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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 718 · 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 6 numbers is 46. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 95 (b) 31 (c) 46 (d) 32
  2. 2.The average of 8 numbers is 14. When one number is taken away, the average of the rest is 9. Which number was taken away? (a) 23 (b) 14 (c) 49 (d) 40
  3. 3.What is the average of 87, 63, 80, 76 and 54? (a) 72 (b) 73 (c) 90 (d) 71
  4. 4.What is the average of 33, 45, 21, 40, 20 and 27? (a) 31 (b) 30 (c) 33 (d) 32
  5. 5.What is the average of all the whole numbers from 22 to 54? (a) 32 (b) 16 (c) 38 (d) 39
  6. 6.What is the average of 45, 37, 47, 32, 32 and 11? (a) 35 (b) 34 (c) 36 (d) 33
  7. 7.What is the average of all the whole numbers from 24 to 30? (a) 27 (b) 6 (c) 28 (d) 3
  8. 8.A batter has an average of 24 runs in 6 matches. How many runs are needed in the next match to raise the average to 27? (a) 30 (b) 45 (c) 27 (d) 21
  9. 9.What is the average of 35, 28, 18, 12 and 42? (a) 28 (b) 29 (c) 26 (d) 27
  10. 10.The average of 4 numbers is 10. When one number is taken away, the average of the rest is 9. Which number was taken away? (a) 4 (b) 13 (c) 10 (d) 19
  11. 11.What is the average of 80, 78, 52, 54 and 71? (a) 69 (b) 68 (c) 66 (d) 67
  12. 12.What is the average of all the whole numbers from 25 to 51? (a) 38 (b) 26 (c) 39 (d) 13
  13. 13.A batter has an average of 59 runs in 9 matches. How many runs are needed in the next match to raise the average to 65? (a) 119 (b) 65 (c) 60 (d) 71
  14. 14.The average of 5 numbers is 33. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 53 (b) 61 (c) 33 (d) 25
  15. 15.What is the average of 25, 30, 21, 30, 11 and 33? (a) 24 (b) 30 (c) 25 (d) 26
  16. 16.What is the average of all the whole numbers from 32 to 70? (a) 38 (b) 52 (c) 19 (d) 51
  17. 17.What is the average of all the whole numbers from 32 to 60? (a) 14 (b) 46 (c) 47 (d) 28
  18. 18.What is the average of 31, 35, 31 and 79? (a) 45 (b) 43 (c) 44 (d) 46
  19. 19.The average of 8 numbers is 10. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 17 (b) 24 (c) 10 (d) 31
  20. 20.What is the average of all the whole numbers from 41 to 69? (a) 14 (b) 28 (c) 55 (d) 56
  21. 21.What is the average of all the whole numbers from 54 to 80? (a) 67 (b) 68 (c) 13 (d) 26
  22. 22.What is the average of all the whole numbers from 38 to 44? (a) 3 (b) 6 (c) 41 (d) 42
  23. 23.What is the average of 48, 57, 48 and 59? (a) 52 (b) 55 (c) 53 (d) 54
  24. 24.What is the average of 80, 65, 76, 77 and 82? (a) 76 (b) 75 (c) 95 (d) 77
  25. 25.The average of 4 numbers is 47. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 96 (b) 47 (c) 42 (d) 41
  26. 26.What is the average of all the whole numbers from 54 to 68? (a) 14 (b) 7 (c) 61 (d) 62
  27. 27.The average of 5 numbers is 36. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 36 (b) 69 (c) 48 (d) 15
  28. 28.A batter has an average of 53 runs in 3 matches. How many runs are needed in the next match to raise the average to 59? (a) 59 (b) 77 (c) 65 (d) 24
  29. 29.A batter has an average of 27 runs in 5 matches. How many runs are needed in the next match to raise the average to 29? (a) 31 (b) 39 (c) 29 (d) 12
  30. 30.A batter has an average of 45 runs in 3 matches. How many runs are needed in the next match to raise the average to 53? (a) 61 (b) 77 (c) 32 (d) 53
  31. 31.What is the average of 12, 28, 7, 31 and 22? (a) 25 (b) 20 (c) 21 (d) 19
  32. 32.What is the average of all the whole numbers from 53 to 61? (a) 4 (b) 57 (c) 8 (d) 58
  33. 33.What is the average of all the whole numbers from 43 to 55? (a) 12 (b) 49 (c) 50 (d) 6
  34. 34.The average of 8 numbers is 48. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 32 (b) 48 (c) 76 (d) 92
  35. 35.A batter has an average of 50 runs in 9 matches. How many runs are needed in the next match to raise the average to 52? (a) 20 (b) 52 (c) 54 (d) 70
  36. 36.What is the average of all the whole numbers from 15 to 41? (a) 26 (b) 13 (c) 29 (d) 28
  37. 37.What is the average of 26, 56, 26 and 56? (a) 40 (b) 41 (c) 43 (d) 42
  38. 38.What is the average of all the whole numbers from 41 to 67? (a) 13 (b) 26 (c) 55 (d) 54
  39. 39.What is the average of all the whole numbers from 9 to 17? (a) 8 (b) 4 (c) 13 (d) 14
  40. 40.What is the average of all the whole numbers from 30 to 44? (a) 37 (b) 14 (c) 38 (d) 7

Answer key

  1. 31
  2. 49
  3. 72
  4. 31
  5. 38
  6. 34
  7. 27
  8. 45
  9. 27
  10. 13
  11. 67
  12. 38
  13. 119
  14. 53
  15. 25
  16. 51
  17. 46
  18. 44
  19. 31
  20. 55
  21. 67
  22. 41
  23. 53
  24. 76
  25. 41
  26. 61
  27. 48
  28. 77
  29. 39
  30. 77
  31. 20
  32. 57
  33. 49
  34. 76
  35. 70
  36. 28
  37. 41
  38. 54
  39. 13
  40. 37

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