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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 226 · 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 59 runs in 3 matches. How many runs are needed in the next match to raise the average to 61? (a) 63 (b) 61 (c) 8 (d) 67
  2. 2.The average of 6 numbers is 13. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 13 (b) 6 (c) 25 (d) 18
  3. 3.The average of 6 numbers is 31. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 31 (b) 51 (c) 58 (d) 24
  4. 4.A batter has an average of 29 runs in 4 matches. How many runs are needed in the next match to raise the average to 31? (a) 10 (b) 31 (c) 33 (d) 39
  5. 5.The average of 8 numbers is 43. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 43 (b) 89 (c) 23 (d) 22
  6. 6.The average of 8 numbers is 21. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 8 (b) 21 (c) 44 (d) 7
  7. 7.What is the average of 66, 50, 51, 59, 44 and 60? (a) 54 (b) 66 (c) 56 (d) 55
  8. 8.What is the average of 63, 65, 66, 74 and 117? (a) 78 (b) 79 (c) 76 (d) 77
  9. 9.The average of 8 numbers is 46. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 46 (b) 81 (c) 40 (d) 87
  10. 10.The average of 7 numbers is 25. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 25 (b) 20 (c) 19 (d) 51
  11. 11.The average of 5 numbers is 33. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 69 (b) 33 (c) 22 (d) 21
  12. 12.The average of 5 numbers is 23. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 43 (b) 23 (c) 41 (d) 25
  13. 13.The average of 8 numbers is 23. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 9 (b) 23 (c) 48 (d) 10
  14. 14.What is the average of all the whole numbers from 20 to 48? (a) 34 (b) 28 (c) 35 (d) 14
  15. 15.What is the average of 32, 47, 29, 24 and 38? (a) 33 (b) 34 (c) 35 (d) 36
  16. 16.The average of 6 numbers is 50. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 97 (b) 18 (c) 65 (d) 50
  17. 17.What is the average of 18, 42, 37 and 11? (a) 26 (b) 27 (c) 28 (d) 36
  18. 18.What is the average of 14, 21, 28, 28, 24 and 59? (a) 28 (b) 29 (c) 30 (d) 31
  19. 19.The average of 5 numbers is 36. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 20 (b) 76 (c) 36 (d) 21
  20. 20.What is the average of 50, 57, 52, 63, 55 and 71? (a) 60 (b) 57 (c) 59 (d) 58
  21. 21.What is the average of all the whole numbers from 16 to 34? (a) 18 (b) 9 (c) 25 (d) 26
  22. 22.What is the average of all the whole numbers from 18 to 42? (a) 12 (b) 24 (c) 31 (d) 30
  23. 23.What is the average of all the whole numbers from 57 to 81? (a) 70 (b) 69 (c) 24 (d) 12
  24. 24.The average of 8 numbers is 34. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 8 (b) 67 (c) 41 (d) 34
  25. 25.The average of 7 numbers is 50. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 99 (b) 7 (c) 56 (d) 50
  26. 26.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) 14 (b) 30 (c) 58 (d) 42
  27. 27.What is the average of all the whole numbers from 19 to 39? (a) 20 (b) 10 (c) 29 (d) 30
  28. 28.The average of 4 numbers is 17. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 36 (b) 17 (c) 12 (d) 11
  29. 29.What is the average of all the whole numbers from 13 to 31? (a) 23 (b) 18 (c) 9 (d) 22
  30. 30.What is the average of 42, 52, 71, 68, 47 and 62? (a) 56 (b) 58 (c) 57 (d) 59
  31. 31.What is the average of all the whole numbers from 9 to 45? (a) 28 (b) 27 (c) 36 (d) 18
  32. 32.What is the average of all the whole numbers from 33 to 73? (a) 20 (b) 53 (c) 54 (d) 40
  33. 33.The average of 5 numbers is 17. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 1 (b) 2 (c) 38 (d) 17
  34. 34.The average of 8 numbers is 24. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 24 (b) 51 (c) 3 (d) 4
  35. 35.What is the average of 27, 15, 10 and 48? (a) 27 (b) 26 (c) 25 (d) 24
  36. 36.What is the average of 23, 35, 50, 44, 28 and 30? (a) 42 (b) 35 (c) 36 (d) 34
  37. 37.What is the average of 35, 52, 44, 47, 37 and 31? (a) 40 (b) 41 (c) 42 (d) 43
  38. 38.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) 28 (d) 17
  39. 39.What is the average of all the whole numbers from 44 to 80? (a) 62 (b) 63 (c) 36 (d) 18
  40. 40.What is the average of all the whole numbers from 58 to 80? (a) 70 (b) 22 (c) 11 (d) 69

Answer key

  1. 67
  2. 18
  3. 51
  4. 39
  5. 22
  6. 7
  7. 55
  8. 77
  9. 81
  10. 19
  11. 21
  12. 43
  13. 9
  14. 34
  15. 34
  16. 65
  17. 27
  18. 29
  19. 20
  20. 58
  21. 25
  22. 30
  23. 69
  24. 41
  25. 56
  26. 42
  27. 29
  28. 11
  29. 22
  30. 57
  31. 27
  32. 53
  33. 1
  34. 3
  35. 25
  36. 35
  37. 41
  38. 41
  39. 62
  40. 69

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