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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 79 · 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.A batter has an average of 55 runs in 9 matches. How many runs are needed in the next match to raise the average to 57? (a) 57 (b) 20 (c) 59 (d) 75
  2. 2.The average of 6 numbers is 38. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 24 (b) 58 (c) 72 (d) 38
  3. 3.What is the average of all the whole numbers from 49 to 79? (a) 64 (b) 30 (c) 65 (d) 15
  4. 4.The average of 8 numbers is 26. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 26 (b) 54 (c) 13 (d) 12
  5. 5.The average of 4 numbers is 16. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 31 (b) 16 (c) 27 (d) 20
  6. 6.The average of 5 numbers is 44. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 41 (b) 89 (c) 40 (d) 44
  7. 7.A batter has an average of 50 runs in 7 matches. How many runs are needed in the next match to raise the average to 52? (a) 66 (b) 16 (c) 54 (d) 52
  8. 8.What is the average of 16, 28, 40, 18, 23 and 61? (a) 32 (b) 30 (c) 31 (d) 33
  9. 9.The average of 8 numbers is 16. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 37 (b) 24 (c) 29 (d) 16
  10. 10.What is the average of all the whole numbers from 38 to 54? (a) 46 (b) 16 (c) 8 (d) 47
  11. 11.What is the average of all the whole numbers from 26 to 62? (a) 36 (b) 44 (c) 45 (d) 18
  12. 12.What is the average of 40, 65, 65, 47 and 58? (a) 55 (b) 57 (c) 56 (d) 54
  13. 13.What is the average of all the whole numbers from 56 to 82? (a) 13 (b) 26 (c) 70 (d) 69
  14. 14.What is the average of 34, 33, 33 and 84? (a) 47 (b) 48 (c) 46 (d) 45
  15. 15.What is the average of 37, 16, 16, 22 and 59? (a) 32 (b) 30 (c) 29 (d) 31
  16. 16.What is the average of 77, 54, 60 and 61? (a) 84 (b) 62 (c) 63 (d) 64
  17. 17.What is the average of all the whole numbers from 48 to 54? (a) 3 (b) 52 (c) 6 (d) 51
  18. 18.What is the average of all the whole numbers from 37 to 51? (a) 14 (b) 7 (c) 45 (d) 44
  19. 19.The average of 4 numbers is 39. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 31 (b) 81 (c) 30 (d) 39
  20. 20.What is the average of all the whole numbers from 53 to 69? (a) 16 (b) 8 (c) 62 (d) 61
  21. 21.What is the average of all the whole numbers from 20 to 52? (a) 37 (b) 16 (c) 36 (d) 32
  22. 22.What is the average of 24, 25, 21, 48 and 52? (a) 36 (b) 34 (c) 33 (d) 35
  23. 23.What is the average of all the whole numbers from 55 to 89? (a) 34 (b) 72 (c) 17 (d) 73
  24. 24.What is the average of 80, 63, 65 and 80? (a) 73 (b) 96 (c) 72 (d) 71
  25. 25.The average of 6 numbers is 42. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 18 (b) 42 (c) 81 (d) 57
  26. 26.The average of 8 numbers is 27. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 27 (b) 51 (c) 48 (d) 24
  27. 27.What is the average of 43, 35, 35, 49 and 48? (a) 44 (b) 41 (c) 43 (d) 42
  28. 28.A batter has an average of 28 runs in 7 matches. How many runs are needed in the next match to raise the average to 31? (a) 31 (b) 34 (c) 52 (d) 24
  29. 29.What is the average of 34, 40, 44 and 42? (a) 39 (b) 41 (c) 40 (d) 42
  30. 30.What is the average of 72, 55, 59, 60 and 54? (a) 75 (b) 61 (c) 60 (d) 59
  31. 31.The average of 7 numbers is 37. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 73 (b) 43 (c) 7 (d) 37
  32. 32.The average of 8 numbers is 26. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 49 (b) 24 (c) 47 (d) 26
  33. 33.What is the average of 63, 42, 47 and 44? (a) 50 (b) 48 (c) 51 (d) 49
  34. 34.A batter has an average of 24 runs in 3 matches. How many runs are needed in the next match to raise the average to 31? (a) 28 (b) 38 (c) 52 (d) 31
  35. 35.The average of 6 numbers is 33. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 43 (b) 12 (c) 33 (d) 64
  36. 36.The average of 4 numbers is 33. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 67 (b) 33 (c) 31 (d) 30
  37. 37.What is the average of 47, 47, 49, 44, 47 and 54? (a) 49 (b) 47 (c) 50 (d) 48
  38. 38.What is the average of all the whole numbers from 17 to 31? (a) 7 (b) 24 (c) 14 (d) 25
  39. 39.What is the average of all the whole numbers from 41 to 77? (a) 59 (b) 60 (c) 18 (d) 36
  40. 40.A batter has an average of 20 runs in 4 matches. How many runs are needed in the next match to raise the average to 23? (a) 26 (b) 35 (c) 15 (d) 23

Answer key

  1. 75
  2. 58
  3. 64
  4. 12
  5. 31
  6. 40
  7. 66
  8. 31
  9. 37
  10. 46
  11. 44
  12. 55
  13. 69
  14. 46
  15. 30
  16. 63
  17. 51
  18. 44
  19. 30
  20. 61
  21. 36
  22. 34
  23. 72
  24. 72
  25. 57
  26. 48
  27. 42
  28. 52
  29. 40
  30. 60
  31. 43
  32. 47
  33. 49
  34. 52
  35. 43
  36. 30
  37. 48
  38. 24
  39. 59
  40. 35

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