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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 737 · 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 6 to 24? (a) 9 (b) 16 (c) 15 (d) 18
  2. 2.A batter has an average of 57 runs in 7 matches. How many runs are needed in the next match to raise the average to 63? (a) 105 (b) 48 (c) 69 (d) 63
  3. 3.A batter has an average of 30 runs in 9 matches. How many runs are needed in the next match to raise the average to 32? (a) 32 (b) 20 (c) 50 (d) 34
  4. 4.The average of 7 numbers is 50. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 74 (b) 96 (c) 50 (d) 28
  5. 5.The average of 5 numbers is 48. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 48 (b) 25 (c) 68 (d) 91
  6. 6.The average of 6 numbers is 33. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 33 (b) 6 (c) 65 (d) 38
  7. 7.A batter has an average of 31 runs in 6 matches. How many runs are needed in the next match to raise the average to 33? (a) 14 (b) 45 (c) 33 (d) 35
  8. 8.What is the average of all the whole numbers from 34 to 54? (a) 44 (b) 10 (c) 45 (d) 20
  9. 9.What is the average of all the whole numbers from 36 to 44? (a) 40 (b) 41 (c) 8 (d) 4
  10. 10.The average of 4 numbers is 26. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 26 (b) 35 (c) 12 (d) 49
  11. 11.The average of 7 numbers is 12. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 35 (b) 12 (c) 19 (d) 42
  12. 12.What is the average of all the whole numbers from 42 to 78? (a) 18 (b) 60 (c) 61 (d) 36
  13. 13.What is the average of 24, 14, 29, 10, 31 and 18? (a) 20 (b) 23 (c) 22 (d) 21
  14. 14.The average of 6 numbers is 22. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 45 (b) 18 (c) 22 (d) 17
  15. 15.The average of 6 numbers is 42. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 81 (b) 42 (c) 57 (d) 18
  16. 16.What is the average of all the whole numbers from 26 to 48? (a) 37 (b) 22 (c) 38 (d) 11
  17. 17.What is the average of 24, 37, 25, 27 and 2? (a) 24 (b) 25 (c) 23 (d) 22
  18. 18.What is the average of all the whole numbers from 30 to 62? (a) 32 (b) 16 (c) 47 (d) 46
  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 22? (a) 32 (b) 22 (c) 12 (d) 24
  20. 20.What is the average of all the whole numbers from 60 to 66? (a) 63 (b) 3 (c) 64 (d) 6
  21. 21.A batter has an average of 51 runs in 9 matches. How many runs are needed in the next match to raise the average to 54? (a) 57 (b) 54 (c) 81 (d) 30
  22. 22.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) 65 (b) 55 (c) 30 (d) 40
  23. 23.The average of 5 numbers is 11. When one number is taken away, the average of the rest is 9. Which number was taken away? (a) 20 (b) 11 (c) 19 (d) 10
  24. 24.The average of 7 numbers is 24. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 30 (b) 24 (c) 7 (d) 47
  25. 25.What is the average of 39, 22, 25, 32 and 32? (a) 29 (b) 31 (c) 32 (d) 30
  26. 26.What is the average of 49, 69, 69, 47, 44 and 70? (a) 60 (b) 59 (c) 58 (d) 57
  27. 27.What is the average of 44, 55, 38, 39, 41 and 71? (a) 47 (b) 50 (c) 49 (d) 48
  28. 28.A batter has an average of 44 runs in 8 matches. How many runs are needed in the next match to raise the average to 49? (a) 49 (b) 89 (c) 54 (d) 45
  29. 29.A batter has an average of 23 runs in 7 matches. How many runs are needed in the next match to raise the average to 27? (a) 55 (b) 27 (c) 31 (d) 32
  30. 30.What is the average of all the whole numbers from 26 to 52? (a) 40 (b) 13 (c) 39 (d) 26
  31. 31.The average of 5 numbers is 42. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 31 (b) 42 (c) 87 (d) 30
  32. 32.What is the average of all the whole numbers from 58 to 72? (a) 14 (b) 7 (c) 65 (d) 66
  33. 33.The average of 4 numbers is 42. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 86 (b) 42 (c) 37 (d) 36
  34. 34.The average of 4 numbers is 48. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 36 (b) 37 (c) 100 (d) 48
  35. 35.What is the average of all the whole numbers from 11 to 27? (a) 20 (b) 16 (c) 8 (d) 19
  36. 36.What is the average of 67, 69, 62, 70, 63 and 23? (a) 61 (b) 58 (c) 60 (d) 59
  37. 37.What is the average of 78, 80, 60 and 82? (a) 76 (b) 75 (c) 100 (d) 74
  38. 38.A batter has an average of 35 runs in 9 matches. How many runs are needed in the next match to raise the average to 37? (a) 39 (b) 20 (c) 55 (d) 37
  39. 39.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 38? (a) 45 (b) 70 (c) 38 (d) 101
  40. 40.What is the average of 73, 82, 93, 88 and 59? (a) 78 (b) 81 (c) 79 (d) 80

Answer key

  1. 15
  2. 105
  3. 50
  4. 74
  5. 68
  6. 38
  7. 45
  8. 44
  9. 40
  10. 35
  11. 42
  12. 60
  13. 21
  14. 17
  15. 57
  16. 37
  17. 23
  18. 46
  19. 32
  20. 63
  21. 81
  22. 65
  23. 19
  24. 30
  25. 30
  26. 58
  27. 48
  28. 89
  29. 55
  30. 39
  31. 30
  32. 65
  33. 36
  34. 36
  35. 19
  36. 59
  37. 75
  38. 55
  39. 101
  40. 79

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