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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 23 · 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 49 runs in 9 matches. How many runs are needed in the next match to raise the average to 55? (a) 109 (b) 55 (c) 61 (d) 60
  2. 2.The average of 5 numbers is 46. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 93 (b) 43 (c) 46 (d) 42
  3. 3.What is the average of all the whole numbers from 12 to 34? (a) 22 (b) 24 (c) 11 (d) 23
  4. 4.What is the average of all the whole numbers from 34 to 60? (a) 47 (b) 13 (c) 26 (d) 48
  5. 5.What is the average of all the whole numbers from 5 to 11? (a) 8 (b) 6 (c) 3 (d) 9
  6. 6.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 44? (a) 44 (b) 27 (c) 47 (d) 68
  7. 7.A batter has an average of 35 runs in 8 matches. How many runs are needed in the next match to raise the average to 37? (a) 39 (b) 18 (c) 37 (d) 53
  8. 8.A batter has an average of 40 runs in 4 matches. How many runs are needed in the next match to raise the average to 48? (a) 40 (b) 80 (c) 48 (d) 56
  9. 9.What is the average of all the whole numbers from 35 to 41? (a) 39 (b) 6 (c) 3 (d) 38
  10. 10.The average of 6 numbers is 27. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 27 (b) 58 (c) 8 (d) 7
  11. 11.What is the average of 68, 63, 60, 58 and 91? (a) 69 (b) 68 (c) 67 (d) 85
  12. 12.A batter has an average of 20 runs in 9 matches. How many runs are needed in the next match to raise the average to 27? (a) 90 (b) 70 (c) 34 (d) 27
  13. 13.What is the average of 79, 65, 67 and 109? (a) 79 (b) 80 (c) 81 (d) 82
  14. 14.What is the average of all the whole numbers from 36 to 72? (a) 55 (b) 54 (c) 18 (d) 36
  15. 15.What is the average of 22, 32, 30 and 60? (a) 35 (b) 48 (c) 37 (d) 36
  16. 16.The average of 6 numbers is 25. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 18 (b) 25 (c) 40 (d) 47
  17. 17.What is the average of 27, 19, 11, 24 and 39? (a) 24 (b) 23 (c) 25 (d) 30
  18. 18.What is the average of 47, 38, 58, 57 and 50? (a) 50 (b) 52 (c) 49 (d) 51
  19. 19.A batter has an average of 37 runs in 8 matches. How many runs are needed in the next match to raise the average to 41? (a) 45 (b) 41 (c) 73 (d) 36
  20. 20.What is the average of all the whole numbers from 46 to 62? (a) 16 (b) 54 (c) 55 (d) 8
  21. 21.What is the average of all the whole numbers from 37 to 71? (a) 17 (b) 34 (c) 54 (d) 55
  22. 22.A batter has an average of 25 runs in 8 matches. How many runs are needed in the next match to raise the average to 32? (a) 39 (b) 63 (c) 32 (d) 88
  23. 23.A batter has an average of 59 runs in 3 matches. How many runs are needed in the next match to raise the average to 63? (a) 75 (b) 67 (c) 16 (d) 63
  24. 24.A batter has an average of 34 runs in 7 matches. How many runs are needed in the next match to raise the average to 36? (a) 16 (b) 50 (c) 36 (d) 38
  25. 25.The average of 6 numbers is 32. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 59 (b) 32 (c) 30 (d) 57
  26. 26.A batter has an average of 31 runs in 4 matches. How many runs are needed in the next match to raise the average to 34? (a) 37 (b) 15 (c) 46 (d) 34
  27. 27.A batter has an average of 25 runs in 8 matches. How many runs are needed in the next match to raise the average to 33? (a) 72 (b) 33 (c) 97 (d) 41
  28. 28.What is the average of 61, 79, 83, 68 and 54? (a) 70 (b) 69 (c) 68 (d) 71
  29. 29.The average of 6 numbers is 18. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 32 (b) 18 (c) 34 (d) 33
  30. 30.The average of 8 numbers is 16. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 10 (b) 16 (c) 9 (d) 33
  31. 31.What is the average of 87, 70, 64 and 79? (a) 100 (b) 74 (c) 75 (d) 76
  32. 32.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 37? (a) 41 (b) 36 (c) 37 (d) 69
  33. 33.The average of 4 numbers is 18. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 18 (b) 7 (c) 40 (d) 6
  34. 34.The average of 8 numbers is 17. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 17 (b) 4 (c) 36 (d) 3
  35. 35.The average of 5 numbers is 50. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 50 (b) 5 (c) 99 (d) 54
  36. 36.What is the average of 70, 66, 73, 83, 69 and 65? (a) 70 (b) 72 (c) 71 (d) 73
  37. 37.What is the average of 25, 37, 40, 40 and 28? (a) 34 (b) 35 (c) 36 (d) 33
  38. 38.What is the average of 18, 16, 23, 31 and 62? (a) 32 (b) 31 (c) 30 (d) 29
  39. 39.What is the average of all the whole numbers from 12 to 30? (a) 9 (b) 21 (c) 18 (d) 22
  40. 40.What is the average of 67, 65, 64, 58, 60 and 76? (a) 66 (b) 78 (c) 64 (d) 65

Answer key

  1. 109
  2. 42
  3. 23
  4. 47
  5. 8
  6. 68
  7. 53
  8. 80
  9. 38
  10. 7
  11. 68
  12. 90
  13. 80
  14. 54
  15. 36
  16. 40
  17. 24
  18. 50
  19. 73
  20. 54
  21. 54
  22. 88
  23. 75
  24. 50
  25. 57
  26. 46
  27. 97
  28. 69
  29. 33
  30. 9
  31. 75
  32. 69
  33. 6
  34. 3
  35. 54
  36. 71
  37. 34
  38. 30
  39. 21
  40. 65

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