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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 185 · 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 41 runs in 6 matches. How many runs are needed in the next match to raise the average to 47? (a) 42 (b) 83 (c) 53 (d) 47
  2. 2.The average of 7 numbers is 17. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 41 (b) 30 (c) 17 (d) 28
  3. 3.What is the average of 45, 39, 59, 51 and 31? (a) 44 (b) 47 (c) 46 (d) 45
  4. 4.What is the average of 27, 22, 21, 40, 40 and 48? (a) 35 (b) 32 (c) 33 (d) 34
  5. 5.A batter has an average of 29 runs in 3 matches. How many runs are needed in the next match to raise the average to 32? (a) 12 (b) 32 (c) 35 (d) 41
  6. 6.A batter has an average of 48 runs in 8 matches. How many runs are needed in the next match to raise the average to 50? (a) 52 (b) 50 (c) 66 (d) 18
  7. 7.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) 87 (c) 42 (d) 22
  8. 8.The average of 7 numbers is 48. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 48 (b) 7 (c) 95 (d) 54
  9. 9.The average of 6 numbers is 42. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 37 (b) 42 (c) 85 (d) 38
  10. 10.The average of 7 numbers is 30. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 30 (b) 58 (c) 14 (d) 42
  11. 11.What is the average of 84, 93, 71, 91 and 51? (a) 79 (b) 78 (c) 77 (d) 80
  12. 12.The average of 5 numbers is 21. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 21 (b) 37 (c) 38 (d) 20
  13. 13.What is the average of all the whole numbers from 22 to 56? (a) 34 (b) 39 (c) 17 (d) 40
  14. 14.What is the average of 53, 54, 45 and 72? (a) 55 (b) 58 (c) 56 (d) 57
  15. 15.The average of 8 numbers is 38. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 38 (b) 32 (c) 31 (d) 77
  16. 16.What is the average of 44, 46, 34, 56 and 45? (a) 46 (b) 47 (c) 44 (d) 45
  17. 17.The average of 8 numbers is 47. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 20 (b) 47 (c) 19 (d) 98
  18. 18.What is the average of all the whole numbers from 50 to 56? (a) 53 (b) 3 (c) 54 (d) 6
  19. 19.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) 17 (b) 33 (c) 30 (d) 20
  20. 20.The average of 5 numbers is 28. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 28 (b) 12 (c) 13 (d) 60
  21. 21.What is the average of 54, 58, 74 and 70? (a) 66 (b) 63 (c) 64 (d) 65
  22. 22.The average of 8 numbers is 39. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 46 (b) 8 (c) 39 (d) 77
  23. 23.What is the average of 75, 62, 64, 89, 75 and 85? (a) 74 (b) 76 (c) 75 (d) 90
  24. 24.What is the average of 22, 22, 37 and 23? (a) 26 (b) 25 (c) 27 (d) 28
  25. 25.What is the average of 16, 14, 37, 15 and 58? (a) 27 (b) 29 (c) 28 (d) 35
  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) 25 (b) 38 (c) 31 (d) 18
  27. 27.The average of 6 numbers is 28. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 28 (b) 19 (c) 18 (d) 58
  28. 28.What is the average of 28, 39, 19, 33, 38 and 11? (a) 27 (b) 28 (c) 30 (d) 29
  29. 29.What is the average of 52, 34, 61, 49 and 34? (a) 47 (b) 48 (c) 46 (d) 45
  30. 30.A batter has an average of 46 runs in 5 matches. How many runs are needed in the next match to raise the average to 51? (a) 30 (b) 56 (c) 76 (d) 51
  31. 31.A batter has an average of 52 runs in 7 matches. How many runs are needed in the next match to raise the average to 58? (a) 64 (b) 100 (c) 48 (d) 58
  32. 32.A batter has an average of 60 runs in 6 matches. How many runs are needed in the next match to raise the average to 63? (a) 63 (b) 66 (c) 81 (d) 21
  33. 33.What is the average of all the whole numbers from 14 to 32? (a) 18 (b) 9 (c) 23 (d) 24
  34. 34.The average of 7 numbers is 46. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 94 (b) 35 (c) 34 (d) 46
  35. 35.What is the average of all the whole numbers from 24 to 48? (a) 36 (b) 24 (c) 12 (d) 37
  36. 36.What is the average of 71, 59, 58 and 100? (a) 72 (b) 71 (c) 96 (d) 73
  37. 37.What is the average of 12, 21, 6 and 41? (a) 22 (b) 20 (c) 21 (d) 19
  38. 38.What is the average of 20, 32, 15 and 49? (a) 31 (b) 28 (c) 29 (d) 30
  39. 39.The average of 8 numbers is 47. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 8 (b) 93 (c) 47 (d) 54
  40. 40.What is the average of 40, 29, 23 and 40? (a) 33 (b) 34 (c) 44 (d) 32

Answer key

  1. 83
  2. 41
  3. 45
  4. 33
  5. 41
  6. 66
  7. 21
  8. 54
  9. 37
  10. 42
  11. 78
  12. 37
  13. 39
  14. 56
  15. 31
  16. 45
  17. 19
  18. 53
  19. 33
  20. 12
  21. 64
  22. 46
  23. 75
  24. 26
  25. 28
  26. 38
  27. 18
  28. 28
  29. 46
  30. 76
  31. 100
  32. 81
  33. 23
  34. 34
  35. 36
  36. 72
  37. 20
  38. 29
  39. 54
  40. 33

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