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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 100 · 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 14 to 28? (a) 22 (b) 21 (c) 14 (d) 7
  2. 2.What is the average of 43, 71, 51, 51 and 64? (a) 56 (b) 55 (c) 57 (d) 70
  3. 3.What is the average of 60, 64, 50, 63, 42 and 39? (a) 52 (b) 54 (c) 55 (d) 53
  4. 4.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 31? (a) 60 (b) 31 (c) 37 (d) 85
  5. 5.The average of 7 numbers is 30. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 21 (b) 57 (c) 48 (d) 30
  6. 6.What is the average of all the whole numbers from 36 to 50? (a) 44 (b) 43 (c) 7 (d) 14
  7. 7.A batter has an average of 35 runs in 4 matches. How many runs are needed in the next match to raise the average to 40? (a) 45 (b) 60 (c) 40 (d) 25
  8. 8.The average of 4 numbers is 19. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 28 (b) 19 (c) 12 (d) 35
  9. 9.The average of 7 numbers is 24. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 24 (b) 7 (c) 6 (d) 51
  10. 10.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) 65 (d) 41
  11. 11.What is the average of all the whole numbers from 15 to 53? (a) 38 (b) 35 (c) 19 (d) 34
  12. 12.What is the average of all the whole numbers from 56 to 74? (a) 66 (b) 9 (c) 65 (d) 18
  13. 13.The average of 7 numbers is 10. When one number is taken away, the average of the rest is 9. Which number was taken away? (a) 16 (b) 19 (c) 10 (d) 7
  14. 14.A batter has an average of 55 runs in 5 matches. How many runs are needed in the next match to raise the average to 60? (a) 65 (b) 85 (c) 60 (d) 30
  15. 15.What is the average of all the whole numbers from 47 to 77? (a) 62 (b) 63 (c) 15 (d) 30
  16. 16.The average of 8 numbers is 43. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 40 (b) 78 (c) 43 (d) 81
  17. 17.What is the average of all the whole numbers from 57 to 95? (a) 76 (b) 77 (c) 38 (d) 19
  18. 18.The average of 4 numbers is 41. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 41 (b) 27 (c) 26 (d) 87
  19. 19.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 47? (a) 47 (b) 54 (c) 49 (d) 89
  20. 20.The average of 8 numbers is 29. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 29 (b) 62 (c) 2 (d) 1
  21. 21.What is the average of 36, 48, 18 and 30? (a) 34 (b) 33 (c) 32 (d) 44
  22. 22.What is the average of 13, 18, 13, 9 and 67? (a) 24 (b) 30 (c) 23 (d) 25
  23. 23.What is the average of all the whole numbers from 41 to 71? (a) 57 (b) 15 (c) 30 (d) 56
  24. 24.What is the average of all the whole numbers from 11 to 49? (a) 19 (b) 38 (c) 30 (d) 31
  25. 25.What is the average of 66, 84, 84, 69, 72 and 105? (a) 96 (b) 79 (c) 81 (d) 80
  26. 26.What is the average of all the whole numbers from 55 to 73? (a) 64 (b) 18 (c) 65 (d) 9
  27. 27.What is the average of 78, 92, 65, 83, 73 and 77? (a) 77 (b) 78 (c) 80 (d) 79
  28. 28.A batter has an average of 24 runs in 4 matches. How many runs are needed in the next match to raise the average to 27? (a) 30 (b) 15 (c) 27 (d) 39
  29. 29.What is the average of all the whole numbers from 43 to 53? (a) 49 (b) 10 (c) 5 (d) 48
  30. 30.A batter has an average of 53 runs in 3 matches. How many runs are needed in the next match to raise the average to 55? (a) 57 (b) 61 (c) 55 (d) 8
  31. 31.What is the average of all the whole numbers from 44 to 58? (a) 51 (b) 14 (c) 7 (d) 52
  32. 32.What is the average of all the whole numbers from 57 to 73? (a) 65 (b) 16 (c) 66 (d) 8
  33. 33.The average of 4 numbers is 32. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 16 (b) 32 (c) 44 (d) 60
  34. 34.What is the average of 70, 65, 56 and 77? (a) 68 (b) 67 (c) 69 (d) 66
  35. 35.What is the average of all the whole numbers from 22 to 28? (a) 6 (b) 25 (c) 3 (d) 26
  36. 36.What is the average of all the whole numbers from 32 to 40? (a) 8 (b) 4 (c) 36 (d) 37
  37. 37.The average of 6 numbers is 47. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 52 (b) 6 (c) 47 (d) 93
  38. 38.What is the average of 34, 26, 31 and 25? (a) 28 (b) 31 (c) 29 (d) 30
  39. 39.The average of 6 numbers is 29. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 18 (b) 29 (c) 55 (d) 44
  40. 40.A batter has an average of 23 runs in 6 matches. How many runs are needed in the next match to raise the average to 29? (a) 29 (b) 42 (c) 35 (d) 65

Answer key

  1. 21
  2. 56
  3. 53
  4. 85
  5. 48
  6. 43
  7. 60
  8. 28
  9. 6
  10. 65
  11. 34
  12. 65
  13. 16
  14. 85
  15. 62
  16. 78
  17. 76
  18. 26
  19. 89
  20. 1
  21. 33
  22. 24
  23. 56
  24. 30
  25. 80
  26. 64
  27. 78
  28. 39
  29. 48
  30. 61
  31. 51
  32. 65
  33. 44
  34. 67
  35. 25
  36. 36
  37. 52
  38. 29
  39. 44
  40. 65

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