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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 253 · 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 17. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 17 (b) 16 (c) 31 (d) 32
  2. 2.What is the average of 18, 13, 17, 13 and 74? (a) 28 (b) 27 (c) 26 (d) 29
  3. 3.What is the average of all the whole numbers from 26 to 36? (a) 31 (b) 32 (c) 10 (d) 5
  4. 4.The average of 6 numbers is 31. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 30 (b) 31 (c) 57 (d) 56
  5. 5.The average of 8 numbers is 12. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 12 (b) 16 (c) 22 (d) 26
  6. 6.What is the average of all the whole numbers from 7 to 17? (a) 13 (b) 12 (c) 5 (d) 10
  7. 7.A batter has an average of 54 runs in 4 matches. How many runs are needed in the next match to raise the average to 59? (a) 59 (b) 64 (c) 25 (d) 79
  8. 8.What is the average of all the whole numbers from 57 to 71? (a) 14 (b) 7 (c) 64 (d) 65
  9. 9.A batter has an average of 32 runs in 4 matches. How many runs are needed in the next match to raise the average to 38? (a) 30 (b) 38 (c) 44 (d) 62
  10. 10.What is the average of all the whole numbers from 45 to 57? (a) 12 (b) 6 (c) 51 (d) 52
  11. 11.What is the average of 54, 48, 56, 47, 48 and 89? (a) 58 (b) 56 (c) 59 (d) 57
  12. 12.What is the average of 26, 28, 21, 10, 19 and 22? (a) 23 (b) 22 (c) 21 (d) 20
  13. 13.What is the average of 33, 50, 30 and 63? (a) 43 (b) 46 (c) 45 (d) 44
  14. 14.What is the average of 69, 43, 65 and 55? (a) 57 (b) 59 (c) 60 (d) 58
  15. 15.What is the average of all the whole numbers from 29 to 35? (a) 33 (b) 3 (c) 32 (d) 6
  16. 16.What is the average of all the whole numbers from 17 to 45? (a) 28 (b) 32 (c) 14 (d) 31
  17. 17.What is the average of all the whole numbers from 14 to 44? (a) 30 (b) 28 (c) 29 (d) 15
  18. 18.The average of 4 numbers is 14. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 11 (b) 14 (c) 12 (d) 29
  19. 19.A batter has an average of 28 runs in 8 matches. How many runs are needed in the next match to raise the average to 32? (a) 32 (b) 36 (c) 64 (d) 65
  20. 20.The average of 5 numbers is 38. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 38 (b) 23 (c) 22 (d) 80
  21. 21.A batter has an average of 23 runs in 7 matches. How many runs are needed in the next match to raise the average to 31? (a) 64 (b) 31 (c) 39 (d) 87
  22. 22.The average of 7 numbers is 27. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 21 (b) 51 (c) 45 (d) 27
  23. 23.The average of 7 numbers is 32. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 60 (b) 56 (c) 32 (d) 28
  24. 24.The average of 8 numbers is 24. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 17 (b) 18 (c) 49 (d) 24
  25. 25.A batter has an average of 31 runs in 8 matches. How many runs are needed in the next match to raise the average to 36? (a) 45 (b) 76 (c) 41 (d) 36
  26. 26.What is the average of all the whole numbers from 59 to 71? (a) 66 (b) 12 (c) 65 (d) 6
  27. 27.What is the average of all the whole numbers from 57 to 85? (a) 71 (b) 28 (c) 72 (d) 14
  28. 28.What is the average of 83, 84, 60 and 65? (a) 74 (b) 72 (c) 75 (d) 73
  29. 29.What is the average of 29, 52, 32 and 47? (a) 40 (b) 39 (c) 41 (d) 42
  30. 30.What is the average of 56, 41, 66 and 45? (a) 54 (b) 53 (c) 51 (d) 52
  31. 31.A batter has an average of 52 runs in 8 matches. How many runs are needed in the next match to raise the average to 56? (a) 60 (b) 88 (c) 56 (d) 36
  32. 32.The average of 5 numbers is 45. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 45 (b) 41 (c) 91 (d) 42
  33. 33.What is the average of all the whole numbers from 43 to 75? (a) 32 (b) 59 (c) 16 (d) 60
  34. 34.What is the average of all the whole numbers from 58 to 94? (a) 76 (b) 77 (c) 36 (d) 18
  35. 35.The average of 7 numbers is 48. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 35 (b) 48 (c) 91 (d) 78
  36. 36.The average of 4 numbers is 35. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 35 (b) 8 (c) 68 (d) 41
  37. 37.The average of 4 numbers is 49. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 61 (b) 49 (c) 16 (d) 94
  38. 38.What is the average of 56, 69, 79 and 76? (a) 72 (b) 71 (c) 70 (d) 69
  39. 39.The average of 4 numbers is 37. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 79 (b) 37 (c) 23 (d) 22
  40. 40.A batter has an average of 51 runs in 4 matches. How many runs are needed in the next match to raise the average to 53? (a) 10 (b) 61 (c) 55 (d) 53

Answer key

  1. 31
  2. 27
  3. 31
  4. 56
  5. 26
  6. 12
  7. 79
  8. 64
  9. 62
  10. 51
  11. 57
  12. 21
  13. 44
  14. 58
  15. 32
  16. 31
  17. 29
  18. 11
  19. 64
  20. 22
  21. 87
  22. 45
  23. 56
  24. 17
  25. 76
  26. 65
  27. 71
  28. 73
  29. 40
  30. 52
  31. 88
  32. 41
  33. 59
  34. 76
  35. 78
  36. 41
  37. 61
  38. 70
  39. 22
  40. 61

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