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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 157 · 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 7 numbers is 31. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 8 (b) 31 (c) 7 (d) 66
  2. 2.What is the average of all the whole numbers from 40 to 66? (a) 54 (b) 26 (c) 13 (d) 53
  3. 3.The average of 8 numbers is 46. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 12 (b) 46 (c) 97 (d) 11
  4. 4.A batter has an average of 54 runs in 9 matches. How many runs are needed in the next match to raise the average to 57? (a) 60 (b) 57 (c) 30 (d) 84
  5. 5.The average of 6 numbers is 33. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 65 (b) 38 (c) 6 (d) 33
  6. 6.The average of 5 numbers is 14. When one number is taken away, the average of the rest is 9. Which number was taken away? (a) 25 (b) 34 (c) 23 (d) 14
  7. 7.The average of 5 numbers is 30. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 30 (b) 55 (c) 25 (d) 50
  8. 8.What is the average of 78, 61, 84 and 61? (a) 71 (b) 73 (c) 70 (d) 72
  9. 9.The average of 7 numbers is 45. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 45 (b) 7 (c) 51 (d) 89
  10. 10.What is the average of 88, 67, 74, 64, 66 and 103? (a) 78 (b) 79 (c) 77 (d) 76
  11. 11.What is the average of 43, 34, 24 and 55? (a) 38 (b) 39 (c) 52 (d) 40
  12. 12.A batter has an average of 58 runs in 6 matches. How many runs are needed in the next match to raise the average to 66? (a) 66 (b) 114 (c) 56 (d) 74
  13. 13.What is the average of 74, 51, 45, 69 and 56? (a) 61 (b) 60 (c) 59 (d) 58
  14. 14.The average of 8 numbers is 44. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 86 (b) 16 (c) 58 (d) 44
  15. 15.A batter has an average of 24 runs in 5 matches. How many runs are needed in the next match to raise the average to 31? (a) 66 (b) 38 (c) 31 (d) 42
  16. 16.The average of 4 numbers is 18. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 33 (b) 31 (c) 18 (d) 20
  17. 17.What is the average of 29, 42, 23, 22, 43 and 45? (a) 34 (b) 33 (c) 36 (d) 35
  18. 18.The average of 7 numbers is 19. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 19 (b) 40 (c) 7 (d) 8
  19. 19.What is the average of 68, 68, 71, 86, 61 and 96? (a) 74 (b) 90 (c) 76 (d) 75
  20. 20.What is the average of 23, 36, 21 and 4? (a) 22 (b) 20 (c) 21 (d) 28
  21. 21.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 29? (a) 20 (b) 34 (c) 29 (d) 44
  22. 22.What is the average of all the whole numbers from 21 to 59? (a) 40 (b) 41 (c) 38 (d) 19
  23. 23.What is the average of 30, 32, 47 and 59? (a) 42 (b) 43 (c) 41 (d) 56
  24. 24.A batter has an average of 37 runs in 3 matches. How many runs are needed in the next match to raise the average to 41? (a) 53 (b) 41 (c) 45 (d) 16
  25. 25.The average of 4 numbers is 43. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 41 (b) 40 (c) 87 (d) 43
  26. 26.What is the average of all the whole numbers from 48 to 58? (a) 10 (b) 53 (c) 5 (d) 54
  27. 27.What is the average of 71, 42, 46, 53, 53 and 77? (a) 59 (b) 58 (c) 57 (d) 56
  28. 28.What is the average of all the whole numbers from 45 to 61? (a) 16 (b) 53 (c) 54 (d) 8
  29. 29.What is the average of all the whole numbers from 21 to 41? (a) 20 (b) 10 (c) 31 (d) 32
  30. 30.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) 42 (b) 22 (c) 87 (d) 21
  31. 31.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 42? (a) 14 (b) 44 (c) 42 (d) 54
  32. 32.What is the average of all the whole numbers from 46 to 78? (a) 63 (b) 16 (c) 32 (d) 62
  33. 33.The average of 7 numbers is 41. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 41 (b) 30 (c) 84 (d) 29
  34. 34.A batter has an average of 23 runs in 5 matches. How many runs are needed in the next match to raise the average to 28? (a) 33 (b) 28 (c) 53 (d) 30
  35. 35.What is the average of all the whole numbers from 12 to 44? (a) 29 (b) 16 (c) 32 (d) 28
  36. 36.What is the average of 57, 70, 45 and 68? (a) 61 (b) 80 (c) 59 (d) 60
  37. 37.The average of 5 numbers is 29. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 62 (b) 13 (c) 29 (d) 14
  38. 38.The average of 8 numbers is 30. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 30 (b) 37 (c) 59 (d) 8
  39. 39.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 61? (a) 67 (b) 60 (c) 61 (d) 115
  40. 40.The average of 7 numbers is 47. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 41 (b) 47 (c) 42 (d) 95

Answer key

  1. 7
  2. 53
  3. 11
  4. 84
  5. 38
  6. 34
  7. 50
  8. 71
  9. 51
  10. 77
  11. 39
  12. 114
  13. 59
  14. 58
  15. 66
  16. 33
  17. 34
  18. 7
  19. 75
  20. 21
  21. 44
  22. 40
  23. 42
  24. 53
  25. 40
  26. 53
  27. 57
  28. 53
  29. 31
  30. 21
  31. 54
  32. 62
  33. 29
  34. 53
  35. 28
  36. 60
  37. 13
  38. 37
  39. 115
  40. 41

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