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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 670 · 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 8 numbers is 50. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 36 (b) 37 (c) 102 (d) 50
  2. 2.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 34? (a) 40 (b) 34 (c) 82 (d) 54
  3. 3.A batter has an average of 37 runs in 4 matches. How many runs are needed in the next match to raise the average to 45? (a) 45 (b) 40 (c) 77 (d) 53
  4. 4.The average of 6 numbers is 28. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 4 (b) 28 (c) 61 (d) 3
  5. 5.What is the average of all the whole numbers from 52 to 84? (a) 16 (b) 69 (c) 32 (d) 68
  6. 6.What is the average of 50, 49, 26, 34 and 36? (a) 38 (b) 39 (c) 40 (d) 41
  7. 7.A batter has an average of 32 runs in 8 matches. How many runs are needed in the next match to raise the average to 36? (a) 36 (b) 69 (c) 68 (d) 40
  8. 8.What is the average of all the whole numbers from 12 to 50? (a) 31 (b) 38 (c) 32 (d) 19
  9. 9.What is the average of all the whole numbers from 17 to 43? (a) 30 (b) 31 (c) 13 (d) 26
  10. 10.What is the average of 55, 33, 49, 37, 32 and 70? (a) 48 (b) 46 (c) 45 (d) 47
  11. 11.What is the average of all the whole numbers from 21 to 59? (a) 40 (b) 41 (c) 19 (d) 38
  12. 12.What is the average of 72, 57, 71 and 40? (a) 59 (b) 61 (c) 60 (d) 80
  13. 13.The average of 6 numbers is 18. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 18 (b) 31 (c) 30 (d) 43
  14. 14.A batter has an average of 34 runs in 5 matches. How many runs are needed in the next match to raise the average to 42? (a) 42 (b) 82 (c) 48 (d) 50
  15. 15.The average of 7 numbers is 48. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 21 (b) 66 (c) 93 (d) 48
  16. 16.What is the average of all the whole numbers from 56 to 88? (a) 16 (b) 73 (c) 72 (d) 32
  17. 17.A batter has an average of 34 runs in 4 matches. How many runs are needed in the next match to raise the average to 36? (a) 38 (b) 10 (c) 36 (d) 44
  18. 18.What is the average of 16, 33, 20 and 43? (a) 29 (b) 28 (c) 30 (d) 27
  19. 19.A batter has an average of 42 runs in 8 matches. How many runs are needed in the next match to raise the average to 45? (a) 45 (b) 69 (c) 27 (d) 48
  20. 20.The average of 5 numbers is 11. When one number is taken away, the average of the rest is 9. Which number was taken away? (a) 20 (b) 10 (c) 19 (d) 11
  21. 21.The average of 4 numbers is 34. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 69 (b) 34 (c) 31 (d) 32
  22. 22.What is the average of 81, 64, 59, 76, 78 and 80? (a) 75 (b) 74 (c) 73 (d) 72
  23. 23.What is the average of all the whole numbers from 23 to 53? (a) 39 (b) 38 (c) 15 (d) 30
  24. 24.What is the average of all the whole numbers from 16 to 46? (a) 15 (b) 32 (c) 31 (d) 30
  25. 25.The average of 5 numbers is 39. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 32 (b) 39 (c) 80 (d) 31
  26. 26.The average of 8 numbers is 16. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 37 (b) 24 (c) 29 (d) 16
  27. 27.The average of 6 numbers is 37. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 57 (b) 70 (c) 24 (d) 37
  28. 28.What is the average of 47, 47, 51 and 79? (a) 56 (b) 55 (c) 57 (d) 58
  29. 29.What is the average of 19, 7, 13 and 49? (a) 23 (b) 24 (c) 22 (d) 21
  30. 30.What is the average of 63, 72, 87 and 86? (a) 76 (b) 79 (c) 77 (d) 78
  31. 31.What is the average of all the whole numbers from 24 to 34? (a) 29 (b) 5 (c) 30 (d) 10
  32. 32.A batter has an average of 37 runs in 3 matches. How many runs are needed in the next match to raise the average to 40? (a) 43 (b) 12 (c) 40 (d) 49
  33. 33.The average of 4 numbers is 12. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 12 (b) 9 (c) 25 (d) 10
  34. 34.What is the average of 51, 54, 29 and 26? (a) 39 (b) 40 (c) 42 (d) 41
  35. 35.What is the average of all the whole numbers from 36 to 66? (a) 30 (b) 15 (c) 52 (d) 51
  36. 36.What is the average of all the whole numbers from 33 to 61? (a) 47 (b) 48 (c) 28 (d) 14
  37. 37.A batter has an average of 26 runs in 8 matches. How many runs are needed in the next match to raise the average to 31? (a) 45 (b) 71 (c) 31 (d) 36
  38. 38.The average of 4 numbers is 38. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 20 (b) 53 (c) 71 (d) 38
  39. 39.What is the average of 51, 52, 35, 40 and 37? (a) 44 (b) 43 (c) 45 (d) 42
  40. 40.A batter has an average of 53 runs in 8 matches. How many runs are needed in the next match to raise the average to 58? (a) 45 (b) 98 (c) 63 (d) 58

Answer key

  1. 36
  2. 82
  3. 77
  4. 3
  5. 68
  6. 39
  7. 68
  8. 31
  9. 30
  10. 46
  11. 40
  12. 60
  13. 43
  14. 82
  15. 66
  16. 72
  17. 44
  18. 28
  19. 69
  20. 19
  21. 31
  22. 73
  23. 38
  24. 31
  25. 31
  26. 37
  27. 57
  28. 56
  29. 22
  30. 77
  31. 29
  32. 49
  33. 9
  34. 40
  35. 51
  36. 47
  37. 71
  38. 53
  39. 43
  40. 98

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