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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 728 · 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 35 to 67? (a) 32 (b) 16 (c) 52 (d) 51
  2. 2.What is the average of all the whole numbers from 19 to 29? (a) 5 (b) 25 (c) 10 (d) 24
  3. 3.The average of 4 numbers is 22. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 40 (b) 22 (c) 34 (d) 16
  4. 4.What is the average of all the whole numbers from 33 to 73? (a) 54 (b) 53 (c) 40 (d) 20
  5. 5.What is the average of all the whole numbers from 9 to 37? (a) 24 (b) 14 (c) 23 (d) 28
  6. 6.What is the average of all the whole numbers from 55 to 91? (a) 73 (b) 36 (c) 18 (d) 74
  7. 7.What is the average of 23, 33, 35, 36, 36 and 17? (a) 29 (b) 30 (c) 31 (d) 36
  8. 8.What is the average of 71, 65, 88 and 80? (a) 75 (b) 78 (c) 77 (d) 76
  9. 9.What is the average of 17, 35, 27 and 29? (a) 36 (b) 26 (c) 28 (d) 27
  10. 10.What is the average of 34, 54, 51, 50, 40 and 41? (a) 46 (b) 44 (c) 54 (d) 45
  11. 11.What is the average of all the whole numbers from 26 to 36? (a) 32 (b) 10 (c) 31 (d) 5
  12. 12.What is the average of 46, 44, 18 and 16? (a) 32 (b) 31 (c) 33 (d) 30
  13. 13.The average of 6 numbers is 18. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 18 (b) 4 (c) 39 (d) 3
  14. 14.A batter has an average of 50 runs in 6 matches. How many runs are needed in the next match to raise the average to 57? (a) 99 (b) 57 (c) 64 (d) 49
  15. 15.A batter has an average of 54 runs in 3 matches. How many runs are needed in the next match to raise the average to 61? (a) 82 (b) 28 (c) 61 (d) 68
  16. 16.What is the average of all the whole numbers from 42 to 78? (a) 18 (b) 36 (c) 61 (d) 60
  17. 17.The average of 5 numbers is 46. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 89 (b) 46 (c) 15 (d) 58
  18. 18.What is the average of all the whole numbers from 53 to 71? (a) 18 (b) 9 (c) 63 (d) 62
  19. 19.A batter has an average of 39 runs in 7 matches. How many runs are needed in the next match to raise the average to 47? (a) 55 (b) 47 (c) 64 (d) 103
  20. 20.What is the average of 75, 55, 71, 70, 55 and 94? (a) 70 (b) 84 (c) 69 (d) 71
  21. 21.The average of 4 numbers is 10. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 21 (b) 7 (c) 10 (d) 8
  22. 22.What is the average of 30, 35, 32, 20, 17 and 10? (a) 23 (b) 25 (c) 24 (d) 26
  23. 23.What is the average of all the whole numbers from 47 to 55? (a) 8 (b) 51 (c) 52 (d) 4
  24. 24.The average of 7 numbers is 12. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 12 (b) 24 (c) 14 (d) 22
  25. 25.What is the average of all the whole numbers from 58 to 84? (a) 13 (b) 72 (c) 71 (d) 26
  26. 26.The average of 6 numbers is 40. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 76 (b) 24 (c) 60 (d) 40
  27. 27.What is the average of 44, 71, 52 and 65? (a) 59 (b) 60 (c) 57 (d) 58
  28. 28.What is the average of 29, 16, 31, 25 and 54? (a) 33 (b) 30 (c) 31 (d) 32
  29. 29.What is the average of 40, 54, 52, 59 and 35? (a) 49 (b) 47 (c) 48 (d) 60
  30. 30.What is the average of 85, 88, 76, 68, 83 and 80? (a) 81 (b) 96 (c) 80 (d) 79
  31. 31.The average of 5 numbers is 17. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 9 (b) 36 (c) 17 (d) 10
  32. 32.What is the average of 41, 11, 13, 18 and 47? (a) 27 (b) 28 (c) 25 (d) 26
  33. 33.What is the average of all the whole numbers from 50 to 84? (a) 17 (b) 34 (c) 67 (d) 68
  34. 34.A batter has an average of 39 runs in 6 matches. How many runs are needed in the next match to raise the average to 44? (a) 49 (b) 35 (c) 44 (d) 74
  35. 35.What is the average of 19, 18, 45 and 46? (a) 33 (b) 32 (c) 34 (d) 31
  36. 36.What is the average of 33, 41, 25, 23, 19 and 21? (a) 26 (b) 28 (c) 27 (d) 29
  37. 37.A batter has an average of 33 runs in 7 matches. How many runs are needed in the next match to raise the average to 40? (a) 89 (b) 56 (c) 40 (d) 47
  38. 38.What is the average of all the whole numbers from 25 to 57? (a) 32 (b) 41 (c) 42 (d) 16
  39. 39.The average of 8 numbers is 38. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 38 (b) 16 (c) 74 (d) 52
  40. 40.The average of 5 numbers is 17. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 15 (b) 31 (c) 17 (d) 29

Answer key

  1. 51
  2. 24
  3. 34
  4. 53
  5. 23
  6. 73
  7. 30
  8. 76
  9. 27
  10. 45
  11. 31
  12. 31
  13. 3
  14. 99
  15. 82
  16. 60
  17. 58
  18. 62
  19. 103
  20. 70
  21. 7
  22. 24
  23. 51
  24. 24
  25. 71
  26. 60
  27. 58
  28. 31
  29. 48
  30. 80
  31. 9
  32. 26
  33. 67
  34. 74
  35. 32
  36. 27
  37. 89
  38. 41
  39. 52
  40. 29

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