58
  13. 40
  14. 38
  15. 49
  16. 42
  17. 61
  18. 54
  19. 8
  20. 68
  21. 49
  22. 38
  23. 34
  24. 57
  25. 31
  26. 44
  27. 64
  28. 74
  29. 13
  30. 11
  31. 27
  32. 7
  33. 42
  34. 59
  35. 37
  36. 40
  37. 52
  38. 48
  39. 48
  40. 47

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