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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 786 · 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 33. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 63 (b) 54 (c) 24 (d) 33
  2. 2.What is the average of 49, 43, 47 and 89? (a) 58 (b) 57 (c) 76 (d) 56
  3. 3.What is the average of 36, 44, 54, 55, 42 and 9? (a) 48 (b) 39 (c) 40 (d) 41
  4. 4.A batter has an average of 37 runs in 7 matches. How many runs are needed in the next match to raise the average to 42? (a) 47 (b) 40 (c) 42 (d) 77
  5. 5.The average of 4 numbers is 33. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 68 (b) 28 (c) 33 (d) 27
  6. 6.What is the average of all the whole numbers from 55 to 73? (a) 18 (b) 64 (c) 65 (d) 9
  7. 7.The average of 5 numbers is 19. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 19 (b) 11 (c) 12 (d) 40
  8. 8.A batter has an average of 39 runs in 4 matches. How many runs are needed in the next match to raise the average to 41? (a) 10 (b) 49 (c) 41 (d) 43
  9. 9.A batter has an average of 38 runs in 8 matches. How many runs are needed in the next match to raise the average to 42? (a) 46 (b) 74 (c) 36 (d) 42
  10. 10.What is the average of 30, 34, 49 and 55? (a) 43 (b) 56 (c) 41 (d) 42
  11. 11.What is the average of 65, 66, 74, 72 and 33? (a) 64 (b) 62 (c) 63 (d) 61
  12. 12.The average of 6 numbers is 31. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 22 (b) 31 (c) 64 (d) 21
  13. 13.What is the average of 62, 62, 67 and 49? (a) 59 (b) 61 (c) 60 (d) 80
  14. 14.The average of 4 numbers is 44. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 50 (b) 86 (c) 8 (d) 44
  15. 15.What is the average of all the whole numbers from 23 to 57? (a) 34 (b) 40 (c) 17 (d) 41
  16. 16.What is the average of all the whole numbers from 24 to 32? (a) 28 (b) 4 (c) 29 (d) 8
  17. 17.A batter has an average of 36 runs in 5 matches. How many runs are needed in the next match to raise the average to 39? (a) 54 (b) 39 (c) 18 (d) 42
  18. 18.What is the average of 83, 79, 86 and 60? (a) 78 (b) 79 (c) 77 (d) 76
  19. 19.What is the average of 65, 50, 54 and 39? (a) 52 (b) 51 (c) 54 (d) 53
  20. 20.The average of 8 numbers is 27. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 27 (b) 41 (c) 52 (d) 16
  21. 21.What is the average of 36, 18, 46, 48, 48 and 2? (a) 35 (b) 34 (c) 32 (d) 33
  22. 22.What is the average of 49, 50, 48, 51, 47 and 61? (a) 53 (b) 51 (c) 52 (d) 50
  23. 23.What is the average of all the whole numbers from 44 to 72? (a) 28 (b) 59 (c) 58 (d) 14
  24. 24.The average of 6 numbers is 48. When one number is taken away, the average of the rest is 50. Which number was taken away? (a) 98 (b) 38 (c) 39 (d) 48
  25. 25.What is the average of 47, 27, 34, 45, 37 and 2? (a) 33 (b) 34 (c) 32 (d) 31
  26. 26.What is the average of 47, 57, 53 and 59? (a) 54 (b) 53 (c) 72 (d) 55
  27. 27.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) 10 (c) 23 (d) 48
  28. 28.The average of 7 numbers is 49. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 28 (b) 73 (c) 49 (d) 94
  29. 29.What is the average of 76, 70, 77, 58 and 49? (a) 67 (b) 66 (c) 68 (d) 65
  30. 30.The average of 7 numbers is 17. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 35 (b) 17 (c) 21 (d) 31
  31. 31.What is the average of 40, 38, 35, 18 and 14? (a) 28 (b) 31 (c) 30 (d) 29
  32. 32.What is the average of all the whole numbers from 58 to 90? (a) 32 (b) 75 (c) 16 (d) 74
  33. 33.What is the average of all the whole numbers from 17 to 31? (a) 7 (b) 14 (c) 25 (d) 24
  34. 34.The average of 7 numbers is 28. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 28 (b) 40 (c) 54 (d) 14
  35. 35.A batter has an average of 40 runs in 6 matches. How many runs are needed in the next match to raise the average to 48? (a) 48 (b) 97 (c) 96 (d) 56
  36. 36.A batter has an average of 27 runs in 4 matches. How many runs are needed in the next match to raise the average to 35? (a) 43 (b) 35 (c) 40 (d) 67
  37. 37.The average of 6 numbers is 49. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 34 (b) 35 (c) 49 (d) 101
  38. 38.The average of 6 numbers is 19. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 39 (b) 19 (c) 15 (d) 14
  39. 39.What is the average of all the whole numbers from 14 to 44? (a) 30 (b) 15 (c) 28 (d) 29
  40. 40.What is the average of 26, 34, 32, 18, 22 and 42? (a) 29 (b) 28 (c) 31 (d) 30

Answer key

  1. 54
  2. 57
  3. 40
  4. 77
  5. 27
  6. 64
  7. 11
  8. 49
  9. 74
  10. 42
  11. 62
  12. 21
  13. 60
  14. 50
  15. 40
  16. 28
  17. 54
  18. 77
  19. 52
  20. 41
  21. 33
  22. 51
  23. 58
  24. 38
  25. 32
  26. 54
  27. 9
  28. 73
  29. 66
  30. 35
  31. 29
  32. 74
  33. 24
  34. 40
  35. 96
  36. 67
  37. 34
  38. 14
  39. 29
  40. 29

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