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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 43 · 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 39, 29, 21 and 43? (a) 32 (b) 44 (c) 33 (d) 34
  2. 2.What is the average of all the whole numbers from 28 to 48? (a) 39 (b) 10 (c) 20 (d) 38
  3. 3.A batter has an average of 27 runs in 8 matches. How many runs are needed in the next match to raise the average to 35? (a) 35 (b) 99 (c) 72 (d) 43
  4. 4.A batter has an average of 46 runs in 4 matches. How many runs are needed in the next match to raise the average to 52? (a) 76 (b) 58 (c) 30 (d) 52
  5. 5.The average of 6 numbers is 50. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 41 (b) 102 (c) 40 (d) 50
  6. 6.The average of 4 numbers is 47. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 44 (b) 47 (c) 95 (d) 45
  7. 7.The average of 6 numbers is 11. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 11 (b) 2 (c) 1 (d) 24
  8. 8.A batter has an average of 40 runs in 5 matches. How many runs are needed in the next match to raise the average to 44? (a) 44 (b) 48 (c) 24 (d) 64
  9. 9.A batter has an average of 55 runs in 4 matches. How many runs are needed in the next match to raise the average to 59? (a) 59 (b) 63 (c) 20 (d) 75
  10. 10.The average of 6 numbers is 27. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 27 (b) 18 (c) 51 (d) 42
  11. 11.What is the average of 21, 45, 29 and 45? (a) 37 (b) 36 (c) 35 (d) 34
  12. 12.The average of 8 numbers is 16. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 27 (b) 51 (c) 40 (d) 16
  13. 13.The average of 7 numbers is 10. When one number is taken away, the average of the rest is 6. Which number was taken away? (a) 10 (b) 16 (c) 28 (d) 34
  14. 14.What is the average of 24, 45, 47 and 32? (a) 38 (b) 36 (c) 37 (d) 39
  15. 15.What is the average of all the whole numbers from 19 to 41? (a) 31 (b) 30 (c) 22 (d) 11
  16. 16.A batter has an average of 50 runs in 7 matches. How many runs are needed in the next match to raise the average to 54? (a) 32 (b) 58 (c) 54 (d) 82
  17. 17.The average of 7 numbers is 40. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 83 (b) 22 (c) 40 (d) 23
  18. 18.The average of 5 numbers is 15. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 15 (b) 4 (c) 3 (d) 33
  19. 19.The average of 4 numbers is 45. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 45 (b) 57 (c) 86 (d) 16
  20. 20.What is the average of 40, 46, 20, 31, 40 and 15? (a) 31 (b) 34 (c) 33 (d) 32
  21. 21.What is the average of all the whole numbers from 21 to 33? (a) 27 (b) 28 (c) 12 (d) 6
  22. 22.A batter has an average of 31 runs in 8 matches. How many runs are needed in the next match to raise the average to 37? (a) 37 (b) 43 (c) 54 (d) 85
  23. 23.What is the average of all the whole numbers from 50 to 74? (a) 12 (b) 63 (c) 24 (d) 62
  24. 24.What is the average of all the whole numbers from 32 to 66? (a) 17 (b) 49 (c) 34 (d) 50
  25. 25.The average of 4 numbers is 48. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 36 (b) 100 (c) 37 (d) 48
  26. 26.A batter has an average of 27 runs in 5 matches. How many runs are needed in the next match to raise the average to 35? (a) 43 (b) 35 (c) 48 (d) 75
  27. 27.A batter has an average of 20 runs in 5 matches. How many runs are needed in the next match to raise the average to 25? (a) 30 (b) 50 (c) 25 (d) 51
  28. 28.The average of 7 numbers is 37. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 8 (b) 37 (c) 79 (d) 7
  29. 29.What is the average of all the whole numbers from 44 to 72? (a) 59 (b) 28 (c) 58 (d) 14
  30. 30.What is the average of all the whole numbers from 41 to 61? (a) 10 (b) 52 (c) 51 (d) 20
  31. 31.What is the average of all the whole numbers from 38 to 52? (a) 7 (b) 46 (c) 14 (d) 45
  32. 32.What is the average of 81, 84, 91, 85, 69 and 64? (a) 80 (b) 78 (c) 79 (d) 81
  33. 33.What is the average of 81, 91, 91, 83 and 54? (a) 79 (b) 80 (c) 81 (d) 100
  34. 34.The average of 6 numbers is 32. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 27 (b) 65 (c) 32 (d) 28
  35. 35.What is the average of all the whole numbers from 47 to 65? (a) 9 (b) 56 (c) 18 (d) 57
  36. 36.What is the average of 67, 71, 80, 71, 68 and 45? (a) 66 (b) 68 (c) 69 (d) 67
  37. 37.What is the average of all the whole numbers from 60 to 78? (a) 9 (b) 69 (c) 70 (d) 18
  38. 38.What is the average of all the whole numbers from 20 to 26? (a) 23 (b) 6 (c) 3 (d) 24
  39. 39.What is the average of 56, 53, 59 and 96? (a) 67 (b) 88 (c) 65 (d) 66
  40. 40.What is the average of 49, 48, 69, 52 and 77? (a) 58 (b) 59 (c) 60 (d) 61

Answer key

  1. 33
  2. 38
  3. 99
  4. 76
  5. 40
  6. 44
  7. 1
  8. 64
  9. 75
  10. 42
  11. 35
  12. 51
  13. 34
  14. 37
  15. 30
  16. 82
  17. 22
  18. 3
  19. 57
  20. 32
  21. 27
  22. 85
  23. 62
  24. 49
  25. 36
  26. 75
  27. 50
  28. 7
  29. 58
  30. 51
  31. 45
  32. 79
  33. 80
  34. 27
  35. 56
  36. 67
  37. 69
  38. 23
  39. 66
  40. 59

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