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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 269 · 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 74, 68, 63 and 31? (a) 59 (b) 61 (c) 58 (d) 60
  2. 2.What is the average of all the whole numbers from 55 to 81? (a) 26 (b) 13 (c) 69 (d) 68
  3. 3.What is the average of all the whole numbers from 15 to 51? (a) 18 (b) 33 (c) 36 (d) 34
  4. 4.What is the average of all the whole numbers from 24 to 64? (a) 40 (b) 44 (c) 20 (d) 45
  5. 5.What is the average of 15, 19, 21, 7 and 48? (a) 22 (b) 24 (c) 23 (d) 21
  6. 6.The average of 7 numbers is 39. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 35 (b) 69 (c) 39 (d) 73
  7. 7.What is the average of all the whole numbers from 39 to 73? (a) 56 (b) 57 (c) 34 (d) 17
  8. 8.The average of 6 numbers is 28. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 57 (b) 24 (c) 28 (d) 23
  9. 9.What is the average of 22, 23, 43 and 60? (a) 36 (b) 38 (c) 37 (d) 39
  10. 10.What is the average of 38, 44, 46, 43 and 54? (a) 45 (b) 46 (c) 44 (d) 47
  11. 11.What is the average of 60, 77, 56, 49, 50 and 80? (a) 63 (b) 64 (c) 61 (d) 62
  12. 12.The average of 8 numbers is 39. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 53 (b) 39 (c) 16 (d) 76
  13. 13.The average of 8 numbers is 18. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 18 (b) 5 (c) 4 (d) 38
  14. 14.A batter has an average of 35 runs in 4 matches. How many runs are needed in the next match to raise the average to 42? (a) 35 (b) 70 (c) 49 (d) 42
  15. 15.What is the average of all the whole numbers from 14 to 20? (a) 18 (b) 6 (c) 17 (d) 3
  16. 16.A batter has an average of 58 runs in 7 matches. How many runs are needed in the next match to raise the average to 64? (a) 64 (b) 48 (c) 70 (d) 106
  17. 17.The average of 5 numbers is 15. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 31 (b) 26 (c) 15 (d) 20
  18. 18.The average of 5 numbers is 34. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 34 (b) 38 (c) 5 (d) 67
  19. 19.A batter has an average of 58 runs in 3 matches. How many runs are needed in the next match to raise the average to 60? (a) 62 (b) 60 (c) 8 (d) 66
  20. 20.A batter has an average of 27 runs in 9 matches. How many runs are needed in the next match to raise the average to 35? (a) 80 (b) 35 (c) 107 (d) 43
  21. 21.What is the average of 70, 71, 63, 83 and 93? (a) 75 (b) 77 (c) 95 (d) 76
  22. 22.The average of 7 numbers is 10. When one number is taken away, the average of the rest is 9. Which number was taken away? (a) 10 (b) 7 (c) 16 (d) 19
  23. 23.What is the average of 51, 40, 42, 45 and 57? (a) 46 (b) 47 (c) 48 (d) 49
  24. 24.The average of 5 numbers is 17. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 30 (b) 33 (c) 20 (d) 17
  25. 25.A batter has an average of 43 runs in 8 matches. How many runs are needed in the next match to raise the average to 49? (a) 54 (b) 49 (c) 55 (d) 97
  26. 26.What is the average of 46, 68, 45, 68 and 38? (a) 55 (b) 54 (c) 52 (d) 53
  27. 27.What is the average of all the whole numbers from 28 to 68? (a) 49 (b) 40 (c) 20 (d) 48
  28. 28.What is the average of 24, 42, 17 and 33? (a) 30 (b) 28 (c) 29 (d) 31
  29. 29.What is the average of all the whole numbers from 46 to 74? (a) 28 (b) 60 (c) 14 (d) 61
  30. 30.What is the average of all the whole numbers from 5 to 31? (a) 19 (b) 18 (c) 13 (d) 26
  31. 31.What is the average of 53, 28, 53, 30, 41 and 29? (a) 38 (b) 41 (c) 40 (d) 39
  32. 32.What is the average of 83, 67, 88, 81, 89 and 60? (a) 79 (b) 77 (c) 80 (d) 78
  33. 33.The average of 4 numbers is 41. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 32 (b) 41 (c) 85 (d) 33
  34. 34.What is the average of all the whole numbers from 50 to 64? (a) 14 (b) 7 (c) 58 (d) 57
  35. 35.What is the average of 55, 71, 83, 57, 63 and 79? (a) 69 (b) 68 (c) 67 (d) 70
  36. 36.The average of 8 numbers is 40. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 40 (b) 8 (c) 47 (d) 79
  37. 37.The average of 5 numbers is 23. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 47 (b) 20 (c) 19 (d) 23
  38. 38.What is the average of 29, 28, 39, 16 and 43? (a) 31 (b) 32 (c) 33 (d) 30
  39. 39.The average of 5 numbers is 10. When one number is taken away, the average of the rest is 5. Which number was taken away? (a) 25 (b) 30 (c) 15 (d) 10
  40. 40.What is the average of 89, 74, 76, 73, 71 and 67? (a) 74 (b) 75 (c) 76 (d) 90

Answer key

  1. 59
  2. 68
  3. 33
  4. 44
  5. 22
  6. 69
  7. 56
  8. 23
  9. 37
  10. 45
  11. 62
  12. 53
  13. 4
  14. 70
  15. 17
  16. 106
  17. 31
  18. 38
  19. 66
  20. 107
  21. 76
  22. 16
  23. 47
  24. 33
  25. 97
  26. 53
  27. 48
  28. 29
  29. 60
  30. 18
  31. 39
  32. 78
  33. 32
  34. 57
  35. 68
  36. 47
  37. 19
  38. 31
  39. 30
  40. 75

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