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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 41 · 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.The average of 7 numbers is 31. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 26 (b) 31 (c) 63 (d) 25
  2. 2.A batter has an average of 34 runs in 6 matches. How many runs are needed in the next match to raise the average to 39? (a) 69 (b) 39 (c) 35 (d) 44
  3. 3.A batter has an average of 26 runs in 8 matches. How many runs are needed in the next match to raise the average to 28? (a) 30 (b) 28 (c) 18 (d) 44
  4. 4.The average of 4 numbers is 38. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 75 (b) 38 (c) 41 (d) 4
  5. 5.What is the average of all the whole numbers from 53 to 63? (a) 59 (b) 58 (c) 10 (d) 5
  6. 6.The average of 4 numbers is 43. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 29 (b) 43 (c) 91 (d) 28
  7. 7.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 60? (a) 65 (b) 60 (c) 105 (d) 50
  8. 8.The average of 5 numbers is 36. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 70 (b) 10 (c) 36 (d) 44
  9. 9.The average of 6 numbers is 44. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 34 (b) 90 (c) 44 (d) 35
  10. 10.What is the average of all the whole numbers from 44 to 72? (a) 28 (b) 58 (c) 59 (d) 14
  11. 11.The average of 8 numbers is 22. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 22 (b) 16 (c) 15 (d) 45
  12. 12.A batter has an average of 34 runs in 5 matches. How many runs are needed in the next match to raise the average to 37? (a) 18 (b) 52 (c) 40 (d) 37
  13. 13.The average of 6 numbers is 32. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 12 (b) 32 (c) 62 (d) 42
  14. 14.The average of 6 numbers is 11. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 31 (b) 11 (c) 18 (d) 24
  15. 15.The average of 5 numbers is 41. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 41 (b) 78 (c) 20 (d) 57
  16. 16.A batter has an average of 40 runs in 3 matches. How many runs are needed in the next match to raise the average to 42? (a) 48 (b) 8 (c) 44 (d) 42
  17. 17.The average of 7 numbers is 14. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 14 (b) 29 (c) 8 (d) 9
  18. 18.What is the average of 24, 35, 23, 22 and 66? (a) 33 (b) 36 (c) 34 (d) 35
  19. 19.What is the average of 37, 45, 37 and 85? (a) 51 (b) 50 (c) 68 (d) 52
  20. 20.What is the average of 64, 46, 57 and 73? (a) 80 (b) 60 (c) 61 (d) 59
  21. 21.The average of 4 numbers is 38. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 38 (b) 35 (c) 36 (d) 77
  22. 22.What is the average of all the whole numbers from 15 to 31? (a) 24 (b) 16 (c) 8 (d) 23
  23. 23.What is the average of all the whole numbers from 49 to 85? (a) 18 (b) 36 (c) 67 (d) 68
  24. 24.The average of 8 numbers is 40. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 81 (b) 40 (c) 34 (d) 33
  25. 25.What is the average of 13, 16, 36, 13, 14 and 64? (a) 25 (b) 27 (c) 28 (d) 26
  26. 26.What is the average of all the whole numbers from 28 to 62? (a) 46 (b) 17 (c) 34 (d) 45
  27. 27.What is the average of all the whole numbers from 56 to 62? (a) 6 (b) 59 (c) 3 (d) 60
  28. 28.What is the average of 21, 10, 23, 10, 8 and 66? (a) 23 (b) 22 (c) 25 (d) 24
  29. 29.What is the average of 77, 93, 76, 68, 69 and 91? (a) 79 (b) 78 (c) 81 (d) 80
  30. 30.What is the average of all the whole numbers from 55 to 95? (a) 20 (b) 76 (c) 40 (d) 75
  31. 31.What is the average of all the whole numbers from 12 to 28? (a) 8 (b) 21 (c) 20 (d) 16
  32. 32.What is the average of 55, 50, 51, 64 and 85? (a) 61 (b) 63 (c) 62 (d) 60
  33. 33.The average of 6 numbers is 36. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 27 (b) 36 (c) 74 (d) 26
  34. 34.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 60? (a) 67 (b) 60 (c) 49 (d) 102
  35. 35.The average of 5 numbers is 38. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 38 (b) 27 (c) 79 (d) 26
  36. 36.The average of 4 numbers is 47. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 59 (b) 16 (c) 90 (d) 47
  37. 37.What is the average of 55, 43, 39, 41 and 72? (a) 49 (b) 51 (c) 52 (d) 50
  38. 38.What is the average of 38, 48, 60 and 54? (a) 51 (b) 50 (c) 49 (d) 52
  39. 39.What is the average of 43, 39, 37 and 41? (a) 39 (b) 41 (c) 40 (d) 42
  40. 40.What is the average of 57, 53, 67, 67 and 26? (a) 54 (b) 55 (c) 53 (d) 56

Answer key

  1. 25
  2. 69
  3. 44
  4. 41
  5. 58
  6. 28
  7. 105
  8. 44
  9. 34
  10. 58
  11. 15
  12. 52
  13. 42
  14. 31
  15. 57
  16. 48
  17. 8
  18. 34
  19. 51
  20. 60
  21. 35
  22. 23
  23. 67
  24. 33
  25. 26
  26. 45
  27. 59
  28. 23
  29. 79
  30. 75
  31. 20
  32. 61
  33. 26
  34. 102
  35. 26
  36. 59
  37. 50
  38. 50
  39. 40
  40. 54

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