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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 564 · 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 21 to 37? (a) 8 (b) 30 (c) 29 (d) 16
  2. 2.The average of 4 numbers is 25. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 25 (b) 23 (c) 22 (d) 51
  3. 3.The average of 7 numbers is 28. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 46 (b) 21 (c) 28 (d) 53
  4. 4.What is the average of 76, 57, 70, 65 and 72? (a) 69 (b) 67 (c) 85 (d) 68
  5. 5.The average of 5 numbers is 50. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 50 (b) 46 (c) 101 (d) 47
  6. 6.What is the average of all the whole numbers from 10 to 26? (a) 16 (b) 8 (c) 19 (d) 18
  7. 7.The average of 4 numbers is 48. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 94 (b) 8 (c) 54 (d) 48
  8. 8.What is the average of 90, 67, 93 and 70? (a) 82 (b) 81 (c) 79 (d) 80
  9. 9.A batter has an average of 43 runs in 8 matches. How many runs are needed in the next match to raise the average to 45? (a) 61 (b) 47 (c) 45 (d) 18
  10. 10.A batter has an average of 22 runs in 9 matches. How many runs are needed in the next match to raise the average to 29? (a) 29 (b) 92 (c) 70 (d) 36
  11. 11.A batter has an average of 28 runs in 9 matches. How many runs are needed in the next match to raise the average to 31? (a) 58 (b) 34 (c) 31 (d) 30
  12. 12.The average of 6 numbers is 27. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 6 (b) 32 (c) 27 (d) 53
  13. 13.What is the average of 17, 43, 45, 28, 45 and 8? (a) 30 (b) 32 (c) 33 (d) 31
  14. 14.What is the average of all the whole numbers from 58 to 76? (a) 68 (b) 9 (c) 18 (d) 67
  15. 15.A batter has an average of 49 runs in 4 matches. How many runs are needed in the next match to raise the average to 53? (a) 69 (b) 20 (c) 53 (d) 57
  16. 16.What is the average of 32, 42, 45, 34 and 17? (a) 35 (b) 36 (c) 34 (d) 33
  17. 17.What is the average of 22, 14, 18, 22 and 49? (a) 24 (b) 25 (c) 26 (d) 27
  18. 18.What is the average of all the whole numbers from 56 to 82? (a) 69 (b) 26 (c) 70 (d) 13
  19. 19.What is the average of all the whole numbers from 17 to 45? (a) 31 (b) 32 (c) 28 (d) 14
  20. 20.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 46? (a) 46 (b) 70 (c) 30 (d) 52
  21. 21.What is the average of all the whole numbers from 53 to 73? (a) 64 (b) 63 (c) 20 (d) 10
  22. 22.A batter has an average of 56 runs in 8 matches. How many runs are needed in the next match to raise the average to 63? (a) 63 (b) 120 (c) 119 (d) 70
  23. 23.The average of 5 numbers is 23. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 20 (b) 19 (c) 23 (d) 47
  24. 24.A batter has an average of 25 runs in 5 matches. How many runs are needed in the next match to raise the average to 31? (a) 61 (b) 36 (c) 37 (d) 31
  25. 25.What is the average of all the whole numbers from 19 to 35? (a) 27 (b) 16 (c) 28 (d) 8
  26. 26.What is the average of 55, 44, 44 and 45? (a) 49 (b) 47 (c) 46 (d) 48
  27. 27.What is the average of 82, 76, 73, 68, 66 and 73? (a) 75 (b) 72 (c) 74 (d) 73
  28. 28.What is the average of all the whole numbers from 57 to 65? (a) 8 (b) 62 (c) 61 (d) 4
  29. 29.The average of 8 numbers is 15. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 9 (b) 31 (c) 15 (d) 8
  30. 30.The average of 8 numbers is 44. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 44 (b) 84 (c) 72 (d) 32
  31. 31.A batter has an average of 47 runs in 5 matches. How many runs are needed in the next match to raise the average to 54? (a) 61 (b) 89 (c) 42 (d) 54
  32. 32.What is the average of 57, 46, 52, 57 and 73? (a) 56 (b) 59 (c) 57 (d) 58
  33. 33.A batter has an average of 37 runs in 5 matches. How many runs are needed in the next match to raise the average to 39? (a) 41 (b) 12 (c) 49 (d) 39
  34. 34.What is the average of all the whole numbers from 28 to 66? (a) 48 (b) 19 (c) 38 (d) 47
  35. 35.What is the average of all the whole numbers from 20 to 50? (a) 35 (b) 36 (c) 15 (d) 30
  36. 36.What is the average of 60, 66, 62 and 84? (a) 67 (b) 69 (c) 70 (d) 68
  37. 37.What is the average of 45, 25, 23, 30, 23 and 76? (a) 39 (b) 38 (c) 37 (d) 36
  38. 38.What is the average of 35, 55, 40, 45, 34 and 43? (a) 44 (b) 42 (c) 43 (d) 41
  39. 39.The average of 4 numbers is 50. When one number is taken away, the average of the rest is 55. Which number was taken away? (a) 105 (b) 35 (c) 50 (d) 36
  40. 40.What is the average of 77, 70, 60, 68, 60 and 79? (a) 71 (b) 68 (c) 70 (d) 69

Answer key

  1. 29
  2. 22
  3. 46
  4. 68
  5. 46
  6. 18
  7. 54
  8. 80
  9. 61
  10. 92
  11. 58
  12. 32
  13. 31
  14. 67
  15. 69
  16. 34
  17. 25
  18. 69
  19. 31
  20. 70
  21. 63
  22. 119
  23. 19
  24. 61
  25. 27
  26. 47
  27. 73
  28. 61
  29. 8
  30. 72
  31. 89
  32. 57
  33. 49
  34. 47
  35. 35
  36. 68
  37. 37
  38. 42
  39. 35
  40. 69

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