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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 93 · 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 60 runs in 7 matches. How many runs are needed in the next match to raise the average to 67? (a) 74 (b) 56 (c) 67 (d) 116
  2. 2.What is the average of 70, 77, 79, 61 and 38? (a) 67 (b) 65 (c) 66 (d) 64
  3. 3.The average of 6 numbers is 50. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 102 (b) 50 (c) 41 (d) 40
  4. 4.What is the average of 48, 39, 30 and 31? (a) 38 (b) 39 (c) 37 (d) 36
  5. 5.What is the average of 32, 45, 47, 31 and 55? (a) 42 (b) 41 (c) 44 (d) 43
  6. 6.What is the average of 56, 49, 53, 60, 50 and 74? (a) 57 (b) 59 (c) 56 (d) 58
  7. 7.The average of 7 numbers is 42. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 89 (b) 12 (c) 13 (d) 42
  8. 8.A batter has an average of 53 runs in 5 matches. How many runs are needed in the next match to raise the average to 60? (a) 60 (b) 95 (c) 67 (d) 42
  9. 9.The average of 5 numbers is 43. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 85 (b) 47 (c) 43 (d) 5
  10. 10.A batter has an average of 54 runs in 5 matches. How many runs are needed in the next match to raise the average to 61? (a) 42 (b) 61 (c) 68 (d) 96
  11. 11.What is the average of 46, 38, 36 and 12? (a) 33 (b) 34 (c) 32 (d) 44
  12. 12.A batter has an average of 27 runs in 6 matches. How many runs are needed in the next match to raise the average to 30? (a) 33 (b) 21 (c) 30 (d) 48
  13. 13.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) 66 (b) 21 (c) 81 (d) 63
  14. 14.The average of 4 numbers is 15. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 29 (b) 15 (c) 4 (d) 18
  15. 15.What is the average of all the whole numbers from 51 to 57? (a) 3 (b) 6 (c) 54 (d) 55
  16. 16.The average of 5 numbers is 33. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 61 (b) 53 (c) 33 (d) 25
  17. 17.What is the average of 44, 26, 33, 27 and 55? (a) 37 (b) 38 (c) 39 (d) 36
  18. 18.The average of 8 numbers is 29. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 32 (b) 57 (c) 54 (d) 29
  19. 19.What is the average of 60, 79, 82, 70 and 44? (a) 69 (b) 68 (c) 66 (d) 67
  20. 20.What is the average of all the whole numbers from 54 to 78? (a) 67 (b) 66 (c) 12 (d) 24
  21. 21.What is the average of all the whole numbers from 49 to 69? (a) 20 (b) 10 (c) 59 (d) 60
  22. 22.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 40? (a) 56 (b) 42 (c) 18 (d) 40
  23. 23.The average of 4 numbers is 50. When one number is taken away, the average of the rest is 53. Which number was taken away? (a) 42 (b) 50 (c) 103 (d) 41
  24. 24.A batter has an average of 25 runs in 5 matches. How many runs are needed in the next match to raise the average to 31? (a) 31 (b) 37 (c) 61 (d) 36
  25. 25.The average of 4 numbers is 44. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 44 (b) 84 (c) 16 (d) 56
  26. 26.A batter has an average of 45 runs in 7 matches. How many runs are needed in the next match to raise the average to 47? (a) 49 (b) 61 (c) 16 (d) 47
  27. 27.What is the average of all the whole numbers from 59 to 89? (a) 15 (b) 30 (c) 74 (d) 75
  28. 28.What is the average of 15, 26, 29, 23, 28 and 53? (a) 30 (b) 28 (c) 31 (d) 29
  29. 29.The average of 7 numbers is 34. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 34 (b) 29 (c) 28 (d) 69
  30. 30.What is the average of all the whole numbers from 36 to 50? (a) 44 (b) 14 (c) 7 (d) 43
  31. 31.What is the average of all the whole numbers from 15 to 21? (a) 19 (b) 18 (c) 3 (d) 6
  32. 32.What is the average of 67, 71, 78 and 80? (a) 73 (b) 74 (c) 76 (d) 75
  33. 33.What is the average of 21, 45, 21, 42 and 36? (a) 33 (b) 35 (c) 32 (d) 34
  34. 34.The average of 4 numbers is 22. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 25 (b) 22 (c) 43 (d) 4
  35. 35.What is the average of 63, 50, 65, 61 and 56? (a) 61 (b) 60 (c) 59 (d) 58
  36. 36.The average of 4 numbers is 50. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 102 (b) 44 (c) 50 (d) 45
  37. 37.The average of 8 numbers is 32. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 59 (b) 67 (c) 40 (d) 32
  38. 38.What is the average of all the whole numbers from 41 to 51? (a) 46 (b) 10 (c) 5 (d) 47
  39. 39.What is the average of 47, 40, 32 and 57? (a) 43 (b) 45 (c) 46 (d) 44
  40. 40.A batter has an average of 24 runs in 6 matches. How many runs are needed in the next match to raise the average to 32? (a) 40 (b) 56 (c) 80 (d) 32

Answer key

  1. 116
  2. 65
  3. 40
  4. 37
  5. 42
  6. 57
  7. 12
  8. 95
  9. 47
  10. 96
  11. 33
  12. 48
  13. 81
  14. 18
  15. 54
  16. 53
  17. 37
  18. 57
  19. 67
  20. 66
  21. 59
  22. 56
  23. 41
  24. 61
  25. 56
  26. 61
  27. 74
  28. 29
  29. 28
  30. 43
  31. 18
  32. 74
  33. 33
  34. 25
  35. 59
  36. 44
  37. 67
  38. 46
  39. 44
  40. 80

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