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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 326 · 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 4 numbers is 28. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 12 (b) 37 (c) 28 (d) 53
  2. 2.A batter has an average of 37 runs in 6 matches. How many runs are needed in the next match to raise the average to 41? (a) 41 (b) 28 (c) 45 (d) 65
  3. 3.The average of 4 numbers is 14. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 3 (b) 2 (c) 32 (d) 14
  4. 4.A batter has an average of 45 runs in 9 matches. How many runs are needed in the next match to raise the average to 50? (a) 96 (b) 50 (c) 95 (d) 55
  5. 5.What is the average of all the whole numbers from 6 to 12? (a) 3 (b) 9 (c) 10 (d) 6
  6. 6.What is the average of 6, 11, 11 and 56? (a) 21 (b) 22 (c) 28 (d) 20
  7. 7.The average of 8 numbers is 22. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 40 (b) 22 (c) 39 (d) 57
  8. 8.What is the average of all the whole numbers from 8 to 34? (a) 13 (b) 21 (c) 22 (d) 26
  9. 9.The average of 7 numbers is 35. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 65 (b) 64 (c) 66 (d) 35
  10. 10.The average of 6 numbers is 50. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 101 (b) 45 (c) 50 (d) 46
  11. 11.A batter has an average of 28 runs in 7 matches. How many runs are needed in the next match to raise the average to 32? (a) 32 (b) 61 (c) 60 (d) 36
  12. 12.A batter has an average of 46 runs in 5 matches. How many runs are needed in the next match to raise the average to 54? (a) 48 (b) 62 (c) 94 (d) 54
  13. 13.What is the average of 25, 21, 37, 10 and 32? (a) 27 (b) 26 (c) 24 (d) 25
  14. 14.What is the average of all the whole numbers from 7 to 29? (a) 11 (b) 18 (c) 19 (d) 22
  15. 15.What is the average of 80, 77, 70, 73 and 85? (a) 78 (b) 77 (c) 79 (d) 76
  16. 16.The average of 7 numbers is 12. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 20 (b) 12 (c) 28 (d) 36
  17. 17.The average of 5 numbers is 45. When one number is taken away, the average of the rest is 50. Which number was taken away? (a) 95 (b) 26 (c) 45 (d) 25
  18. 18.What is the average of 28, 27, 51, 50 and 44? (a) 41 (b) 39 (c) 50 (d) 40
  19. 19.The average of 7 numbers is 45. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 45 (b) 51 (c) 7 (d) 89
  20. 20.The average of 4 numbers is 26. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 53 (b) 24 (c) 23 (d) 26
  21. 21.What is the average of 34, 35, 34, 51, 54 and 86? (a) 49 (b) 48 (c) 51 (d) 50
  22. 22.What is the average of 40, 16, 42, 22 and 20? (a) 28 (b) 29 (c) 35 (d) 27
  23. 23.What is the average of all the whole numbers from 31 to 69? (a) 50 (b) 19 (c) 51 (d) 38
  24. 24.The average of 5 numbers is 44. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 20 (b) 84 (c) 44 (d) 60
  25. 25.What is the average of all the whole numbers from 54 to 94? (a) 75 (b) 74 (c) 40 (d) 20
  26. 26.The average of 7 numbers is 20. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 20 (b) 2 (c) 3 (d) 43
  27. 27.A batter has an average of 24 runs in 5 matches. How many runs are needed in the next match to raise the average to 31? (a) 31 (b) 66 (c) 42 (d) 38
  28. 28.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 49? (a) 57 (b) 72 (c) 113 (d) 49
  29. 29.The average of 4 numbers is 49. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 49 (b) 4 (c) 52 (d) 97
  30. 30.A batter has an average of 33 runs in 9 matches. How many runs are needed in the next match to raise the average to 35? (a) 35 (b) 20 (c) 37 (d) 53
  31. 31.A batter has an average of 20 runs in 7 matches. How many runs are needed in the next match to raise the average to 27? (a) 27 (b) 34 (c) 56 (d) 76
  32. 32.What is the average of 26, 15, 38, 8 and 28? (a) 22 (b) 24 (c) 23 (d) 25
  33. 33.The average of 4 numbers is 23. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 38 (b) 20 (c) 23 (d) 41
  34. 34.What is the average of 47, 42, 51, 47 and 98? (a) 59 (b) 58 (c) 56 (d) 57
  35. 35.What is the average of 44, 39, 19 and 22? (a) 30 (b) 32 (c) 31 (d) 33
  36. 36.The average of 4 numbers is 23. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 9 (b) 8 (c) 51 (d) 23
  37. 37.A batter has an average of 49 runs in 8 matches. How many runs are needed in the next match to raise the average to 57? (a) 121 (b) 57 (c) 72 (d) 65
  38. 38.What is the average of 54, 46, 57, 61 and 37? (a) 50 (b) 53 (c) 51 (d) 52
  39. 39.The average of 4 numbers is 24. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 51 (b) 15 (c) 16 (d) 24
  40. 40.A batter has an average of 20 runs in 8 matches. How many runs are needed in the next match to raise the average to 26? (a) 54 (b) 32 (c) 74 (d) 26

Answer key

  1. 37
  2. 65
  3. 2
  4. 95
  5. 9
  6. 21
  7. 57
  8. 21
  9. 65
  10. 45
  11. 60
  12. 94
  13. 25
  14. 18
  15. 77
  16. 36
  17. 25
  18. 40
  19. 51
  20. 23
  21. 49
  22. 28
  23. 50
  24. 60
  25. 74
  26. 2
  27. 66
  28. 113
  29. 52
  30. 53
  31. 76
  32. 23
  33. 38
  34. 57
  35. 31
  36. 8
  37. 121
  38. 51
  39. 15
  40. 74

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