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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 180 · 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 44 runs in 3 matches. How many runs are needed in the next match to raise the average to 46? (a) 8 (b) 48 (c) 52 (d) 46
  2. 2.A batter has an average of 46 runs in 3 matches. How many runs are needed in the next match to raise the average to 49? (a) 52 (b) 58 (c) 49 (d) 12
  3. 3.What is the average of all the whole numbers from 46 to 70? (a) 12 (b) 24 (c) 59 (d) 58
  4. 4.The average of 4 numbers is 47. When one number is taken away, the average of the rest is 50. Which number was taken away? (a) 38 (b) 39 (c) 97 (d) 47
  5. 5.What is the average of 39, 22, 24, 24 and 11? (a) 23 (b) 30 (c) 24 (d) 25
  6. 6.What is the average of all the whole numbers from 40 to 48? (a) 4 (b) 8 (c) 44 (d) 45
  7. 7.A batter has an average of 27 runs in 9 matches. How many runs are needed in the next match to raise the average to 33? (a) 39 (b) 60 (c) 33 (d) 87
  8. 8.The average of 5 numbers is 17. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 17 (b) 36 (c) 10 (d) 9
  9. 9.What is the average of 75, 73, 53 and 47? (a) 64 (b) 61 (c) 62 (d) 63
  10. 10.What is the average of all the whole numbers from 42 to 60? (a) 51 (b) 18 (c) 52 (d) 9
  11. 11.What is the average of all the whole numbers from 51 to 89? (a) 71 (b) 70 (c) 19 (d) 38
  12. 12.What is the average of 61, 48, 65, 47 and 89? (a) 63 (b) 62 (c) 64 (d) 61
  13. 13.What is the average of 43, 48, 51, 60, 54 and 44? (a) 49 (b) 50 (c) 51 (d) 60
  14. 14.What is the average of all the whole numbers from 49 to 87? (a) 69 (b) 19 (c) 68 (d) 38
  15. 15.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 46? (a) 54 (b) 72 (c) 110 (d) 46
  16. 16.What is the average of 65, 74, 69, 80, 73 and 77? (a) 74 (b) 72 (c) 75 (d) 73
  17. 17.What is the average of 71, 75, 75, 75, 59 and 5? (a) 72 (b) 59 (c) 60 (d) 61
  18. 18.The average of 4 numbers is 34. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 73 (b) 20 (c) 19 (d) 34
  19. 19.The average of 8 numbers is 24. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 24 (b) 16 (c) 46 (d) 38
  20. 20.The average of 6 numbers is 35. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 21 (b) 73 (c) 35 (d) 20
  21. 21.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) 42 (b) 36 (c) 46 (d) 74
  22. 22.The average of 6 numbers is 32. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 32 (b) 52 (c) 60 (d) 24
  23. 23.What is the average of 12, 12, 16, 30, 31 and 31? (a) 21 (b) 23 (c) 22 (d) 24
  24. 24.The average of 4 numbers is 50. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 4 (b) 50 (c) 99 (d) 53
  25. 25.The average of 6 numbers is 24. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 43 (b) 44 (c) 45 (d) 24
  26. 26.What is the average of all the whole numbers from 54 to 84? (a) 69 (b) 15 (c) 30 (d) 70
  27. 27.What is the average of 48, 72, 70 and 38? (a) 58 (b) 56 (c) 76 (d) 57
  28. 28.What is the average of all the whole numbers from 60 to 76? (a) 68 (b) 16 (c) 69 (d) 8
  29. 29.A batter has an average of 55 runs in 4 matches. How many runs are needed in the next match to raise the average to 62? (a) 62 (b) 69 (c) 90 (d) 35
  30. 30.What is the average of all the whole numbers from 39 to 77? (a) 58 (b) 19 (c) 38 (d) 59
  31. 31.The average of 8 numbers is 11. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 24 (b) 19 (c) 11 (d) 32
  32. 32.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) 12 (b) 19 (c) 11 (d) 40
  33. 33.What is the average of 55, 53, 47, 45, 30 and 34? (a) 44 (b) 43 (c) 45 (d) 46
  34. 34.The average of 6 numbers is 26. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 51 (b) 30 (c) 26 (d) 47
  35. 35.A batter has an average of 34 runs in 4 matches. How many runs are needed in the next match to raise the average to 42? (a) 42 (b) 74 (c) 40 (d) 50
  36. 36.The average of 5 numbers is 44. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 83 (b) 64 (c) 44 (d) 25
  37. 37.A batter has an average of 47 runs in 6 matches. How many runs are needed in the next match to raise the average to 53? (a) 59 (b) 53 (c) 42 (d) 89
  38. 38.A batter has an average of 31 runs in 9 matches. How many runs are needed in the next match to raise the average to 35? (a) 39 (b) 35 (c) 71 (d) 40
  39. 39.The average of 5 numbers is 16. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 16 (b) 24 (c) 30 (d) 10
  40. 40.What is the average of all the whole numbers from 10 to 20? (a) 5 (b) 15 (c) 16 (d) 10

Answer key

  1. 52
  2. 58
  3. 58
  4. 38
  5. 24
  6. 44
  7. 87
  8. 9
  9. 62
  10. 51
  11. 70
  12. 62
  13. 50
  14. 68
  15. 110
  16. 73
  17. 60
  18. 19
  19. 38
  20. 20
  21. 74
  22. 52
  23. 22
  24. 53
  25. 44
  26. 69
  27. 57
  28. 68
  29. 90
  30. 58
  31. 32
  32. 11
  33. 44
  34. 51
  35. 74
  36. 64
  37. 89
  38. 71
  39. 24
  40. 15

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