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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 907 · 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 8 numbers is 18. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 18 (b) 32 (c) 34 (d) 16
  2. 2.A batter has an average of 23 runs in 7 matches. How many runs are needed in the next match to raise the average to 29? (a) 48 (b) 29 (c) 35 (d) 71
  3. 3.What is the average of all the whole numbers from 6 to 12? (a) 6 (b) 10 (c) 9 (d) 3
  4. 4.The average of 4 numbers is 31. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 31 (b) 58 (c) 16 (d) 43
  5. 5.The average of 5 numbers is 25. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 17 (b) 52 (c) 18 (d) 25
  6. 6.The average of 4 numbers is 16. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 16 (b) 29 (c) 27 (d) 28
  7. 7.What is the average of 49, 72, 46, 55, 50 and 70? (a) 56 (b) 58 (c) 59 (d) 57
  8. 8.What is the average of all the whole numbers from 7 to 15? (a) 4 (b) 11 (c) 12 (d) 8
  9. 9.A batter has an average of 38 runs in 4 matches. How many runs are needed in the next match to raise the average to 42? (a) 42 (b) 58 (c) 20 (d) 46
  10. 10.A batter has an average of 24 runs in 8 matches. How many runs are needed in the next match to raise the average to 32? (a) 32 (b) 96 (c) 40 (d) 72
  11. 11.What is the average of 40, 20, 18 and 38? (a) 29 (b) 30 (c) 28 (d) 31
  12. 12.What is the average of all the whole numbers from 41 to 65? (a) 54 (b) 12 (c) 53 (d) 24
  13. 13.What is the average of all the whole numbers from 6 to 46? (a) 26 (b) 40 (c) 27 (d) 20
  14. 14.A batter has an average of 58 runs in 9 matches. How many runs are needed in the next match to raise the average to 60? (a) 62 (b) 20 (c) 60 (d) 78
  15. 15.The average of 8 numbers is 43. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 43 (b) 16 (c) 90 (d) 15
  16. 16.What is the average of 37, 40, 37 and 86? (a) 52 (b) 50 (c) 51 (d) 49
  17. 17.A batter has an average of 53 runs in 4 matches. How many runs are needed in the next match to raise the average to 61? (a) 93 (b) 69 (c) 61 (d) 40
  18. 18.What is the average of 58, 51, 33 and 50? (a) 49 (b) 47 (c) 48 (d) 64
  19. 19.What is the average of 28, 32, 42, 50, 39 and 61? (a) 41 (b) 44 (c) 43 (d) 42
  20. 20.What is the average of all the whole numbers from 37 to 59? (a) 22 (b) 11 (c) 49 (d) 48
  21. 21.What is the average of all the whole numbers from 23 to 51? (a) 38 (b) 37 (c) 14 (d) 28
  22. 22.A batter has an average of 46 runs in 6 matches. How many runs are needed in the next match to raise the average to 53? (a) 53 (b) 60 (c) 95 (d) 49
  23. 23.What is the average of 49, 61, 49 and 33? (a) 49 (b) 48 (c) 47 (d) 64
  24. 24.What is the average of all the whole numbers from 42 to 78? (a) 61 (b) 18 (c) 36 (d) 60
  25. 25.The average of 4 numbers is 19. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 39 (b) 16 (c) 19 (d) 17
  26. 26.What is the average of 32, 34, 41 and 53? (a) 41 (b) 40 (c) 42 (d) 39
  27. 27.What is the average of all the whole numbers from 26 to 50? (a) 12 (b) 38 (c) 24 (d) 39
  28. 28.The average of 8 numbers is 45. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 45 (b) 24 (c) 87 (d) 66
  29. 29.What is the average of all the whole numbers from 28 to 66? (a) 38 (b) 48 (c) 47 (d) 19
  30. 30.A batter has an average of 54 runs in 8 matches. How many runs are needed in the next match to raise the average to 57? (a) 81 (b) 57 (c) 60 (d) 27
  31. 31.What is the average of 47, 45, 57, 41, 64 and 58? (a) 54 (b) 51 (c) 52 (d) 53
  32. 32.What is the average of 51, 33, 26, 40 and 35? (a) 36 (b) 38 (c) 37 (d) 39
  33. 33.What is the average of 78, 68, 81 and 69? (a) 73 (b) 75 (c) 76 (d) 74
  34. 34.What is the average of 49, 27, 46, 22 and 41? (a) 38 (b) 37 (c) 36 (d) 39
  35. 35.What is the average of 47, 75, 70, 55, 74 and 45? (a) 60 (b) 63 (c) 62 (d) 61
  36. 36.What is the average of all the whole numbers from 25 to 41? (a) 16 (b) 33 (c) 8 (d) 34
  37. 37.What is the average of all the whole numbers from 40 to 64? (a) 53 (b) 52 (c) 24 (d) 12
  38. 38.What is the average of all the whole numbers from 54 to 76? (a) 22 (b) 66 (c) 65 (d) 11
  39. 39.The average of 7 numbers is 23. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 23 (b) 41 (c) 43 (d) 21
  40. 40.What is the average of all the whole numbers from 54 to 84? (a) 30 (b) 69 (c) 15 (d) 70

Answer key

  1. 32
  2. 71
  3. 9
  4. 43
  5. 17
  6. 28
  7. 57
  8. 11
  9. 58
  10. 96
  11. 29
  12. 53
  13. 26
  14. 78
  15. 15
  16. 50
  17. 93
  18. 48
  19. 42
  20. 48
  21. 37
  22. 95
  23. 48
  24. 60
  25. 16
  26. 40
  27. 38
  28. 66
  29. 47
  30. 81
  31. 52
  32. 37
  33. 74
  34. 37
  35. 61
  36. 33
  37. 52
  38. 65
  39. 41
  40. 69

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