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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 150 · 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.What is the average of all the whole numbers from 56 to 84? (a) 28 (b) 70 (c) 71 (d) 14
  2. 2.A batter has an average of 41 runs in 7 matches. How many runs are needed in the next match to raise the average to 49? (a) 57 (b) 64 (c) 105 (d) 49
  3. 3.The average of 8 numbers is 41. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 41 (b) 85 (c) 20 (d) 21
  4. 4.What is the average of 67, 76, 62 and 87? (a) 72 (b) 75 (c) 74 (d) 73
  5. 5.What is the average of 66, 80, 64 and 50? (a) 64 (b) 67 (c) 66 (d) 65
  6. 6.A batter has an average of 46 runs in 7 matches. How many runs are needed in the next match to raise the average to 48? (a) 62 (b) 50 (c) 16 (d) 48
  7. 7.The average of 8 numbers is 15. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 1 (b) 2 (c) 15 (d) 32
  8. 8.What is the average of all the whole numbers from 11 to 51? (a) 20 (b) 31 (c) 40 (d) 32
  9. 9.A batter has an average of 48 runs in 3 matches. How many runs are needed in the next match to raise the average to 56? (a) 32 (b) 56 (c) 80 (d) 64
  10. 10.What is the average of all the whole numbers from 50 to 74? (a) 62 (b) 24 (c) 63 (d) 12
  11. 11.What is the average of 25, 32, 7 and 16? (a) 22 (b) 21 (c) 20 (d) 19
  12. 12.What is the average of all the whole numbers from 26 to 36? (a) 31 (b) 10 (c) 5 (d) 32
  13. 13.A batter has an average of 43 runs in 5 matches. How many runs are needed in the next match to raise the average to 50? (a) 85 (b) 57 (c) 42 (d) 50
  14. 14.What is the average of all the whole numbers from 5 to 27? (a) 22 (b) 16 (c) 11 (d) 17
  15. 15.The average of 4 numbers is 41. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 41 (b) 78 (c) 16 (d) 53
  16. 16.The average of 4 numbers is 44. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 44 (b) 83 (c) 59 (d) 20
  17. 17.The average of 8 numbers is 38. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 78 (b) 38 (c) 24 (d) 25
  18. 18.The average of 6 numbers is 42. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 6 (b) 47 (c) 83 (d) 42
  19. 19.A batter has an average of 41 runs in 8 matches. How many runs are needed in the next match to raise the average to 43? (a) 43 (b) 18 (c) 45 (d) 59
  20. 20.The average of 4 numbers is 27. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 51 (b) 12 (c) 36 (d) 27
  21. 21.What is the average of all the whole numbers from 52 to 68? (a) 61 (b) 60 (c) 16 (d) 8
  22. 22.A batter has an average of 30 runs in 8 matches. How many runs are needed in the next match to raise the average to 34? (a) 38 (b) 36 (c) 66 (d) 34
  23. 23.The average of 4 numbers is 18. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 18 (b) 34 (c) 8 (d) 24
  24. 24.The average of 7 numbers is 25. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 20 (b) 19 (c) 25 (d) 51
  25. 25.What is the average of all the whole numbers from 41 to 63? (a) 11 (b) 52 (c) 22 (d) 53
  26. 26.What is the average of 38, 33, 27, 22, 17 and 7? (a) 24 (b) 25 (c) 26 (d) 23
  27. 27.A batter has an average of 58 runs in 4 matches. How many runs are needed in the next match to raise the average to 63? (a) 83 (b) 25 (c) 63 (d) 68
  28. 28.What is the average of 71, 54, 54, 52, 77 and 88? (a) 66 (b) 68 (c) 65 (d) 67
  29. 29.What is the average of all the whole numbers from 9 to 41? (a) 16 (b) 26 (c) 32 (d) 25
  30. 30.A batter has an average of 59 runs in 6 matches. How many runs are needed in the next match to raise the average to 62? (a) 21 (b) 62 (c) 65 (d) 80
  31. 31.A batter has an average of 28 runs in 9 matches. How many runs are needed in the next match to raise the average to 34? (a) 34 (b) 40 (c) 88 (d) 60
  32. 32.The average of 6 numbers is 35. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 65 (b) 35 (c) 60 (d) 30
  33. 33.What is the average of all the whole numbers from 54 to 82? (a) 68 (b) 28 (c) 69 (d) 14
  34. 34.The average of 4 numbers is 30. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 8 (b) 58 (c) 36 (d) 30
  35. 35.What is the average of all the whole numbers from 25 to 39? (a) 32 (b) 7 (c) 14 (d) 33
  36. 36.A batter has an average of 53 runs in 6 matches. How many runs are needed in the next match to raise the average to 57? (a) 28 (b) 61 (c) 81 (d) 57
  37. 37.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) 31 (b) 30 (c) 57 (d) 56
  38. 38.What is the average of all the whole numbers from 20 to 42? (a) 11 (b) 32 (c) 31 (d) 22
  39. 39.What is the average of 72, 53, 65, 68, 52 and 74? (a) 64 (b) 65 (c) 63 (d) 66
  40. 40.What is the average of 50, 43, 55, 64, 43 and 57? (a) 51 (b) 53 (c) 54 (d) 52

Answer key

  1. 70
  2. 105
  3. 20
  4. 73
  5. 65
  6. 62
  7. 1
  8. 31
  9. 80
  10. 62
  11. 20
  12. 31
  13. 85
  14. 16
  15. 53
  16. 59
  17. 24
  18. 47
  19. 59
  20. 36
  21. 60
  22. 66
  23. 24
  24. 19
  25. 52
  26. 24
  27. 83
  28. 66
  29. 25
  30. 80
  31. 88
  32. 60
  33. 68
  34. 36
  35. 32
  36. 81
  37. 56
  38. 31
  39. 64
  40. 52

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