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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 118 · 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 14 to 48? (a) 34 (b) 31 (c) 17 (d) 32
  2. 2.The average of 4 numbers is 50. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 50 (b) 45 (c) 102 (d) 44
  3. 3.What is the average of 42, 45, 67, 65 and 66? (a) 58 (b) 56 (c) 59 (d) 57
  4. 4.A batter has an average of 40 runs in 8 matches. How many runs are needed in the next match to raise the average to 46? (a) 46 (b) 94 (c) 54 (d) 52
  5. 5.A batter has an average of 36 runs in 6 matches. How many runs are needed in the next match to raise the average to 39? (a) 57 (b) 42 (c) 39 (d) 21
  6. 6.A batter has an average of 31 runs in 4 matches. How many runs are needed in the next match to raise the average to 35? (a) 51 (b) 39 (c) 20 (d) 35
  7. 7.What is the average of 41, 29, 42, 21 and 22? (a) 30 (b) 33 (c) 32 (d) 31
  8. 8.What is the average of all the whole numbers from 43 to 75? (a) 16 (b) 32 (c) 60 (d) 59
  9. 9.A batter has an average of 53 runs in 6 matches. How many runs are needed in the next match to raise the average to 61? (a) 61 (b) 69 (c) 109 (d) 56
  10. 10.What is the average of 8, 26, 7, 31, 21 and 27? (a) 24 (b) 20 (c) 21 (d) 19
  11. 11.The average of 7 numbers is 19. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 36 (b) 31 (c) 19 (d) 14
  12. 12.The average of 4 numbers is 35. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 20 (b) 65 (c) 35 (d) 50
  13. 13.A batter has an average of 45 runs in 7 matches. How many runs are needed in the next match to raise the average to 49? (a) 49 (b) 32 (c) 77 (d) 53
  14. 14.The average of 7 numbers is 17. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 17 (b) 29 (c) 14 (d) 32
  15. 15.What is the average of all the whole numbers from 27 to 35? (a) 8 (b) 4 (c) 32 (d) 31
  16. 16.What is the average of all the whole numbers from 58 to 68? (a) 64 (b) 10 (c) 63 (d) 5
  17. 17.What is the average of 61, 69, 61, 54, 75 and 82? (a) 66 (b) 68 (c) 67 (d) 69
  18. 18.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 51? (a) 59 (b) 51 (c) 10 (d) 53
  19. 19.The average of 4 numbers is 46. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 44 (b) 93 (c) 46 (d) 43
  20. 20.What is the average of 35, 10, 15 and 20? (a) 21 (b) 19 (c) 22 (d) 20
  21. 21.What is the average of all the whole numbers from 42 to 54? (a) 12 (b) 49 (c) 48 (d) 6
  22. 22.What is the average of all the whole numbers from 6 to 30? (a) 24 (b) 19 (c) 12 (d) 18
  23. 23.A batter has an average of 59 runs in 3 matches. How many runs are needed in the next match to raise the average to 66? (a) 73 (b) 28 (c) 87 (d) 66
  24. 24.What is the average of all the whole numbers from 55 to 81? (a) 69 (b) 68 (c) 13 (d) 26
  25. 25.A batter has an average of 59 runs in 4 matches. How many runs are needed in the next match to raise the average to 61? (a) 63 (b) 69 (c) 61 (d) 10
  26. 26.The average of 7 numbers is 35. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 68 (b) 35 (c) 47 (d) 14
  27. 27.What is the average of all the whole numbers from 40 to 62? (a) 11 (b) 22 (c) 51 (d) 52
  28. 28.What is the average of all the whole numbers from 55 to 89? (a) 17 (b) 72 (c) 34 (d) 73
  29. 29.The average of 6 numbers is 40. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 25 (b) 26 (c) 40 (d) 83
  30. 30.The average of 6 numbers is 20. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 36 (b) 24 (c) 20 (d) 40
  31. 31.What is the average of 62, 41, 64 and 41? (a) 53 (b) 54 (c) 51 (d) 52
  32. 32.What is the average of all the whole numbers from 25 to 65? (a) 40 (b) 46 (c) 45 (d) 20
  33. 33.What is the average of 39, 43, 52 and 46? (a) 44 (b) 45 (c) 60 (d) 46
  34. 34.A batter has an average of 45 runs in 7 matches. How many runs are needed in the next match to raise the average to 52? (a) 52 (b) 56 (c) 101 (d) 59
  35. 35.The average of 4 numbers is 38. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 79 (b) 30 (c) 29 (d) 38
  36. 36.What is the average of all the whole numbers from 60 to 84? (a) 24 (b) 72 (c) 73 (d) 12
  37. 37.A batter has an average of 20 runs in 8 matches. How many runs are needed in the next match to raise the average to 26? (a) 54 (b) 32 (c) 74 (d) 26
  38. 38.A batter has an average of 38 runs in 8 matches. How many runs are needed in the next match to raise the average to 41? (a) 27 (b) 44 (c) 65 (d) 41
  39. 39.What is the average of all the whole numbers from 18 to 26? (a) 22 (b) 8 (c) 4 (d) 23
  40. 40.The average of 4 numbers is 38. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 71 (b) 53 (c) 20 (d) 38

Answer key

  1. 31
  2. 44
  3. 57
  4. 94
  5. 57
  6. 51
  7. 31
  8. 59
  9. 109
  10. 20
  11. 31
  12. 50
  13. 77
  14. 29
  15. 31
  16. 63
  17. 67
  18. 59
  19. 43
  20. 20
  21. 48
  22. 18
  23. 87
  24. 68
  25. 69
  26. 47
  27. 51
  28. 72
  29. 25
  30. 40
  31. 52
  32. 45
  33. 45
  34. 101
  35. 29
  36. 72
  37. 74
  38. 65
  39. 22
  40. 53

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