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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 785 · 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 21 runs in 5 matches. How many runs are needed in the next match to raise the average to 26? (a) 51 (b) 26 (c) 31 (d) 30
  2. 2.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 60? (a) 40 (b) 65 (c) 95 (d) 60
  3. 3.The average of 6 numbers is 28. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 60 (b) 28 (c) 9 (d) 8
  4. 4.What is the average of 28, 27, 34, 27 and 49? (a) 35 (b) 32 (c) 34 (d) 33
  5. 5.The average of 5 numbers is 48. When one number is taken away, the average of the rest is 53. Which number was taken away? (a) 28 (b) 101 (c) 48 (d) 29
  6. 6.The average of 6 numbers is 42. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 17 (b) 89 (c) 18 (d) 42
  7. 7.The average of 6 numbers is 27. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 59 (b) 2 (c) 27 (d) 3
  8. 8.A batter has an average of 25 runs in 9 matches. How many runs are needed in the next match to raise the average to 27? (a) 20 (b) 29 (c) 45 (d) 27
  9. 9.A batter has an average of 23 runs in 9 matches. How many runs are needed in the next match to raise the average to 26? (a) 30 (b) 53 (c) 29 (d) 26
  10. 10.What is the average of all the whole numbers from 16 to 24? (a) 4 (b) 8 (c) 21 (d) 20
  11. 11.The average of 5 numbers is 22. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 15 (b) 22 (c) 34 (d) 41
  12. 12.A batter has an average of 40 runs in 3 matches. How many runs are needed in the next match to raise the average to 46? (a) 24 (b) 64 (c) 52 (d) 46
  13. 13.What is the average of all the whole numbers from 8 to 46? (a) 38 (b) 27 (c) 28 (d) 19
  14. 14.What is the average of 30, 33, 16, 25, 20 and 14? (a) 24 (b) 23 (c) 22 (d) 25
  15. 15.A batter has an average of 41 runs in 3 matches. How many runs are needed in the next match to raise the average to 43? (a) 8 (b) 45 (c) 43 (d) 49
  16. 16.What is the average of 74, 60, 53, 55 and 83? (a) 64 (b) 65 (c) 66 (d) 67
  17. 17.The average of 5 numbers is 28. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 20 (b) 21 (c) 58 (d) 28
  18. 18.What is the average of all the whole numbers from 13 to 33? (a) 20 (b) 23 (c) 24 (d) 10
  19. 19.A batter has an average of 56 runs in 7 matches. How many runs are needed in the next match to raise the average to 58? (a) 72 (b) 60 (c) 16 (d) 58
  20. 20.What is the average of all the whole numbers from 8 to 14? (a) 11 (b) 12 (c) 6 (d) 3
  21. 21.What is the average of 49, 37, 43 and 55? (a) 47 (b) 45 (c) 48 (d) 46
  22. 22.What is the average of all the whole numbers from 45 to 57? (a) 52 (b) 51 (c) 6 (d) 12
  23. 23.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) 14 (b) 38 (c) 24 (d) 28
  24. 24.What is the average of all the whole numbers from 28 to 62? (a) 34 (b) 45 (c) 17 (d) 46
  25. 25.What is the average of all the whole numbers from 60 to 76? (a) 8 (b) 68 (c) 16 (d) 69
  26. 26.What is the average of all the whole numbers from 56 to 72? (a) 64 (b) 8 (c) 16 (d) 65
  27. 27.What is the average of all the whole numbers from 56 to 86? (a) 71 (b) 72 (c) 30 (d) 15
  28. 28.What is the average of 49, 52, 37, 52, 46 and 64? (a) 50 (b) 51 (c) 49 (d) 60
  29. 29.What is the average of all the whole numbers from 40 to 66? (a) 54 (b) 53 (c) 13 (d) 26
  30. 30.The average of 8 numbers is 17. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 11 (b) 35 (c) 17 (d) 10
  31. 31.What is the average of 50, 64, 69, 51, 57 and 75? (a) 63 (b) 60 (c) 62 (d) 61
  32. 32.A batter has an average of 55 runs in 8 matches. How many runs are needed in the next match to raise the average to 58? (a) 58 (b) 61 (c) 82 (d) 27
  33. 33.What is the average of 22, 15, 35, 25 and 28? (a) 26 (b) 25 (c) 24 (d) 27
  34. 34.The average of 7 numbers is 46. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 46 (b) 91 (c) 7 (d) 52
  35. 35.What is the average of 43, 40, 27, 27, 39 and 4? (a) 31 (b) 36 (c) 29 (d) 30
  36. 36.What is the average of 25, 28, 6, 17 and 29? (a) 20 (b) 22 (c) 21 (d) 23
  37. 37.What is the average of 40, 53, 50 and 41? (a) 45 (b) 48 (c) 47 (d) 46
  38. 38.What is the average of 52, 50, 72, 68 and 58? (a) 59 (b) 60 (c) 75 (d) 61
  39. 39.The average of 7 numbers is 25. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 25 (b) 43 (c) 47 (d) 21
  40. 40.The average of 4 numbers is 15. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 15 (b) 27 (c) 24 (d) 12

Answer key

  1. 51
  2. 95
  3. 8
  4. 33
  5. 28
  6. 17
  7. 2
  8. 45
  9. 53
  10. 20
  11. 34
  12. 64
  13. 27
  14. 23
  15. 49
  16. 65
  17. 20
  18. 23
  19. 72
  20. 11
  21. 46
  22. 51
  23. 38
  24. 45
  25. 68
  26. 64
  27. 71
  28. 50
  29. 53
  30. 10
  31. 61
  32. 82
  33. 25
  34. 52
  35. 30
  36. 21
  37. 46
  38. 60
  39. 43
  40. 24

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