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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 4 · 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 46. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 97 (b) 26 (c) 46 (d) 27
  2. 2.What is the average of 45, 23, 16, 20 and 51? (a) 33 (b) 32 (c) 30 (d) 31
  3. 3.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 29? (a) 71 (b) 29 (c) 48 (d) 35
  4. 4.What is the average of 81, 68, 83, 92 and 71? (a) 78 (b) 80 (c) 81 (d) 79
  5. 5.The average of 4 numbers is 26. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 26 (b) 15 (c) 14 (d) 56
  6. 6.A batter has an average of 36 runs in 6 matches. How many runs are needed in the next match to raise the average to 39? (a) 39 (b) 57 (c) 21 (d) 42
  7. 7.What is the average of 41, 38, 35, 38 and 48? (a) 41 (b) 40 (c) 50 (d) 39
  8. 8.A batter has an average of 52 runs in 4 matches. How many runs are needed in the next match to raise the average to 60? (a) 92 (b) 40 (c) 60 (d) 68
  9. 9.What is the average of 22, 13, 15, 27, 35 and 8? (a) 19 (b) 20 (c) 24 (d) 21
  10. 10.What is the average of all the whole numbers from 19 to 41? (a) 31 (b) 11 (c) 22 (d) 30
  11. 11.The average of 4 numbers is 50. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 59 (b) 50 (c) 97 (d) 12
  12. 12.The average of 4 numbers is 24. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 24 (b) 19 (c) 50 (d) 18
  13. 13.A batter has an average of 31 runs in 6 matches. How many runs are needed in the next match to raise the average to 38? (a) 80 (b) 38 (c) 49 (d) 45
  14. 14.A batter has an average of 54 runs in 6 matches. How many runs are needed in the next match to raise the average to 59? (a) 35 (b) 89 (c) 64 (d) 59
  15. 15.What is the average of all the whole numbers from 39 to 71? (a) 56 (b) 16 (c) 55 (d) 32
  16. 16.What is the average of all the whole numbers from 6 to 26? (a) 16 (b) 17 (c) 20 (d) 10
  17. 17.The average of 4 numbers is 27. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 24 (b) 55 (c) 25 (d) 27
  18. 18.The average of 6 numbers is 38. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 6 (b) 38 (c) 75 (d) 43
  19. 19.A batter has an average of 33 runs in 8 matches. How many runs are needed in the next match to raise the average to 36? (a) 36 (b) 39 (c) 60 (d) 27
  20. 20.The average of 4 numbers is 32. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 32 (b) 8 (c) 62 (d) 38
  21. 21.The average of 4 numbers is 42. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 36 (b) 86 (c) 37 (d) 42
  22. 22.What is the average of all the whole numbers from 19 to 25? (a) 6 (b) 22 (c) 3 (d) 23
  23. 23.What is the average of all the whole numbers from 31 to 55? (a) 43 (b) 44 (c) 24 (d) 12
  24. 24.The average of 4 numbers is 18. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 18 (b) 33 (c) 31 (d) 20
  25. 25.What is the average of all the whole numbers from 10 to 38? (a) 24 (b) 14 (c) 28 (d) 25
  26. 26.The average of 7 numbers is 20. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 20 (b) 7 (c) 26 (d) 39
  27. 27.The average of 7 numbers is 16. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 16 (b) 33 (c) 11 (d) 10
  28. 28.The average of 6 numbers is 28. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 48 (b) 24 (c) 52 (d) 28
  29. 29.What is the average of all the whole numbers from 28 to 48? (a) 20 (b) 10 (c) 39 (d) 38
  30. 30.A batter has an average of 54 runs in 3 matches. How many runs are needed in the next match to raise the average to 60? (a) 24 (b) 66 (c) 78 (d) 60
  31. 31.What is the average of all the whole numbers from 46 to 58? (a) 6 (b) 12 (c) 52 (d) 53
  32. 32.What is the average of 53, 56, 39 and 16? (a) 43 (b) 41 (c) 42 (d) 40
  33. 33.What is the average of 32, 21, 40, 30 and 7? (a) 27 (b) 26 (c) 28 (d) 25
  34. 34.A batter has an average of 38 runs in 6 matches. How many runs are needed in the next match to raise the average to 45? (a) 87 (b) 45 (c) 49 (d) 52
  35. 35.What is the average of all the whole numbers from 46 to 76? (a) 61 (b) 15 (c) 62 (d) 30
  36. 36.What is the average of all the whole numbers from 44 to 72? (a) 14 (b) 28 (c) 59 (d) 58
  37. 37.What is the average of all the whole numbers from 47 to 73? (a) 26 (b) 13 (c) 61 (d) 60
  38. 38.What is the average of 43, 50, 40 and 59? (a) 47 (b) 49 (c) 64 (d) 48
  39. 39.What is the average of 30, 41, 46, 43, 31 and 61? (a) 43 (b) 44 (c) 41 (d) 42
  40. 40.What is the average of 53, 64, 49, 41, 40 and 65? (a) 51 (b) 54 (c) 53 (d) 52

Answer key

  1. 26
  2. 31
  3. 71
  4. 79
  5. 14
  6. 57
  7. 40
  8. 92
  9. 20
  10. 30
  11. 59
  12. 18
  13. 80
  14. 89
  15. 55
  16. 16
  17. 24
  18. 43
  19. 60
  20. 38
  21. 36
  22. 22
  23. 43
  24. 33
  25. 24
  26. 26
  27. 10
  28. 48
  29. 38
  30. 78
  31. 52
  32. 41
  33. 26
  34. 87
  35. 61
  36. 58
  37. 60
  38. 48
  39. 42
  40. 52

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