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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 601 · 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 41. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 78 (b) 65 (c) 41 (d) 28
  2. 2.A batter has an average of 35 runs in 9 matches. How many runs are needed in the next match to raise the average to 39? (a) 43 (b) 75 (c) 40 (d) 39
  3. 3.What is the average of 79, 65, 80, 54 and 47? (a) 66 (b) 65 (c) 64 (d) 67
  4. 4.What is the average of all the whole numbers from 41 to 65? (a) 12 (b) 54 (c) 24 (d) 53
  5. 5.What is the average of 48, 28, 32 and 28? (a) 34 (b) 36 (c) 33 (d) 35
  6. 6.What is the average of all the whole numbers from 7 to 17? (a) 13 (b) 10 (c) 12 (d) 5
  7. 7.A batter has an average of 24 runs in 6 matches. How many runs are needed in the next match to raise the average to 28? (a) 32 (b) 52 (c) 28 (d) 53
  8. 8.What is the average of 34, 29, 37, 28 and 77? (a) 41 (b) 40 (c) 42 (d) 43
  9. 9.The average of 4 numbers is 43. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 84 (b) 8 (c) 43 (d) 49
  10. 10.What is the average of 84, 68, 67, 86, 68 and 53? (a) 70 (b) 73 (c) 71 (d) 72
  11. 11.What is the average of 31, 25, 21, 39 and 64? (a) 45 (b) 37 (c) 35 (d) 36
  12. 12.What is the average of all the whole numbers from 23 to 35? (a) 6 (b) 29 (c) 12 (d) 30
  13. 13.What is the average of all the whole numbers from 50 to 84? (a) 67 (b) 68 (c) 17 (d) 34
  14. 14.The average of 6 numbers is 16. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 16 (b) 6 (c) 31 (d) 21
  15. 15.What is the average of all the whole numbers from 22 to 58? (a) 41 (b) 40 (c) 36 (d) 18
  16. 16.What is the average of 73, 55, 55 and 53? (a) 60 (b) 59 (c) 58 (d) 61
  17. 17.What is the average of 43, 61, 62, 61 and 33? (a) 51 (b) 52 (c) 65 (d) 53
  18. 18.The average of 6 numbers is 25. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 30 (b) 49 (c) 6 (d) 25
  19. 19.The average of 5 numbers is 19. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 40 (b) 11 (c) 12 (d) 19
  20. 20.The average of 7 numbers is 41. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 41 (b) 12 (c) 11 (d) 87
  21. 21.A batter has an average of 30 runs in 5 matches. How many runs are needed in the next match to raise the average to 37? (a) 37 (b) 42 (c) 44 (d) 72
  22. 22.The average of 7 numbers is 31. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 21 (b) 31 (c) 49 (d) 59
  23. 23.What is the average of all the whole numbers from 36 to 44? (a) 40 (b) 4 (c) 41 (d) 8
  24. 24.The average of 6 numbers is 39. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 39 (b) 18 (c) 75 (d) 54
  25. 25.The average of 6 numbers is 48. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 95 (b) 6 (c) 48 (d) 53
  26. 26.A batter has an average of 32 runs in 3 matches. How many runs are needed in the next match to raise the average to 37? (a) 37 (b) 42 (c) 20 (d) 52
  27. 27.The average of 4 numbers is 18. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 38 (b) 13 (c) 18 (d) 12
  28. 28.The average of 5 numbers is 42. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 22 (b) 89 (c) 23 (d) 42
  29. 29.What is the average of 81, 66, 89, 69 and 70? (a) 77 (b) 74 (c) 76 (d) 75
  30. 30.What is the average of all the whole numbers from 29 to 43? (a) 36 (b) 37 (c) 14 (d) 7
  31. 31.The average of 4 numbers is 20. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 39 (b) 4 (c) 23 (d) 20
  32. 32.What is the average of 56, 70, 70 and 24? (a) 57 (b) 55 (c) 54 (d) 56
  33. 33.What is the average of 36, 44, 47, 43, 38 and 92? (a) 50 (b) 60 (c) 49 (d) 51
  34. 34.What is the average of 51, 67, 51, 49, 70 and 60? (a) 58 (b) 57 (c) 59 (d) 60
  35. 35.What is the average of all the whole numbers from 23 to 37? (a) 30 (b) 7 (c) 31 (d) 14
  36. 36.What is the average of all the whole numbers from 6 to 44? (a) 38 (b) 26 (c) 25 (d) 19
  37. 37.What is the average of 61, 67, 62, 80, 64 and 116? (a) 74 (b) 76 (c) 90 (d) 75
  38. 38.The average of 5 numbers is 45. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 34 (b) 45 (c) 93 (d) 33
  39. 39.The average of 7 numbers is 15. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 15 (b) 9 (c) 10 (d) 31
  40. 40.What is the average of all the whole numbers from 45 to 65? (a) 10 (b) 55 (c) 20 (d) 56

Answer key

  1. 65
  2. 75
  3. 65
  4. 53
  5. 34
  6. 12
  7. 52
  8. 41
  9. 49
  10. 71
  11. 36
  12. 29
  13. 67
  14. 21
  15. 40
  16. 59
  17. 52
  18. 30
  19. 11
  20. 11
  21. 72
  22. 49
  23. 40
  24. 54
  25. 53
  26. 52
  27. 12
  28. 22
  29. 75
  30. 36
  31. 23
  32. 55
  33. 50
  34. 58
  35. 30
  36. 25
  37. 75
  38. 33
  39. 9
  40. 55

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