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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 788 · 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 23. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 23 (b) 42 (c) 51 (d) 32
  2. 2.The average of 8 numbers is 42. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 42 (b) 56 (c) 16 (d) 82
  3. 3.What is the average of all the whole numbers from 39 to 77? (a) 38 (b) 59 (c) 19 (d) 58
  4. 4.What is the average of 87, 77, 61, 62, 87 and 82? (a) 77 (b) 78 (c) 75 (d) 76
  5. 5.What is the average of all the whole numbers from 54 to 72? (a) 63 (b) 18 (c) 9 (d) 64
  6. 6.The average of 4 numbers is 49. When one number is taken away, the average of the rest is 54. Which number was taken away? (a) 34 (b) 49 (c) 103 (d) 35
  7. 7.The average of 8 numbers is 45. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 94 (b) 17 (c) 45 (d) 18
  8. 8.A batter has an average of 45 runs in 5 matches. How many runs are needed in the next match to raise the average to 47? (a) 12 (b) 47 (c) 49 (d) 57
  9. 9.What is the average of 33, 42, 23, 29 and 53? (a) 37 (b) 36 (c) 35 (d) 45
  10. 10.A batter has an average of 41 runs in 3 matches. How many runs are needed in the next match to raise the average to 49? (a) 57 (b) 32 (c) 73 (d) 49
  11. 11.What is the average of all the whole numbers from 42 to 64? (a) 53 (b) 54 (c) 22 (d) 11
  12. 12.What is the average of 51, 46, 54, 35 and 64? (a) 51 (b) 52 (c) 49 (d) 50
  13. 13.The average of 8 numbers is 41. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 48 (b) 81 (c) 8 (d) 41
  14. 14.What is the average of 34, 24, 14 and 16? (a) 23 (b) 22 (c) 21 (d) 24
  15. 15.What is the average of all the whole numbers from 17 to 41? (a) 30 (b) 12 (c) 24 (d) 29
  16. 16.The average of 7 numbers is 17. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 17 (b) 35 (c) 29 (d) 47
  17. 17.The average of 6 numbers is 21. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 21 (b) 38 (c) 24 (d) 41
  18. 18.What is the average of all the whole numbers from 6 to 38? (a) 23 (b) 22 (c) 16 (d) 32
  19. 19.What is the average of 78, 69, 78, 57, 69 and 57? (a) 70 (b) 68 (c) 67 (d) 69
  20. 20.What is the average of all the whole numbers from 29 to 69? (a) 20 (b) 49 (c) 50 (d) 40
  21. 21.What is the average of 68, 82, 76 and 62? (a) 96 (b) 72 (c) 73 (d) 71
  22. 22.The average of 7 numbers is 25. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 43 (b) 25 (c) 47 (d) 21
  23. 23.A batter has an average of 26 runs in 9 matches. How many runs are needed in the next match to raise the average to 32? (a) 60 (b) 86 (c) 38 (d) 32
  24. 24.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 39? (a) 43 (b) 39 (c) 36 (d) 71
  25. 25.A batter has an average of 24 runs in 4 matches. How many runs are needed in the next match to raise the average to 27? (a) 30 (b) 15 (c) 27 (d) 39
  26. 26.A batter has an average of 30 runs in 4 matches. How many runs are needed in the next match to raise the average to 32? (a) 40 (b) 32 (c) 34 (d) 10
  27. 27.What is the average of 10, 22, 26 and 42? (a) 27 (b) 26 (c) 24 (d) 25
  28. 28.What is the average of all the whole numbers from 31 to 71? (a) 20 (b) 51 (c) 40 (d) 52
  29. 29.A batter has an average of 48 runs in 7 matches. How many runs are needed in the next match to raise the average to 56? (a) 113 (b) 112 (c) 56 (d) 64
  30. 30.What is the average of 30, 23, 10, 18, 8 and 31? (a) 24 (b) 20 (c) 21 (d) 19
  31. 31.A batter has an average of 55 runs in 7 matches. How many runs are needed in the next match to raise the average to 58? (a) 24 (b) 79 (c) 61 (d) 58
  32. 32.A batter has an average of 42 runs in 3 matches. How many runs are needed in the next match to raise the average to 46? (a) 16 (b) 58 (c) 50 (d) 46
  33. 33.What is the average of 88, 64, 80, 69, 63 and 86? (a) 76 (b) 75 (c) 74 (d) 90
  34. 34.The average of 5 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) 10 (d) 28
  35. 35.A batter has an average of 52 runs in 5 matches. How many runs are needed in the next match to raise the average to 56? (a) 56 (b) 24 (c) 60 (d) 76
  36. 36.The average of 7 numbers is 14. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 30 (b) 14 (c) 3 (d) 2
  37. 37.What is the average of 18, 36, 41, 22 and 38? (a) 32 (b) 33 (c) 30 (d) 31
  38. 38.The average of 7 numbers is 33. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 33 (b) 67 (c) 27 (d) 28
  39. 39.What is the average of all the whole numbers from 28 to 36? (a) 33 (b) 8 (c) 4 (d) 32
  40. 40.A batter has an average of 58 runs in 5 matches. How many runs are needed in the next match to raise the average to 66? (a) 106 (b) 48 (c) 66 (d) 74

Answer key

  1. 51
  2. 56
  3. 58
  4. 76
  5. 63
  6. 34
  7. 17
  8. 57
  9. 36
  10. 73
  11. 53
  12. 50
  13. 48
  14. 22
  15. 29
  16. 47
  17. 41
  18. 22
  19. 68
  20. 49
  21. 72
  22. 43
  23. 86
  24. 71
  25. 39
  26. 40
  27. 25
  28. 51
  29. 112
  30. 20
  31. 79
  32. 58
  33. 75
  34. 28
  35. 76
  36. 2
  37. 31
  38. 27
  39. 32
  40. 106

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