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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 802 · 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.A batter has an average of 29 runs in 7 matches. How many runs are needed in the next match to raise the average to 31? (a) 16 (b) 31 (c) 33 (d) 45
  2. 2.What is the average of 29, 29, 13 and 13? (a) 20 (b) 21 (c) 28 (d) 22
  3. 3.The average of 6 numbers is 49. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 69 (b) 49 (c) 94 (d) 24
  4. 4.What is the average of all the whole numbers from 8 to 26? (a) 9 (b) 18 (c) 16 (d) 17
  5. 5.What is the average of all the whole numbers from 29 to 69? (a) 50 (b) 40 (c) 20 (d) 49
  6. 6.What is the average of 36, 30, 22 and 60? (a) 36 (b) 38 (c) 39 (d) 37
  7. 7.The average of 7 numbers is 20. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 9 (b) 8 (c) 42 (d) 20
  8. 8.What is the average of 63, 89, 85, 82, 74 and 63? (a) 75 (b) 77 (c) 76 (d) 78
  9. 9.What is the average of all the whole numbers from 19 to 37? (a) 18 (b) 9 (c) 29 (d) 28
  10. 10.What is the average of all the whole numbers from 59 to 65? (a) 62 (b) 63 (c) 3 (d) 6
  11. 11.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) 35 (b) 50 (c) 36 (d) 105
  12. 12.The average of 5 numbers is 50. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 97 (b) 50 (c) 15 (d) 62
  13. 13.What is the average of 13, 15, 7, 31 and 39? (a) 22 (b) 23 (c) 20 (d) 21
  14. 14.What is the average of all the whole numbers from 16 to 26? (a) 22 (b) 21 (c) 10 (d) 5
  15. 15.The average of 5 numbers is 43. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 47 (b) 5 (c) 85 (d) 43
  16. 16.What is the average of all the whole numbers from 31 to 37? (a) 6 (b) 34 (c) 3 (d) 35
  17. 17.What is the average of all the whole numbers from 8 to 46? (a) 28 (b) 27 (c) 19 (d) 38
  18. 18.What is the average of 40, 20, 21, 27, 36 and 24? (a) 30 (b) 27 (c) 29 (d) 28
  19. 19.What is the average of 67, 59, 71 and 47? (a) 63 (b) 61 (c) 62 (d) 60
  20. 20.A batter has an average of 34 runs in 4 matches. How many runs are needed in the next match to raise the average to 40? (a) 46 (b) 40 (c) 64 (d) 30
  21. 21.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 62? (a) 62 (b) 70 (c) 86 (d) 32
  22. 22.A batter has an average of 24 runs in 4 matches. How many runs are needed in the next match to raise the average to 28? (a) 28 (b) 32 (c) 44 (d) 20
  23. 23.What is the average of 27, 35, 39, 47 and 12? (a) 40 (b) 32 (c) 31 (d) 33
  24. 24.What is the average of all the whole numbers from 58 to 86? (a) 73 (b) 14 (c) 72 (d) 28
  25. 25.The average of 6 numbers is 24. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 24 (b) 45 (c) 39 (d) 18
  26. 26.What is the average of 30, 21, 15 and 54? (a) 31 (b) 40 (c) 29 (d) 30
  27. 27.The average of 7 numbers is 47. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 77 (b) 89 (c) 47 (d) 35
  28. 28.What is the average of 45, 59, 48 and 52? (a) 51 (b) 52 (c) 68 (d) 50
  29. 29.What is the average of 36, 35, 31, 27, 37 and 14? (a) 31 (b) 29 (c) 36 (d) 30
  30. 30.What is the average of all the whole numbers from 39 to 57? (a) 18 (b) 48 (c) 49 (d) 9
  31. 31.What is the average of all the whole numbers from 28 to 38? (a) 33 (b) 5 (c) 10 (d) 34
  32. 32.What is the average of all the whole numbers from 48 to 88? (a) 68 (b) 20 (c) 69 (d) 40
  33. 33.The average of 5 numbers is 12. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 4 (b) 5 (c) 12 (d) 26
  34. 34.What is the average of all the whole numbers from 16 to 22? (a) 6 (b) 20 (c) 3 (d) 19
  35. 35.The average of 5 numbers is 40. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 48 (b) 10 (c) 40 (d) 78
  36. 36.What is the average of 34, 47, 36 and 11? (a) 33 (b) 32 (c) 31 (d) 34
  37. 37.A batter has an average of 58 runs in 4 matches. How many runs are needed in the next match to raise the average to 61? (a) 61 (b) 73 (c) 15 (d) 64
  38. 38.A batter has an average of 48 runs in 7 matches. How many runs are needed in the next match to raise the average to 52? (a) 56 (b) 52 (c) 32 (d) 80
  39. 39.The average of 8 numbers is 27. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 34 (b) 8 (c) 27 (d) 53
  40. 40.The average of 4 numbers is 49. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 97 (b) 52 (c) 4 (d) 49

Answer key

  1. 45
  2. 21
  3. 69
  4. 17
  5. 49
  6. 37
  7. 8
  8. 76
  9. 28
  10. 62
  11. 35
  12. 62
  13. 21
  14. 21
  15. 47
  16. 34
  17. 27
  18. 28
  19. 61
  20. 64
  21. 86
  22. 44
  23. 32
  24. 72
  25. 39
  26. 30
  27. 77
  28. 51
  29. 30
  30. 48
  31. 33
  32. 68
  33. 4
  34. 19
  35. 48
  36. 32
  37. 73
  38. 80
  39. 34
  40. 52

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