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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 32 · 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 51 runs in 6 matches. How many runs are needed in the next match to raise the average to 53? (a) 55 (b) 14 (c) 53 (d) 65
  2. 2.A batter has an average of 35 runs in 5 matches. How many runs are needed in the next match to raise the average to 41? (a) 41 (b) 47 (c) 71 (d) 36
  3. 3.What is the average of 61, 60, 71, 71 and 47? (a) 62 (b) 61 (c) 63 (d) 64
  4. 4.What is the average of all the whole numbers from 15 to 21? (a) 6 (b) 3 (c) 19 (d) 18
  5. 5.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 45? (a) 45 (b) 52 (c) 28 (d) 66
  6. 6.The average of 8 numbers is 37. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 58 (b) 37 (c) 24 (d) 71
  7. 7.What is the average of 78, 54, 54, 69 and 85? (a) 85 (b) 67 (c) 69 (d) 68
  8. 8.What is the average of all the whole numbers from 54 to 66? (a) 60 (b) 61 (c) 12 (d) 6
  9. 9.A batter has an average of 27 runs in 6 matches. How many runs are needed in the next match to raise the average to 29? (a) 14 (b) 29 (c) 41 (d) 31
  10. 10.What is the average of all the whole numbers from 50 to 74? (a) 12 (b) 63 (c) 62 (d) 24
  11. 11.What is the average of all the whole numbers from 10 to 38? (a) 14 (b) 28 (c) 24 (d) 25
  12. 12.What is the average of 62, 58, 71, 74, 59 and 90? (a) 69 (b) 71 (c) 68 (d) 70
  13. 13.What is the average of all the whole numbers from 17 to 31? (a) 14 (b) 25 (c) 7 (d) 24
  14. 14.The average of 6 numbers is 49. When one number is taken away, the average of the rest is 54. Which number was taken away? (a) 49 (b) 103 (c) 24 (d) 25
  15. 15.What is the average of 33, 18, 38, 25 and 51? (a) 32 (b) 34 (c) 35 (d) 33
  16. 16.A batter has an average of 39 runs in 8 matches. How many runs are needed in the next match to raise the average to 43? (a) 47 (b) 43 (c) 75 (d) 36
  17. 17.A batter has an average of 43 runs in 3 matches. How many runs are needed in the next match to raise the average to 46? (a) 12 (b) 46 (c) 55 (d) 49
  18. 18.The average of 4 numbers is 20. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 20 (b) 38 (c) 8 (d) 26
  19. 19.What is the average of 19, 18, 33 and 38? (a) 28 (b) 36 (c) 26 (d) 27
  20. 20.What is the average of 76, 56, 65 and 71? (a) 67 (b) 66 (c) 68 (d) 69
  21. 21.A batter has an average of 28 runs in 8 matches. How many runs are needed in the next match to raise the average to 33? (a) 73 (b) 33 (c) 38 (d) 45
  22. 22.A batter has an average of 50 runs in 3 matches. How many runs are needed in the next match to raise the average to 56? (a) 62 (b) 24 (c) 56 (d) 74
  23. 23.What is the average of all the whole numbers from 19 to 25? (a) 22 (b) 6 (c) 23 (d) 3
  24. 24.What is the average of all the whole numbers from 27 to 55? (a) 42 (b) 41 (c) 28 (d) 14
  25. 25.What is the average of 43, 27, 27, 25 and 48? (a) 35 (b) 34 (c) 36 (d) 33
  26. 26.A batter has an average of 54 runs in 5 matches. How many runs are needed in the next match to raise the average to 62? (a) 62 (b) 48 (c) 102 (d) 70
  27. 27.What is the average of 63, 67, 81 and 93? (a) 78 (b) 77 (c) 76 (d) 75
  28. 28.The average of 6 numbers is 34. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 12 (b) 34 (c) 44 (d) 66
  29. 29.What is the average of 42, 34, 54, 45 and 60? (a) 48 (b) 46 (c) 47 (d) 49
  30. 30.What is the average of 61, 57, 38, 61 and 43? (a) 51 (b) 65 (c) 53 (d) 52
  31. 31.What is the average of 56, 69, 68 and 43? (a) 60 (b) 61 (c) 58 (d) 59
  32. 32.The average of 5 numbers is 12. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 20 (b) 12 (c) 22 (d) 10
  33. 33.The average of 5 numbers is 32. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 32 (b) 60 (c) 20 (d) 48
  34. 34.What is the average of all the whole numbers from 40 to 66? (a) 54 (b) 13 (c) 26 (d) 53
  35. 35.What is the average of 10, 27, 18 and 37? (a) 25 (b) 23 (c) 24 (d) 22
  36. 36.A batter has an average of 39 runs in 5 matches. How many runs are needed in the next match to raise the average to 46? (a) 46 (b) 53 (c) 81 (d) 42
  37. 37.What is the average of 25, 6, 23, 18, 25 and 23? (a) 21 (b) 19 (c) 20 (d) 24
  38. 38.What is the average of 45, 45, 60, 68 and 67? (a) 58 (b) 57 (c) 59 (d) 56
  39. 39.The average of 8 numbers is 49. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 49 (b) 28 (c) 101 (d) 29
  40. 40.The average of 6 numbers is 23. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 14 (b) 23 (c) 48 (d) 13

Answer key

  1. 65
  2. 71
  3. 62
  4. 18
  5. 66
  6. 58
  7. 68
  8. 60
  9. 41
  10. 62
  11. 24
  12. 69
  13. 24
  14. 24
  15. 33
  16. 75
  17. 55
  18. 26
  19. 27
  20. 67
  21. 73
  22. 74
  23. 22
  24. 41
  25. 34
  26. 102
  27. 76
  28. 44
  29. 47
  30. 52
  31. 59
  32. 20
  33. 48
  34. 53
  35. 23
  36. 81
  37. 20
  38. 57
  39. 28
  40. 13

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