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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 986 · 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 30. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 39 (b) 12 (c) 30 (d) 57
  2. 2.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 40? (a) 40 (b) 45 (c) 80 (d) 81
  3. 3.What is the average of 34, 26, 21 and 59? (a) 37 (b) 35 (c) 36 (d) 34
  4. 4.What is the average of all the whole numbers from 8 to 20? (a) 12 (b) 6 (c) 15 (d) 14
  5. 5.A batter has an average of 28 runs in 6 matches. How many runs are needed in the next match to raise the average to 30? (a) 30 (b) 14 (c) 32 (d) 42
  6. 6.The average of 4 numbers is 41. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 84 (b) 41 (c) 35 (d) 36
  7. 7.A batter has an average of 27 runs in 6 matches. How many runs are needed in the next match to raise the average to 30? (a) 48 (b) 30 (c) 33 (d) 21
  8. 8.What is the average of 62, 77, 86 and 79? (a) 77 (b) 76 (c) 75 (d) 78
  9. 9.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 42? (a) 25 (b) 47 (c) 42 (d) 62
  10. 10.What is the average of 90, 95, 78, 83 and 54? (a) 81 (b) 80 (c) 79 (d) 100
  11. 11.What is the average of all the whole numbers from 51 to 67? (a) 8 (b) 16 (c) 59 (d) 60
  12. 12.A batter has an average of 39 runs in 9 matches. How many runs are needed in the next match to raise the average to 45? (a) 45 (b) 51 (c) 60 (d) 99
  13. 13.What is the average of all the whole numbers from 45 to 85? (a) 66 (b) 20 (c) 40 (d) 65
  14. 14.The average of 8 numbers is 39. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 24 (b) 39 (c) 60 (d) 75
  15. 15.A batter has an average of 26 runs in 5 matches. How many runs are needed in the next match to raise the average to 28? (a) 28 (b) 30 (c) 12 (d) 38
  16. 16.A batter has an average of 40 runs in 6 matches. How many runs are needed in the next match to raise the average to 43? (a) 21 (b) 43 (c) 46 (d) 61
  17. 17.What is the average of 81, 80, 63, 60, 79 and 87? (a) 90 (b) 74 (c) 75 (d) 76
  18. 18.A batter has an average of 30 runs in 7 matches. How many runs are needed in the next match to raise the average to 35? (a) 71 (b) 35 (c) 70 (d) 40
  19. 19.The average of 4 numbers is 17. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 31 (b) 17 (c) 26 (d) 12
  20. 20.What is the average of 26, 45, 34, 29 and 31? (a) 33 (b) 35 (c) 34 (d) 32
  21. 21.What is the average of all the whole numbers from 59 to 71? (a) 66 (b) 65 (c) 12 (d) 6
  22. 22.The average of 4 numbers is 10. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 2 (b) 10 (c) 23 (d) 1
  23. 23.What is the average of 58, 56, 61 and 65? (a) 59 (b) 80 (c) 61 (d) 60
  24. 24.The average of 8 numbers is 21. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 21 (b) 56 (c) 40 (d) 37
  25. 25.What is the average of all the whole numbers from 49 to 61? (a) 6 (b) 12 (c) 56 (d) 55
  26. 26.What is the average of 22, 26, 45 and 47? (a) 36 (b) 34 (c) 37 (d) 35
  27. 27.The average of 5 numbers is 43. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 90 (b) 43 (c) 27 (d) 28
  28. 28.A batter has an average of 32 runs in 7 matches. How many runs are needed in the next match to raise the average to 34? (a) 34 (b) 48 (c) 16 (d) 36
  29. 29.What is the average of all the whole numbers from 41 to 71? (a) 30 (b) 57 (c) 15 (d) 56
  30. 30.What is the average of all the whole numbers from 42 to 70? (a) 28 (b) 14 (c) 57 (d) 56
  31. 31.What is the average of all the whole numbers from 23 to 61? (a) 19 (b) 42 (c) 38 (d) 43
  32. 32.What is the average of 41, 49, 58 and 48? (a) 48 (b) 49 (c) 51 (d) 50
  33. 33.A batter has an average of 30 runs in 8 matches. How many runs are needed in the next match to raise the average to 38? (a) 38 (b) 72 (c) 46 (d) 102
  34. 34.The average of 5 numbers is 41. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 57 (b) 20 (c) 41 (d) 78
  35. 35.What is the average of all the whole numbers from 53 to 87? (a) 34 (b) 71 (c) 70 (d) 17
  36. 36.What is the average of all the whole numbers from 54 to 92? (a) 38 (b) 73 (c) 19 (d) 74
  37. 37.A batter has an average of 51 runs in 4 matches. How many runs are needed in the next match to raise the average to 54? (a) 66 (b) 57 (c) 54 (d) 15
  38. 38.What is the average of 90, 81, 76 and 69? (a) 80 (b) 78 (c) 79 (d) 81
  39. 39.The average of 8 numbers is 41. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 69 (b) 41 (c) 32 (d) 78
  40. 40.The average of 8 numbers is 33. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 19 (b) 20 (c) 33 (d) 68

Answer key

  1. 39
  2. 80
  3. 35
  4. 14
  5. 42
  6. 35
  7. 48
  8. 76
  9. 62
  10. 80
  11. 59
  12. 99
  13. 65
  14. 60
  15. 38
  16. 61
  17. 75
  18. 70
  19. 26
  20. 33
  21. 65
  22. 1
  23. 60
  24. 56
  25. 55
  26. 35
  27. 27
  28. 48
  29. 56
  30. 56
  31. 42
  32. 49
  33. 102
  34. 57
  35. 70
  36. 73
  37. 66
  38. 79
  39. 69
  40. 19

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