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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 30 · 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 all the whole numbers from 28 to 62? (a) 17 (b) 45 (c) 34 (d) 46
  2. 2.What is the average of all the whole numbers from 28 to 40? (a) 35 (b) 34 (c) 12 (d) 6
  3. 3.What is the average of 84, 74, 81, 67 and 69? (a) 74 (b) 75 (c) 77 (d) 76
  4. 4.What is the average of all the whole numbers from 21 to 41? (a) 20 (b) 10 (c) 32 (d) 31
  5. 5.A batter has an average of 58 runs in 5 matches. How many runs are needed in the next match to raise the average to 60? (a) 62 (b) 70 (c) 12 (d) 60
  6. 6.What is the average of all the whole numbers from 42 to 64? (a) 11 (b) 22 (c) 54 (d) 53
  7. 7.The average of 7 numbers is 39. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 45 (b) 39 (c) 7 (d) 77
  8. 8.The average of 5 numbers is 20. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 38 (b) 28 (c) 20 (d) 10
  9. 9.What is the average of all the whole numbers from 45 to 59? (a) 14 (b) 7 (c) 52 (d) 53
  10. 10.What is the average of 55, 52, 75, 54, 74 and 56? (a) 61 (b) 63 (c) 62 (d) 60
  11. 11.A batter has an average of 44 runs in 3 matches. How many runs are needed in the next match to raise the average to 49? (a) 49 (b) 20 (c) 64 (d) 54
  12. 12.What is the average of 26, 35, 36, 39, 49 and 31? (a) 35 (b) 37 (c) 38 (d) 36
  13. 13.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 45? (a) 108 (b) 45 (c) 70 (d) 52
  14. 14.A batter has an average of 57 runs in 6 matches. How many runs are needed in the next match to raise the average to 59? (a) 59 (b) 71 (c) 61 (d) 14
  15. 15.The average of 5 numbers is 43. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 40 (b) 39 (c) 87 (d) 43
  16. 16.What is the average of 55, 55, 56, 55 and 74? (a) 59 (b) 61 (c) 58 (d) 60
  17. 17.The average of 8 numbers is 49. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 49 (b) 28 (c) 29 (d) 101
  18. 18.The average of 6 numbers is 48. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 93 (b) 48 (c) 63 (d) 18
  19. 19.A batter has an average of 53 runs in 4 matches. How many runs are needed in the next match to raise the average to 57? (a) 57 (b) 20 (c) 73 (d) 61
  20. 20.The average of 6 numbers is 29. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 44 (b) 18 (c) 29 (d) 55
  21. 21.A batter has an average of 39 runs in 9 matches. How many runs are needed in the next match to raise the average to 43? (a) 40 (b) 47 (c) 43 (d) 79
  22. 22.What is the average of all the whole numbers from 30 to 42? (a) 37 (b) 36 (c) 12 (d) 6
  23. 23.The average of 7 numbers is 18. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 42 (b) 28 (c) 18 (d) 32
  24. 24.The average of 7 numbers is 24. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 47 (b) 7 (c) 30 (d) 24
  25. 25.The average of 7 numbers is 10. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 5 (b) 10 (c) 21 (d) 4
  26. 26.What is the average of all the whole numbers from 40 to 80? (a) 61 (b) 20 (c) 40 (d) 60
  27. 27.The average of 5 numbers is 11. When one number is taken away, the average of the rest is 9. Which number was taken away? (a) 11 (b) 20 (c) 19 (d) 10
  28. 28.A batter has an average of 48 runs in 4 matches. How many runs are needed in the next match to raise the average to 50? (a) 50 (b) 58 (c) 52 (d) 10
  29. 29.What is the average of 31, 38, 27 and 64? (a) 39 (b) 40 (c) 42 (d) 41
  30. 30.What is the average of 17, 28, 31, 40 and 24? (a) 29 (b) 35 (c) 28 (d) 27
  31. 31.What is the average of 42, 38, 41 and 83? (a) 52 (b) 68 (c) 50 (d) 51
  32. 32.The average of 6 numbers is 41. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 22 (b) 21 (c) 86 (d) 41
  33. 33.What is the average of all the whole numbers from 41 to 81? (a) 61 (b) 40 (c) 20 (d) 62
  34. 34.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 59? (a) 67 (b) 59 (c) 48 (d) 99
  35. 35.What is the average of all the whole numbers from 26 to 54? (a) 14 (b) 28 (c) 40 (d) 41
  36. 36.What is the average of 38, 50, 45 and 7? (a) 34 (b) 36 (c) 35 (d) 37
  37. 37.What is the average of all the whole numbers from 36 to 62? (a) 26 (b) 50 (c) 49 (d) 13
  38. 38.What is the average of all the whole numbers from 54 to 72? (a) 18 (b) 63 (c) 9 (d) 64
  39. 39.What is the average of 32, 17, 34 and 17? (a) 27 (b) 24 (c) 25 (d) 26
  40. 40.A batter has an average of 41 runs in 7 matches. How many runs are needed in the next match to raise the average to 48? (a) 56 (b) 55 (c) 48 (d) 97

Answer key

  1. 45
  2. 34
  3. 75
  4. 31
  5. 70
  6. 53
  7. 45
  8. 28
  9. 52
  10. 61
  11. 64
  12. 36
  13. 108
  14. 71
  15. 39
  16. 59
  17. 28
  18. 63
  19. 73
  20. 44
  21. 79
  22. 36
  23. 42
  24. 30
  25. 4
  26. 60
  27. 19
  28. 58
  29. 40
  30. 28
  31. 51
  32. 21
  33. 61
  34. 99
  35. 40
  36. 35
  37. 49
  38. 63
  39. 25
  40. 97

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