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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 212 · 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 8 numbers is 39. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 39 (b) 5 (c) 4 (d) 83
  2. 2.A batter has an average of 40 runs in 4 matches. How many runs are needed in the next match to raise the average to 47? (a) 47 (b) 75 (c) 35 (d) 54
  3. 3.What is the average of 14, 36, 9, 34 and 22? (a) 22 (b) 25 (c) 24 (d) 23
  4. 4.What is the average of all the whole numbers from 36 to 62? (a) 13 (b) 26 (c) 49 (d) 50
  5. 5.The average of 8 numbers is 50. When one number is taken away, the average of the rest is 55. Which number was taken away? (a) 105 (b) 15 (c) 16 (d) 50
  6. 6.A batter has an average of 59 runs in 8 matches. How many runs are needed in the next match to raise the average to 66? (a) 66 (b) 63 (c) 73 (d) 122
  7. 7.The average of 6 numbers is 17. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 3 (b) 37 (c) 17 (d) 2
  8. 8.What is the average of 71, 83, 73 and 49? (a) 92 (b) 68 (c) 69 (d) 70
  9. 9.A batter has an average of 23 runs in 6 matches. How many runs are needed in the next match to raise the average to 28? (a) 35 (b) 58 (c) 28 (d) 33
  10. 10.A batter has an average of 59 runs in 4 matches. How many runs are needed in the next match to raise the average to 61? (a) 10 (b) 63 (c) 69 (d) 61
  11. 11.What is the average of 52, 59, 49, 39, 58 and 13? (a) 54 (b) 45 (c) 44 (d) 46
  12. 12.What is the average of all the whole numbers from 20 to 32? (a) 27 (b) 12 (c) 6 (d) 26
  13. 13.A batter has an average of 44 runs in 6 matches. How many runs are needed in the next match to raise the average to 50? (a) 50 (b) 56 (c) 42 (d) 86
  14. 14.The average of 8 numbers is 39. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 24 (b) 39 (c) 75 (d) 60
  15. 15.The average of 6 numbers is 24. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 18 (b) 24 (c) 39 (d) 45
  16. 16.What is the average of all the whole numbers from 18 to 54? (a) 35 (b) 36 (c) 37 (d) 18
  17. 17.What is the average of 31, 14, 27, 12 and 31? (a) 22 (b) 24 (c) 25 (d) 23
  18. 18.A batter has an average of 51 runs in 5 matches. How many runs are needed in the next match to raise the average to 58? (a) 65 (b) 42 (c) 58 (d) 93
  19. 19.What is the average of all the whole numbers from 10 to 16? (a) 13 (b) 14 (c) 3 (d) 6
  20. 20.A batter has an average of 23 runs in 9 matches. How many runs are needed in the next match to raise the average to 26? (a) 29 (b) 30 (c) 26 (d) 53
  21. 21.The average of 4 numbers is 26. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 23 (b) 26 (c) 53 (d) 24
  22. 22.What is the average of all the whole numbers from 5 to 23? (a) 18 (b) 14 (c) 15 (d) 9
  23. 23.What is the average of all the whole numbers from 46 to 62? (a) 16 (b) 8 (c) 55 (d) 54
  24. 24.What is the average of all the whole numbers from 33 to 69? (a) 36 (b) 52 (c) 18 (d) 51
  25. 25.What is the average of 72, 71, 80, 57, 72 and 68? (a) 70 (b) 84 (c) 69 (d) 71
  26. 26.The average of 5 numbers is 48. When one number is taken away, the average of the rest is 53. Which number was taken away? (a) 28 (b) 29 (c) 48 (d) 101
  27. 27.What is the average of all the whole numbers from 39 to 47? (a) 4 (b) 8 (c) 43 (d) 44
  28. 28.What is the average of 27, 22, 41 and 58? (a) 38 (b) 36 (c) 37 (d) 39
  29. 29.What is the average of all the whole numbers from 34 to 50? (a) 43 (b) 8 (c) 42 (d) 16
  30. 30.What is the average of 91, 80, 88, 83, 72 and 66? (a) 96 (b) 79 (c) 81 (d) 80
  31. 31.A batter has an average of 34 runs in 8 matches. How many runs are needed in the next match to raise the average to 38? (a) 70 (b) 36 (c) 42 (d) 38
  32. 32.The average of 7 numbers is 32. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 32 (b) 38 (c) 63 (d) 7
  33. 33.A batter has an average of 60 runs in 4 matches. How many runs are needed in the next match to raise the average to 65? (a) 70 (b) 65 (c) 25 (d) 85
  34. 34.The average of 5 numbers is 42. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 20 (b) 80 (c) 42 (d) 58
  35. 35.What is the average of 51, 71, 56, 65 and 77? (a) 63 (b) 80 (c) 64 (d) 65
  36. 36.The average of 6 numbers is 35. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 65 (b) 60 (c) 30 (d) 35
  37. 37.The average of 8 numbers is 17. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 31 (b) 38 (c) 24 (d) 17
  38. 38.What is the average of all the whole numbers from 36 to 46? (a) 5 (b) 10 (c) 42 (d) 41
  39. 39.The average of 7 numbers is 13. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 31 (b) 23 (c) 21 (d) 13
  40. 40.What is the average of 58, 56, 37 and 21? (a) 43 (b) 44 (c) 45 (d) 42

Answer key

  1. 4
  2. 75
  3. 23
  4. 49
  5. 15
  6. 122
  7. 2
  8. 69
  9. 58
  10. 69
  11. 45
  12. 26
  13. 86
  14. 60
  15. 39
  16. 36
  17. 23
  18. 93
  19. 13
  20. 53
  21. 23
  22. 14
  23. 54
  24. 51
  25. 70
  26. 28
  27. 43
  28. 37
  29. 42
  30. 80
  31. 70
  32. 38
  33. 85
  34. 58
  35. 64
  36. 60
  37. 38
  38. 41
  39. 31
  40. 43

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