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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 220 · 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 21, 44, 17 and 46? (a) 33 (b) 32 (c) 34 (d) 31
  2. 2.What is the average of 67, 60, 78, 88 and 77? (a) 74 (b) 75 (c) 76 (d) 73
  3. 3.A batter has an average of 55 runs in 4 matches. How many runs are needed in the next match to raise the average to 61? (a) 85 (b) 67 (c) 30 (d) 61
  4. 4.A batter has an average of 33 runs in 9 matches. How many runs are needed in the next match to raise the average to 36? (a) 30 (b) 36 (c) 39 (d) 63
  5. 5.The average of 6 numbers is 15. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 20 (b) 6 (c) 15 (d) 29
  6. 6.What is the average of all the whole numbers from 29 to 37? (a) 34 (b) 4 (c) 33 (d) 8
  7. 7.A batter has an average of 20 runs in 3 matches. How many runs are needed in the next match to raise the average to 22? (a) 8 (b) 28 (c) 24 (d) 22
  8. 8.The average of 7 numbers is 19. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 13 (b) 39 (c) 19 (d) 14
  9. 9.What is the average of all the whole numbers from 14 to 26? (a) 20 (b) 21 (c) 12 (d) 6
  10. 10.A batter has an average of 34 runs in 8 matches. How many runs are needed in the next match to raise the average to 41? (a) 48 (b) 63 (c) 41 (d) 97
  11. 11.A batter has an average of 48 runs in 8 matches. How many runs are needed in the next match to raise the average to 56? (a) 72 (b) 64 (c) 120 (d) 56
  12. 12.What is the average of all the whole numbers from 37 to 43? (a) 40 (b) 3 (c) 6 (d) 41
  13. 13.What is the average of 61, 75, 64, 55, 62 and 85? (a) 69 (b) 67 (c) 66 (d) 68
  14. 14.The average of 5 numbers is 47. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 32 (b) 98 (c) 31 (d) 47
  15. 15.A batter has an average of 55 runs in 9 matches. How many runs are needed in the next match to raise the average to 63? (a) 80 (b) 135 (c) 63 (d) 71
  16. 16.What is the average of 37, 41, 44 and 62? (a) 48 (b) 47 (c) 46 (d) 45
  17. 17.What is the average of 18, 12, 11, 10 and 59? (a) 22 (b) 23 (c) 21 (d) 24
  18. 18.The average of 5 numbers is 48. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 36 (b) 99 (c) 37 (d) 48
  19. 19.The average of 5 numbers is 37. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 71 (b) 37 (c) 15 (d) 49
  20. 20.What is the average of all the whole numbers from 20 to 60? (a) 41 (b) 20 (c) 39 (d) 40
  21. 21.The average of 7 numbers is 43. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 85 (b) 7 (c) 49 (d) 43
  22. 22.The average of 6 numbers is 20. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 18 (b) 35 (c) 37 (d) 20
  23. 23.The average of 8 numbers is 32. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 59 (b) 67 (c) 32 (d) 40
  24. 24.What is the average of all the whole numbers from 31 to 57? (a) 45 (b) 26 (c) 13 (d) 44
  25. 25.A batter has an average of 29 runs in 5 matches. How many runs are needed in the next match to raise the average to 31? (a) 12 (b) 41 (c) 33 (d) 31
  26. 26.What is the average of 71, 59, 73 and 33? (a) 60 (b) 61 (c) 59 (d) 58
  27. 27.A batter has an average of 24 runs in 6 matches. How many runs are needed in the next match to raise the average to 30? (a) 42 (b) 36 (c) 30 (d) 66
  28. 28.What is the average of 74, 82, 78, 86 and 70? (a) 79 (b) 77 (c) 78 (d) 80
  29. 29.What is the average of 39, 52, 49, 39 and 11? (a) 37 (b) 40 (c) 39 (d) 38
  30. 30.What is the average of 72, 82, 79 and 51? (a) 71 (b) 73 (c) 72 (d) 70
  31. 31.The average of 4 numbers is 43. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 41 (b) 43 (c) 87 (d) 40
  32. 32.The average of 8 numbers is 24. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 10 (b) 50 (c) 11 (d) 24
  33. 33.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 55? (a) 60 (b) 35 (c) 85 (d) 55
  34. 34.The average of 5 numbers is 45. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 45 (b) 42 (c) 41 (d) 91
  35. 35.What is the average of 36, 35, 23 and 22? (a) 30 (b) 28 (c) 31 (d) 29
  36. 36.What is the average of 48, 69, 43 and 56? (a) 72 (b) 53 (c) 54 (d) 55
  37. 37.What is the average of all the whole numbers from 6 to 18? (a) 12 (b) 6 (c) 13 (d) 11
  38. 38.What is the average of 71, 69, 67, 87, 87 and 57? (a) 74 (b) 75 (c) 72 (d) 73
  39. 39.A batter has an average of 57 runs in 3 matches. How many runs are needed in the next match to raise the average to 60? (a) 12 (b) 69 (c) 63 (d) 60
  40. 40.What is the average of 21, 41, 28, 37, 44 and 9? (a) 30 (b) 31 (c) 36 (d) 29

Answer key

  1. 32
  2. 74
  3. 85
  4. 63
  5. 20
  6. 33
  7. 28
  8. 13
  9. 20
  10. 97
  11. 120
  12. 40
  13. 67
  14. 31
  15. 135
  16. 46
  17. 22
  18. 36
  19. 49
  20. 40
  21. 49
  22. 35
  23. 67
  24. 44
  25. 41
  26. 59
  27. 66
  28. 78
  29. 38
  30. 71
  31. 40
  32. 10
  33. 85
  34. 41
  35. 29
  36. 54
  37. 12
  38. 73
  39. 69
  40. 30

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