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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 595 · 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 45. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 43 (b) 45 (c) 42 (d) 91
  2. 2.What is the average of all the whole numbers from 16 to 36? (a) 20 (b) 26 (c) 10 (d) 27
  3. 3.The average of 6 numbers is 22. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 22 (b) 12 (c) 42 (d) 32
  4. 4.What is the average of all the whole numbers from 28 to 58? (a) 44 (b) 15 (c) 43 (d) 30
  5. 5.What is the average of all the whole numbers from 17 to 37? (a) 20 (b) 28 (c) 27 (d) 10
  6. 6.What is the average of 70, 56, 57 and 61? (a) 61 (b) 60 (c) 63 (d) 62
  7. 7.What is the average of all the whole numbers from 15 to 31? (a) 8 (b) 23 (c) 16 (d) 24
  8. 8.The average of 7 numbers is 11. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 19 (b) 11 (c) 21 (d) 29
  9. 9.What is the average of 49, 41, 50, 31 and 4? (a) 34 (b) 36 (c) 37 (d) 35
  10. 10.A batter has an average of 54 runs in 5 matches. How many runs are needed in the next match to raise the average to 61? (a) 42 (b) 68 (c) 96 (d) 61
  11. 11.The average of 6 numbers is 27. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 18 (b) 56 (c) 17 (d) 27
  12. 12.The average of 5 numbers is 15. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 15 (b) 20 (c) 31 (d) 26
  13. 13.A batter has an average of 40 runs in 8 matches. How many runs are needed in the next match to raise the average to 48? (a) 112 (b) 48 (c) 56 (d) 72
  14. 14.The average of 7 numbers is 38. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 38 (b) 8 (c) 9 (d) 81
  15. 15.What is the average of 50, 67, 47, 72, 72 and 40? (a) 60 (b) 58 (c) 57 (d) 59
  16. 16.A batter has an average of 28 runs in 5 matches. How many runs are needed in the next match to raise the average to 32? (a) 32 (b) 36 (c) 24 (d) 52
  17. 17.What is the average of 25, 27, 46 and 42? (a) 37 (b) 35 (c) 36 (d) 34
  18. 18.What is the average of all the whole numbers from 18 to 48? (a) 15 (b) 30 (c) 33 (d) 34
  19. 19.A batter has an average of 20 runs in 5 matches. How many runs are needed in the next match to raise the average to 28? (a) 36 (b) 48 (c) 28 (d) 68
  20. 20.What is the average of 60, 84, 76, 64 and 76? (a) 71 (b) 73 (c) 72 (d) 90
  21. 21.A batter has an average of 29 runs in 7 matches. How many runs are needed in the next match to raise the average to 34? (a) 69 (b) 34 (c) 40 (d) 39
  22. 22.What is the average of all the whole numbers from 57 to 81? (a) 24 (b) 70 (c) 12 (d) 69
  23. 23.What is the average of 76, 57, 57, 66, 57 and 101? (a) 68 (b) 71 (c) 70 (d) 69
  24. 24.What is the average of all the whole numbers from 44 to 74? (a) 30 (b) 15 (c) 59 (d) 60
  25. 25.A batter has an average of 31 runs in 7 matches. How many runs are needed in the next match to raise the average to 33? (a) 33 (b) 16 (c) 35 (d) 47
  26. 26.A batter has an average of 34 runs in 6 matches. How many runs are needed in the next match to raise the average to 37? (a) 37 (b) 21 (c) 40 (d) 55
  27. 27.A batter has an average of 29 runs in 8 matches. How many runs are needed in the next match to raise the average to 32? (a) 27 (b) 56 (c) 32 (d) 35
  28. 28.What is the average of 15, 37, 38 and 22? (a) 27 (b) 30 (c) 28 (d) 29
  29. 29.What is the average of all the whole numbers from 38 to 76? (a) 38 (b) 19 (c) 57 (d) 58
  30. 30.What is the average of all the whole numbers from 54 to 88? (a) 17 (b) 34 (c) 71 (d) 72
  31. 31.What is the average of 80, 85, 64 and 59? (a) 73 (b) 96 (c) 71 (d) 72
  32. 32.What is the average of 84, 81, 76 and 79? (a) 81 (b) 80 (c) 82 (d) 79
  33. 33.The average of 8 numbers is 11. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 23 (b) 11 (c) 5 (d) 4
  34. 34.The average of 4 numbers is 50. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 45 (b) 50 (c) 102 (d) 44
  35. 35.The average of 8 numbers is 30. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 55 (b) 40 (c) 65 (d) 30
  36. 36.What is the average of all the whole numbers from 51 to 81? (a) 30 (b) 66 (c) 15 (d) 67
  37. 37.What is the average of 52, 54, 80 and 82? (a) 69 (b) 67 (c) 68 (d) 66
  38. 38.What is the average of all the whole numbers from 49 to 69? (a) 60 (b) 59 (c) 20 (d) 10
  39. 39.What is the average of 39, 46, 45, 61 and 64? (a) 53 (b) 52 (c) 50 (d) 51
  40. 40.What is the average of all the whole numbers from 60 to 90? (a) 30 (b) 75 (c) 76 (d) 15

Answer key

  1. 42
  2. 26
  3. 32
  4. 43
  5. 27
  6. 61
  7. 23
  8. 29
  9. 35
  10. 96
  11. 17
  12. 31
  13. 112
  14. 8
  15. 58
  16. 52
  17. 35
  18. 33
  19. 68
  20. 72
  21. 69
  22. 69
  23. 69
  24. 59
  25. 47
  26. 55
  27. 56
  28. 28
  29. 57
  30. 71
  31. 72
  32. 80
  33. 4
  34. 44
  35. 65
  36. 66
  37. 67
  38. 59
  39. 51
  40. 75

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