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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 926 · 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.What is the average of all the whole numbers from 58 to 88? (a) 30 (b) 15 (c) 74 (d) 73
  2. 2.What is the average of 57, 41, 28 and 42? (a) 41 (b) 56 (c) 43 (d) 42
  3. 3.What is the average of all the whole numbers from 58 to 76? (a) 68 (b) 67 (c) 18 (d) 9
  4. 4.A batter has an average of 47 runs in 9 matches. How many runs are needed in the next match to raise the average to 49? (a) 49 (b) 67 (c) 20 (d) 51
  5. 5.A batter has an average of 33 runs in 3 matches. How many runs are needed in the next match to raise the average to 41? (a) 49 (b) 32 (c) 41 (d) 65
  6. 6.What is the average of all the whole numbers from 6 to 22? (a) 14 (b) 15 (c) 8 (d) 16
  7. 7.The average of 8 numbers is 38. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 10 (b) 11 (c) 80 (d) 38
  8. 8.A batter has an average of 59 runs in 3 matches. How many runs are needed in the next match to raise the average to 67? (a) 75 (b) 32 (c) 67 (d) 91
  9. 9.The average of 6 numbers is 16. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 27 (b) 41 (c) 16 (d) 30
  10. 10.What is the average of all the whole numbers from 19 to 33? (a) 26 (b) 7 (c) 14 (d) 27
  11. 11.A batter has an average of 21 runs in 8 matches. How many runs are needed in the next match to raise the average to 23? (a) 25 (b) 39 (c) 18 (d) 23
  12. 12.The average of 5 numbers is 17. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 1 (b) 2 (c) 38 (d) 17
  13. 13.The average of 4 numbers is 41. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 41 (b) 33 (c) 32 (d) 85
  14. 14.The average of 8 numbers is 33. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 6 (b) 5 (c) 33 (d) 70
  15. 15.A batter has an average of 59 runs in 9 matches. How many runs are needed in the next match to raise the average to 65? (a) 60 (b) 65 (c) 119 (d) 71
  16. 16.What is the average of 22, 24, 26, 20 and 53? (a) 31 (b) 28 (c) 30 (d) 29
  17. 17.A batter has an average of 47 runs in 8 matches. How many runs are needed in the next match to raise the average to 54? (a) 61 (b) 63 (c) 54 (d) 110
  18. 18.What is the average of 41, 31, 49 and 63? (a) 45 (b) 47 (c) 48 (d) 46
  19. 19.The average of 4 numbers is 41. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 4 (b) 41 (c) 44 (d) 81
  20. 20.What is the average of all the whole numbers from 9 to 39? (a) 25 (b) 24 (c) 15 (d) 30
  21. 21.A batter has an average of 21 runs in 3 matches. How many runs are needed in the next match to raise the average to 24? (a) 24 (b) 33 (c) 12 (d) 27
  22. 22.The average of 8 numbers is 38. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 8 (b) 45 (c) 38 (d) 75
  23. 23.What is the average of 53, 71, 59 and 89? (a) 67 (b) 70 (c) 69 (d) 68
  24. 24.The average of 8 numbers is 20. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 36 (b) 32 (c) 48 (d) 20
  25. 25.What is the average of 32, 40, 36 and 56? (a) 40 (b) 43 (c) 42 (d) 41
  26. 26.The average of 8 numbers is 40. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 40 (b) 6 (c) 85 (d) 5
  27. 27.The average of 5 numbers is 31. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 43 (b) 15 (c) 59 (d) 31
  28. 28.The average of 4 numbers is 15. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 10 (b) 32 (c) 9 (d) 15
  29. 29.What is the average of 59, 63, 62, 42 and 29? (a) 50 (b) 52 (c) 51 (d) 53
  30. 30.What is the average of 13, 34, 35, 18, 23 and 39? (a) 28 (b) 27 (c) 29 (d) 26
  31. 31.What is the average of 20, 32, 37 and 23? (a) 28 (b) 30 (c) 27 (d) 29
  32. 32.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 35? (a) 40 (b) 35 (c) 25 (d) 55
  33. 33.What is the average of 70, 76, 66, 88, 68 and 88? (a) 75 (b) 77 (c) 76 (d) 78
  34. 34.What is the average of 41, 33, 30 and 48? (a) 40 (b) 37 (c) 39 (d) 38
  35. 35.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) 11 (b) 21 (c) 29 (d) 19
  36. 36.What is the average of 45, 25, 45, 29, 41 and 1? (a) 30 (b) 33 (c) 31 (d) 32
  37. 37.What is the average of 20, 16, 23 and 49? (a) 36 (b) 28 (c) 26 (d) 27
  38. 38.The average of 5 numbers is 50. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 50 (b) 66 (c) 96 (d) 20
  39. 39.What is the average of 39, 22, 45 and 18? (a) 32 (b) 31 (c) 33 (d) 30
  40. 40.What is the average of all the whole numbers from 51 to 61? (a) 57 (b) 10 (c) 5 (d) 56

Answer key

  1. 73
  2. 42
  3. 67
  4. 67
  5. 65
  6. 14
  7. 10
  8. 91
  9. 41
  10. 26
  11. 39
  12. 1
  13. 32
  14. 5
  15. 119
  16. 29
  17. 110
  18. 46
  19. 44
  20. 24
  21. 33
  22. 45
  23. 68
  24. 48
  25. 41
  26. 5
  27. 43
  28. 9
  29. 51
  30. 27
  31. 28
  32. 55
  33. 76
  34. 38
  35. 29
  36. 31
  37. 27
  38. 66
  39. 31
  40. 56

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