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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 622 · 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 46 to 86? (a) 66 (b) 67 (c) 20 (d) 40
  2. 2.What is the average of all the whole numbers from 40 to 54? (a) 7 (b) 48 (c) 47 (d) 14
  3. 3.The average of 7 numbers is 42. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 28 (b) 66 (c) 80 (d) 42
  4. 4.What is the average of all the whole numbers from 55 to 73? (a) 18 (b) 64 (c) 9 (d) 65
  5. 5.What is the average of 29, 43, 33 and 11? (a) 29 (b) 31 (c) 28 (d) 30
  6. 6.The average of 7 numbers is 44. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 28 (b) 84 (c) 44 (d) 68
  7. 7.What is the average of 65, 70, 87 and 66? (a) 73 (b) 71 (c) 72 (d) 96
  8. 8.What is the average of all the whole numbers from 22 to 62? (a) 40 (b) 20 (c) 42 (d) 43
  9. 9.The average of 8 numbers is 19. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 39 (b) 13 (c) 12 (d) 19
  10. 10.A batter has an average of 46 runs in 8 matches. How many runs are needed in the next match to raise the average to 49? (a) 73 (b) 49 (c) 52 (d) 27
  11. 11.What is the average of all the whole numbers from 32 to 72? (a) 40 (b) 53 (c) 20 (d) 52
  12. 12.What is the average of all the whole numbers from 23 to 53? (a) 30 (b) 39 (c) 15 (d) 38
  13. 13.A batter has an average of 23 runs in 8 matches. How many runs are needed in the next match to raise the average to 29? (a) 35 (b) 54 (c) 77 (d) 29
  14. 14.What is the average of all the whole numbers from 45 to 51? (a) 3 (b) 49 (c) 48 (d) 6
  15. 15.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 23? (a) 23 (b) 26 (c) 32 (d) 12
  16. 16.What is the average of 47, 54, 54, 49 and 71? (a) 55 (b) 56 (c) 57 (d) 54
  17. 17.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) 61 (b) 82 (c) 68 (d) 28
  18. 18.What is the average of 83, 70, 70, 66, 73 and 100? (a) 79 (b) 76 (c) 78 (d) 77
  19. 19.The average of 8 numbers is 24. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 24 (b) 16 (c) 46 (d) 38
  20. 20.The average of 7 numbers is 30. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 62 (b) 19 (c) 30 (d) 18
  21. 21.What is the average of 62, 44, 51, 50 and 88? (a) 59 (b) 61 (c) 58 (d) 60
  22. 22.A batter has an average of 24 runs in 5 matches. How many runs are needed in the next match to raise the average to 27? (a) 42 (b) 30 (c) 18 (d) 27
  23. 23.What is the average of all the whole numbers from 51 to 87? (a) 69 (b) 18 (c) 70 (d) 36
  24. 24.A batter has an average of 58 runs in 3 matches. How many runs are needed in the next match to raise the average to 61? (a) 64 (b) 61 (c) 12 (d) 70
  25. 25.What is the average of all the whole numbers from 48 to 54? (a) 3 (b) 6 (c) 51 (d) 52
  26. 26.The average of 7 numbers is 22. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 21 (b) 41 (c) 22 (d) 40
  27. 27.What is the average of all the whole numbers from 31 to 49? (a) 41 (b) 40 (c) 18 (d) 9
  28. 28.The average of 6 numbers is 23. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 47 (b) 23 (c) 19 (d) 18
  29. 29.What is the average of 56, 52, 42, 58, 40 and 64? (a) 54 (b) 53 (c) 51 (d) 52
  30. 30.The average of 4 numbers is 43. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 37 (b) 38 (c) 88 (d) 43
  31. 31.The average of 4 numbers is 16. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 16 (b) 5 (c) 36 (d) 4
  32. 32.The average of 4 numbers is 28. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 17 (b) 60 (c) 16 (d) 28
  33. 33.The average of 7 numbers is 38. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 72 (b) 38 (c) 62 (d) 28
  34. 34.The average of 8 numbers is 34. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 34 (b) 14 (c) 71 (d) 13
  35. 35.The average of 6 numbers is 35. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 35 (b) 74 (c) 15 (d) 16
  36. 36.What is the average of all the whole numbers from 25 to 53? (a) 14 (b) 39 (c) 28 (d) 40
  37. 37.What is the average of all the whole numbers from 35 to 47? (a) 41 (b) 6 (c) 42 (d) 12
  38. 38.The average of 8 numbers is 48. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 48 (b) 94 (c) 16 (d) 62
  39. 39.What is the average of 52, 56, 35 and 25? (a) 43 (b) 41 (c) 42 (d) 56
  40. 40.The average of 5 numbers is 35. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 35 (b) 23 (c) 73 (d) 24

Answer key

  1. 66
  2. 47
  3. 66
  4. 64
  5. 29
  6. 68
  7. 72
  8. 42
  9. 12
  10. 73
  11. 52
  12. 38
  13. 77
  14. 48
  15. 32
  16. 55
  17. 82
  18. 77
  19. 38
  20. 18
  21. 59
  22. 42
  23. 69
  24. 70
  25. 51
  26. 40
  27. 40
  28. 18
  29. 52
  30. 37
  31. 4
  32. 16
  33. 62
  34. 13
  35. 15
  36. 39
  37. 41
  38. 62
  39. 42
  40. 23

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