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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 113 · 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 5 numbers is 35. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 31 (b) 35 (c) 71 (d) 32
  2. 2.A batter has an average of 38 runs in 3 matches. How many runs are needed in the next match to raise the average to 46? (a) 32 (b) 70 (c) 46 (d) 54
  3. 3.The average of 8 numbers is 46. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 46 (b) 33 (c) 94 (d) 32
  4. 4.What is the average of all the whole numbers from 13 to 29? (a) 16 (b) 8 (c) 22 (d) 21
  5. 5.A batter has an average of 39 runs in 3 matches. How many runs are needed in the next match to raise the average to 44? (a) 20 (b) 44 (c) 59 (d) 49
  6. 6.What is the average of 66, 78, 76, 65 and 70? (a) 70 (b) 71 (c) 73 (d) 72
  7. 7.What is the average of all the whole numbers from 47 to 73? (a) 13 (b) 61 (c) 60 (d) 26
  8. 8.What is the average of 35, 42, 40, 50, 33 and 64? (a) 46 (b) 45 (c) 43 (d) 44
  9. 9.What is the average of all the whole numbers from 39 to 53? (a) 46 (b) 47 (c) 14 (d) 7
  10. 10.What is the average of all the whole numbers from 54 to 80? (a) 13 (b) 68 (c) 26 (d) 67
  11. 11.What is the average of 37, 47, 46, 34 and 36? (a) 50 (b) 40 (c) 41 (d) 39
  12. 12.The average of 6 numbers is 34. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 14 (b) 34 (c) 72 (d) 15
  13. 13.What is the average of 28, 31, 32 and 77? (a) 41 (b) 43 (c) 56 (d) 42
  14. 14.What is the average of all the whole numbers from 28 to 68? (a) 49 (b) 48 (c) 40 (d) 20
  15. 15.The average of 4 numbers is 21. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 21 (b) 19 (c) 18 (d) 43
  16. 16.What is the average of all the whole numbers from 9 to 39? (a) 30 (b) 24 (c) 15 (d) 25
  17. 17.What is the average of all the whole numbers from 44 to 60? (a) 16 (b) 53 (c) 52 (d) 8
  18. 18.The average of 7 numbers is 14. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 24 (b) 28 (c) 14 (d) 38
  19. 19.What is the average of 79, 72, 65, 89, 73 and 72? (a) 76 (b) 90 (c) 75 (d) 74
  20. 20.The average of 5 numbers is 35. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 75 (b) 15 (c) 35 (d) 16
  21. 21.The average of 6 numbers is 40. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 76 (b) 40 (c) 24 (d) 60
  22. 22.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 34? (a) 34 (b) 10 (c) 42 (d) 36
  23. 23.What is the average of all the whole numbers from 32 to 66? (a) 17 (b) 49 (c) 34 (d) 50
  24. 24.What is the average of all the whole numbers from 45 to 55? (a) 10 (b) 50 (c) 5 (d) 51
  25. 25.What is the average of all the whole numbers from 22 to 38? (a) 31 (b) 8 (c) 30 (d) 16
  26. 26.The average of 7 numbers is 33. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 10 (b) 33 (c) 9 (d) 70
  27. 27.What is the average of all the whole numbers from 16 to 22? (a) 19 (b) 6 (c) 20 (d) 3
  28. 28.What is the average of 44, 28, 56, 45, 34 and 39? (a) 40 (b) 43 (c) 41 (d) 42
  29. 29.The average of 8 numbers is 50. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 102 (b) 36 (c) 50 (d) 37
  30. 30.What is the average of 54, 57, 39, 59 and 21? (a) 47 (b) 48 (c) 46 (d) 45
  31. 31.What is the average of 82, 83, 81, 73 and 31? (a) 71 (b) 69 (c) 70 (d) 72
  32. 32.What is the average of 36, 22, 12, 14, 36 and 24? (a) 26 (b) 25 (c) 23 (d) 24
  33. 33.What is the average of 53, 70, 57, 54, 68 and 64? (a) 60 (b) 61 (c) 62 (d) 63
  34. 34.What is the average of all the whole numbers from 7 to 31? (a) 19 (b) 20 (c) 24 (d) 12
  35. 35.What is the average of 25, 41, 23 and 43? (a) 32 (b) 44 (c) 33 (d) 34
  36. 36.What is the average of 63, 86, 82, 67, 86 and 60? (a) 74 (b) 73 (c) 76 (d) 75
  37. 37.A batter has an average of 55 runs in 7 matches. How many runs are needed in the next match to raise the average to 58? (a) 24 (b) 58 (c) 61 (d) 79
  38. 38.What is the average of 21, 7, 25, 11 and 41? (a) 22 (b) 20 (c) 23 (d) 21
  39. 39.What is the average of 30, 48, 33 and 49? (a) 41 (b) 39 (c) 42 (d) 40
  40. 40.A batter has an average of 58 runs in 8 matches. How many runs are needed in the next match to raise the average to 62? (a) 94 (b) 62 (c) 66 (d) 36

Answer key

  1. 31
  2. 70
  3. 32
  4. 21
  5. 59
  6. 71
  7. 60
  8. 44
  9. 46
  10. 67
  11. 40
  12. 14
  13. 42
  14. 48
  15. 18
  16. 24
  17. 52
  18. 38
  19. 75
  20. 15
  21. 60
  22. 42
  23. 49
  24. 50
  25. 30
  26. 9
  27. 19
  28. 41
  29. 36
  30. 46
  31. 70
  32. 24
  33. 61
  34. 19
  35. 33
  36. 74
  37. 79
  38. 21
  39. 40
  40. 94

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