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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 126 · 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 5 numbers is 20. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 20 (b) 17 (c) 41 (d) 16
  2. 2.The average of 5 numbers is 40. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 40 (b) 33 (c) 32 (d) 82
  3. 3.The average of 7 numbers is 16. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 11 (b) 33 (c) 10 (d) 16
  4. 4.What is the average of all the whole numbers from 7 to 13? (a) 11 (b) 10 (c) 3 (d) 6
  5. 5.A batter has an average of 60 runs in 4 matches. How many runs are needed in the next match to raise the average to 65? (a) 85 (b) 70 (c) 25 (d) 65
  6. 6.A batter has an average of 25 runs in 9 matches. How many runs are needed in the next match to raise the average to 27? (a) 20 (b) 45 (c) 27 (d) 29
  7. 7.The average of 6 numbers is 28. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 24 (b) 52 (c) 48 (d) 28
  8. 8.A batter has an average of 38 runs in 8 matches. How many runs are needed in the next match to raise the average to 44? (a) 92 (b) 44 (c) 50 (d) 54
  9. 9.A batter has an average of 40 runs in 9 matches. How many runs are needed in the next match to raise the average to 48? (a) 48 (b) 120 (c) 80 (d) 56
  10. 10.What is the average of 57, 29, 36 and 50? (a) 44 (b) 43 (c) 45 (d) 42
  11. 11.What is the average of all the whole numbers from 60 to 76? (a) 8 (b) 68 (c) 69 (d) 16
  12. 12.What is the average of all the whole numbers from 44 to 56? (a) 12 (b) 50 (c) 51 (d) 6
  13. 13.A batter has an average of 20 runs in 9 matches. How many runs are needed in the next match to raise the average to 26? (a) 32 (b) 26 (c) 60 (d) 80
  14. 14.The average of 5 numbers is 36. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 25 (b) 36 (c) 56 (d) 67
  15. 15.What is the average of all the whole numbers from 18 to 38? (a) 29 (b) 20 (c) 10 (d) 28
  16. 16.The average of 8 numbers is 36. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 36 (b) 50 (c) 16 (d) 70
  17. 17.What is the average of 69, 57, 61 and 69? (a) 63 (b) 65 (c) 66 (d) 64
  18. 18.The average of 6 numbers is 23. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 23 (b) 41 (c) 30 (d) 48
  19. 19.A batter has an average of 52 runs in 9 matches. How many runs are needed in the next match to raise the average to 59? (a) 66 (b) 70 (c) 122 (d) 59
  20. 20.The average of 5 numbers is 40. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 81 (b) 37 (c) 36 (d) 40
  21. 21.The average of 7 numbers is 48. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 31 (b) 48 (c) 30 (d) 99
  22. 22.A batter has an average of 23 runs in 8 matches. How many runs are needed in the next match to raise the average to 25? (a) 25 (b) 27 (c) 18 (d) 41
  23. 23.What is the average of 47, 70, 51, 52, 64 and 76? (a) 61 (b) 59 (c) 60 (d) 72
  24. 24.A batter has an average of 27 runs in 5 matches. How many runs are needed in the next match to raise the average to 34? (a) 69 (b) 42 (c) 34 (d) 41
  25. 25.What is the average of all the whole numbers from 41 to 79? (a) 38 (b) 61 (c) 19 (d) 60
  26. 26.What is the average of all the whole numbers from 44 to 76? (a) 60 (b) 16 (c) 61 (d) 32
  27. 27.What is the average of 45, 60, 49, 40, 56 and 50? (a) 49 (b) 51 (c) 50 (d) 60
  28. 28.What is the average of 81, 74, 56 and 73? (a) 70 (b) 72 (c) 73 (d) 71
  29. 29.What is the average of 30, 25, 25, 20, 27 and 83? (a) 35 (b) 34 (c) 36 (d) 42
  30. 30.The average of 5 numbers is 15. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 11 (b) 12 (c) 31 (d) 15
  31. 31.What is the average of all the whole numbers from 16 to 42? (a) 30 (b) 13 (c) 29 (d) 26
  32. 32.What is the average of all the whole numbers from 22 to 32? (a) 5 (b) 28 (c) 27 (d) 10
  33. 33.A batter has an average of 31 runs in 9 matches. How many runs are needed in the next match to raise the average to 35? (a) 39 (b) 71 (c) 40 (d) 35
  34. 34.The average of 4 numbers is 19. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 4 (b) 19 (c) 37 (d) 22
  35. 35.What is the average of 23, 21, 35 and 49? (a) 34 (b) 32 (c) 33 (d) 31
  36. 36.A batter has an average of 54 runs in 4 matches. How many runs are needed in the next match to raise the average to 56? (a) 64 (b) 56 (c) 10 (d) 58
  37. 37.What is the average of 80, 73, 80, 83 and 84? (a) 100 (b) 80 (c) 81 (d) 79
  38. 38.The average of 6 numbers is 41. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 41 (b) 83 (c) 37 (d) 36
  39. 39.The average of 8 numbers is 33. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 13 (b) 33 (c) 69 (d) 12
  40. 40.What is the average of all the whole numbers from 60 to 78? (a) 69 (b) 18 (c) 9 (d) 70

Answer key

  1. 16
  2. 32
  3. 10
  4. 10
  5. 85
  6. 45
  7. 48
  8. 92
  9. 120
  10. 43
  11. 68
  12. 50
  13. 80
  14. 56
  15. 28
  16. 50
  17. 64
  18. 48
  19. 122
  20. 36
  21. 30
  22. 41
  23. 60
  24. 69
  25. 60
  26. 60
  27. 50
  28. 71
  29. 35
  30. 11
  31. 29
  32. 27
  33. 71
  34. 22
  35. 32
  36. 64
  37. 80
  38. 36
  39. 12
  40. 69

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