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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 155 · 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 32 to 64? (a) 49 (b) 16 (c) 32 (d) 48
  2. 2.What is the average of 20, 21, 5 and 34? (a) 19 (b) 22 (c) 21 (d) 20
  3. 3.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 38? (a) 43 (b) 73 (c) 40 (d) 38
  4. 4.What is the average of 19, 23, 33, 39, 17 and 37? (a) 30 (b) 27 (c) 29 (d) 28
  5. 5.What is the average of 40, 25, 25, 26, 50 and 44? (a) 42 (b) 35 (c) 34 (d) 36
  6. 6.The average of 5 numbers is 26. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 26 (b) 22 (c) 53 (d) 23
  7. 7.What is the average of all the whole numbers from 36 to 62? (a) 49 (b) 13 (c) 50 (d) 26
  8. 8.The average of 4 numbers is 18. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 32 (b) 16 (c) 18 (d) 30
  9. 9.What is the average of all the whole numbers from 33 to 45? (a) 40 (b) 39 (c) 6 (d) 12
  10. 10.A batter has an average of 55 runs in 5 matches. How many runs are needed in the next match to raise the average to 57? (a) 67 (b) 12 (c) 59 (d) 57
  11. 11.The average of 4 numbers is 27. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 20 (b) 27 (c) 42 (d) 49
  12. 12.What is the average of 40, 48, 36 and 16? (a) 34 (b) 36 (c) 37 (d) 35
  13. 13.The average of 4 numbers is 11. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 20 (b) 12 (c) 11 (d) 19
  14. 14.What is the average of 27, 12, 20 and 45? (a) 27 (b) 28 (c) 26 (d) 25
  15. 15.What is the average of all the whole numbers from 38 to 48? (a) 44 (b) 10 (c) 5 (d) 43
  16. 16.What is the average of all the whole numbers from 15 to 55? (a) 35 (b) 20 (c) 36 (d) 40
  17. 17.A batter has an average of 42 runs in 9 matches. How many runs are needed in the next match to raise the average to 49? (a) 70 (b) 56 (c) 49 (d) 112
  18. 18.The average of 8 numbers is 49. When one number is taken away, the average of the rest is 50. Which number was taken away? (a) 49 (b) 43 (c) 99 (d) 42
  19. 19.The average of 5 numbers is 38. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 38 (b) 25 (c) 58 (d) 71
  20. 20.The average of 7 numbers is 48. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 48 (b) 99 (c) 30 (d) 31
  21. 21.What is the average of 65, 59, 67, 53 and 51? (a) 61 (b) 60 (c) 59 (d) 58
  22. 22.The average of 5 numbers is 33. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 65 (b) 37 (c) 5 (d) 33
  23. 23.What is the average of 55, 48, 35 and 38? (a) 43 (b) 44 (c) 45 (d) 46
  24. 24.The average of 8 numbers is 17. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 36 (b) 17 (c) 3 (d) 4
  25. 25.The average of 4 numbers is 41. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 12 (b) 41 (c) 50 (d) 79
  26. 26.What is the average of all the whole numbers from 46 to 86? (a) 66 (b) 40 (c) 20 (d) 67
  27. 27.A batter has an average of 30 runs in 8 matches. How many runs are needed in the next match to raise the average to 33? (a) 36 (b) 33 (c) 27 (d) 57
  28. 28.What is the average of all the whole numbers from 5 to 19? (a) 13 (b) 14 (c) 7 (d) 12
  29. 29.What is the average of all the whole numbers from 37 to 71? (a) 55 (b) 17 (c) 34 (d) 54
  30. 30.What is the average of all the whole numbers from 57 to 79? (a) 11 (b) 22 (c) 69 (d) 68
  31. 31.The average of 8 numbers is 48. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 83 (b) 40 (c) 91 (d) 48
  32. 32.What is the average of all the whole numbers from 14 to 24? (a) 10 (b) 5 (c) 19 (d) 20
  33. 33.The average of 8 numbers is 34. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 66 (b) 34 (c) 48 (d) 16
  34. 34.What is the average of all the whole numbers from 52 to 62? (a) 57 (b) 10 (c) 58 (d) 5
  35. 35.What is the average of 65, 84, 88 and 59? (a) 73 (b) 75 (c) 76 (d) 74
  36. 36.What is the average of 43, 45, 29, 43, 25 and 7? (a) 32 (b) 31 (c) 34 (d) 33
  37. 37.What is the average of all the whole numbers from 43 to 51? (a) 48 (b) 47 (c) 8 (d) 4
  38. 38.A batter has an average of 53 runs in 3 matches. How many runs are needed in the next match to raise the average to 56? (a) 56 (b) 59 (c) 12 (d) 65
  39. 39.The average of 6 numbers is 18. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 18 (b) 31 (c) 30 (d) 43
  40. 40.What is the average of all the whole numbers from 41 to 67? (a) 55 (b) 26 (c) 13 (d) 54

Answer key

  1. 48
  2. 20
  3. 73
  4. 28
  5. 35
  6. 22
  7. 49
  8. 30
  9. 39
  10. 67
  11. 42
  12. 35
  13. 20
  14. 26
  15. 43
  16. 35
  17. 112
  18. 42
  19. 58
  20. 30
  21. 59
  22. 37
  23. 44
  24. 3
  25. 50
  26. 66
  27. 57
  28. 12
  29. 54
  30. 68
  31. 83
  32. 19
  33. 48
  34. 57
  35. 74
  36. 32
  37. 47
  38. 65
  39. 43
  40. 54

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