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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 160 · 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 68, 52, 76 and 48? (a) 63 (b) 61 (c) 62 (d) 60
  2. 2.What is the average of all the whole numbers from 24 to 52? (a) 39 (b) 14 (c) 38 (d) 28
  3. 3.What is the average of 51, 51, 52, 54 and 112? (a) 64 (b) 63 (c) 65 (d) 80
  4. 4.What is the average of all the whole numbers from 10 to 28? (a) 18 (b) 19 (c) 9 (d) 20
  5. 5.What is the average of all the whole numbers from 58 to 86? (a) 72 (b) 28 (c) 73 (d) 14
  6. 6.What is the average of all the whole numbers from 9 to 27? (a) 19 (b) 17 (c) 9 (d) 18
  7. 7.The average of 8 numbers is 10. When one number is taken away, the average of the rest is 9. Which number was taken away? (a) 17 (b) 10 (c) 8 (d) 19
  8. 8.What is the average of 59, 55, 36, 61, 47 and 42? (a) 51 (b) 60 (c) 49 (d) 50
  9. 9.A batter has an average of 44 runs in 8 matches. How many runs are needed in the next match to raise the average to 51? (a) 51 (b) 63 (c) 58 (d) 107
  10. 10.A batter has an average of 44 runs in 9 matches. How many runs are needed in the next match to raise the average to 50? (a) 50 (b) 60 (c) 104 (d) 56
  11. 11.What is the average of 69, 68, 79 and 96? (a) 78 (b) 104 (c) 79 (d) 77
  12. 12.What is the average of all the whole numbers from 52 to 84? (a) 32 (b) 16 (c) 68 (d) 69
  13. 13.A batter has an average of 59 runs in 7 matches. How many runs are needed in the next match to raise the average to 64? (a) 69 (b) 99 (c) 64 (d) 40
  14. 14.A batter has an average of 38 runs in 9 matches. How many runs are needed in the next match to raise the average to 43? (a) 88 (b) 48 (c) 43 (d) 50
  15. 15.What is the average of all the whole numbers from 29 to 47? (a) 18 (b) 38 (c) 9 (d) 39
  16. 16.What is the average of 60, 69, 62, 59 and 100? (a) 71 (b) 69 (c) 72 (d) 70
  17. 17.What is the average of 14, 25, 31 and 26? (a) 32 (b) 24 (c) 25 (d) 23
  18. 18.What is the average of all the whole numbers from 6 to 16? (a) 5 (b) 11 (c) 12 (d) 10
  19. 19.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) 55 (b) 49 (c) 54 (d) 97
  20. 20.A batter has an average of 39 runs in 4 matches. How many runs are needed in the next match to raise the average to 42? (a) 15 (b) 45 (c) 54 (d) 42
  21. 21.What is the average of 44, 21, 46 and 13? (a) 30 (b) 33 (c) 32 (d) 31
  22. 22.What is the average of 63, 46, 58, 44 and 54? (a) 54 (b) 52 (c) 55 (d) 53
  23. 23.What is the average of all the whole numbers from 59 to 95? (a) 36 (b) 78 (c) 77 (d) 18
  24. 24.What is the average of 67, 93, 84, 77 and 69? (a) 77 (b) 80 (c) 79 (d) 78
  25. 25.What is the average of all the whole numbers from 41 to 73? (a) 16 (b) 58 (c) 57 (d) 32
  26. 26.The average of 5 numbers is 18. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 38 (b) 25 (c) 18 (d) 31
  27. 27.What is the average of 70, 78, 76, 84, 87 and 85? (a) 96 (b) 79 (c) 81 (d) 80
  28. 28.The average of 4 numbers is 21. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 4 (b) 21 (c) 41 (d) 24
  29. 29.What is the average of all the whole numbers from 5 to 15? (a) 10 (b) 9 (c) 11 (d) 5
  30. 30.What is the average of all the whole numbers from 19 to 31? (a) 25 (b) 12 (c) 26 (d) 6
  31. 31.What is the average of all the whole numbers from 15 to 43? (a) 28 (b) 14 (c) 30 (d) 29
  32. 32.The average of 6 numbers is 36. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 16 (b) 76 (c) 17 (d) 36
  33. 33.The average of 4 numbers is 11. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 23 (b) 11 (c) 8 (d) 9
  34. 34.A batter has an average of 21 runs in 3 matches. How many runs are needed in the next match to raise the average to 26? (a) 26 (b) 31 (c) 41 (d) 20
  35. 35.A batter has an average of 49 runs in 7 matches. How many runs are needed in the next match to raise the average to 51? (a) 65 (b) 51 (c) 53 (d) 16
  36. 36.What is the average of all the whole numbers from 13 to 31? (a) 23 (b) 18 (c) 9 (d) 22
  37. 37.What is the average of 32, 38, 14, 14 and 42? (a) 29 (b) 35 (c) 28 (d) 27
  38. 38.A batter has an average of 42 runs in 4 matches. How many runs are needed in the next match to raise the average to 50? (a) 50 (b) 40 (c) 58 (d) 82
  39. 39.The average of 8 numbers is 42. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 21 (b) 42 (c) 87 (d) 22
  40. 40.The average of 8 numbers is 49. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 8 (b) 56 (c) 49 (d) 97

Answer key

  1. 61
  2. 38
  3. 64
  4. 19
  5. 72
  6. 18
  7. 17
  8. 50
  9. 107
  10. 104
  11. 78
  12. 68
  13. 99
  14. 88
  15. 38
  16. 70
  17. 24
  18. 11
  19. 97
  20. 54
  21. 31
  22. 53
  23. 77
  24. 78
  25. 57
  26. 38
  27. 80
  28. 24
  29. 10
  30. 25
  31. 29
  32. 16
  33. 8
  34. 41
  35. 65
  36. 22
  37. 28
  38. 82
  39. 21
  40. 56

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