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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 590 · 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 45 to 73? (a) 59 (b) 60 (c) 28 (d) 14
  2. 2.The average of 8 numbers is 48. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 24 (b) 93 (c) 48 (d) 69
  3. 3.The average of 8 numbers is 20. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 36 (b) 20 (c) 48 (d) 32
  4. 4.The average of 6 numbers is 17. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 27 (b) 12 (c) 32 (d) 17
  5. 5.What is the average of 47, 22, 26 and 33? (a) 32 (b) 33 (c) 31 (d) 34
  6. 6.What is the average of 71, 60, 76 and 61? (a) 69 (b) 68 (c) 66 (d) 67
  7. 7.What is the average of 58, 47, 59 and 40? (a) 50 (b) 68 (c) 52 (d) 51
  8. 8.What is the average of all the whole numbers from 49 to 75? (a) 62 (b) 26 (c) 13 (d) 63
  9. 9.What is the average of all the whole numbers from 8 to 16? (a) 12 (b) 4 (c) 13 (d) 8
  10. 10.A batter has an average of 57 runs in 8 matches. How many runs are needed in the next match to raise the average to 62? (a) 67 (b) 45 (c) 102 (d) 62
  11. 11.What is the average of 37, 40, 50, 64, 43 and 72? (a) 50 (b) 51 (c) 52 (d) 53
  12. 12.What is the average of all the whole numbers from 11 to 47? (a) 18 (b) 29 (c) 36 (d) 30
  13. 13.What is the average of all the whole numbers from 14 to 28? (a) 14 (b) 7 (c) 21 (d) 22
  14. 14.The average of 4 numbers is 48. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 97 (b) 48 (c) 46 (d) 45
  15. 15.A batter has an average of 52 runs in 3 matches. How many runs are needed in the next match to raise the average to 60? (a) 32 (b) 68 (c) 60 (d) 84
  16. 16.What is the average of 90, 91, 80, 69, 73 and 59? (a) 78 (b) 79 (c) 77 (d) 76
  17. 17.A batter has an average of 37 runs in 4 matches. How many runs are needed in the next match to raise the average to 44? (a) 35 (b) 72 (c) 51 (d) 44
  18. 18.What is the average of 35, 21, 17 and 35? (a) 27 (b) 26 (c) 28 (d) 36
  19. 19.What is the average of all the whole numbers from 11 to 39? (a) 14 (b) 25 (c) 28 (d) 26
  20. 20.What is the average of 65, 47, 59 and 37? (a) 51 (b) 54 (c) 53 (d) 52
  21. 21.What is the average of all the whole numbers from 51 to 89? (a) 38 (b) 71 (c) 70 (d) 19
  22. 22.What is the average of 37, 33, 50, 30 and 45? (a) 39 (b) 38 (c) 41 (d) 40
  23. 23.What is the average of 37, 23, 30 and 18? (a) 27 (b) 36 (c) 26 (d) 28
  24. 24.The average of 5 numbers is 28. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 53 (b) 15 (c) 28 (d) 40
  25. 25.What is the average of 30, 33, 36 and 17? (a) 30 (b) 31 (c) 28 (d) 29
  26. 26.A batter has an average of 28 runs in 4 matches. How many runs are needed in the next match to raise the average to 33? (a) 25 (b) 33 (c) 53 (d) 38
  27. 27.The average of 4 numbers is 45. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 4 (b) 45 (c) 89 (d) 48
  28. 28.The average of 8 numbers is 41. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 41 (b) 62 (c) 24 (d) 79
  29. 29.What is the average of 54, 61, 44 and 61? (a) 57 (b) 54 (c) 55 (d) 56
  30. 30.A batter has an average of 49 runs in 8 matches. How many runs are needed in the next match to raise the average to 55? (a) 61 (b) 54 (c) 55 (d) 103
  31. 31.What is the average of 67, 48, 60, 75, 52 and 64? (a) 63 (b) 60 (c) 62 (d) 61
  32. 32.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 42? (a) 56 (b) 50 (c) 90 (d) 42
  33. 33.What is the average of 34, 34, 17, 32 and 18? (a) 29 (b) 27 (c) 26 (d) 28
  34. 34.A batter has an average of 60 runs in 3 matches. How many runs are needed in the next match to raise the average to 65? (a) 70 (b) 65 (c) 80 (d) 20
  35. 35.What is the average of 79, 81, 62, 59, 78 and 49? (a) 67 (b) 68 (c) 70 (d) 69
  36. 36.The average of 8 numbers is 13. When one number is taken away, the average of the rest is 9. Which number was taken away? (a) 13 (b) 22 (c) 32 (d) 41
  37. 37.A batter has an average of 47 runs in 3 matches. How many runs are needed in the next match to raise the average to 50? (a) 59 (b) 53 (c) 50 (d) 12
  38. 38.A batter has an average of 45 runs in 7 matches. How many runs are needed in the next match to raise the average to 47? (a) 47 (b) 16 (c) 61 (d) 49
  39. 39.What is the average of all the whole numbers from 50 to 82? (a) 16 (b) 66 (c) 67 (d) 32
  40. 40.The average of 8 numbers is 18. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 37 (b) 11 (c) 12 (d) 18

Answer key

  1. 59
  2. 69
  3. 48
  4. 27
  5. 32
  6. 67
  7. 51
  8. 62
  9. 12
  10. 102
  11. 51
  12. 29
  13. 21
  14. 45
  15. 84
  16. 77
  17. 72
  18. 27
  19. 25
  20. 52
  21. 70
  22. 39
  23. 27
  24. 40
  25. 29
  26. 53
  27. 48
  28. 62
  29. 55
  30. 103
  31. 61
  32. 90
  33. 27
  34. 80
  35. 68
  36. 41
  37. 59
  38. 61
  39. 66
  40. 11

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