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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 614 · 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 32 to 66? (a) 34 (b) 50 (c) 49 (d) 17
  2. 2.What is the average of all the whole numbers from 6 to 32? (a) 13 (b) 19 (c) 20 (d) 26
  3. 3.The average of 8 numbers is 21. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 21 (b) 15 (c) 43 (d) 14
  4. 4.The average of 4 numbers is 13. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 13 (b) 4 (c) 25 (d) 16
  5. 5.The average of 8 numbers is 42. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 40 (b) 42 (c) 77 (d) 79
  6. 6.A batter has an average of 52 runs in 8 matches. How many runs are needed in the next match to raise the average to 56? (a) 56 (b) 36 (c) 88 (d) 60
  7. 7.What is the average of 39, 54, 68, 59, 43 and 55? (a) 54 (b) 53 (c) 55 (d) 52
  8. 8.The average of 8 numbers is 20. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 41 (b) 20 (c) 14 (d) 13
  9. 9.A batter has an average of 46 runs in 3 matches. How many runs are needed in the next match to raise the average to 54? (a) 32 (b) 78 (c) 54 (d) 62
  10. 10.A batter has an average of 57 runs in 6 matches. How many runs are needed in the next match to raise the average to 60? (a) 21 (b) 63 (c) 78 (d) 60
  11. 11.What is the average of 66, 53, 66, 55, 39 and 33? (a) 54 (b) 52 (c) 51 (d) 53
  12. 12.A batter has an average of 28 runs in 9 matches. How many runs are needed in the next match to raise the average to 33? (a) 38 (b) 50 (c) 33 (d) 78
  13. 13.A batter has an average of 26 runs in 4 matches. How many runs are needed in the next match to raise the average to 29? (a) 32 (b) 41 (c) 29 (d) 15
  14. 14.The average of 5 numbers is 49. When one number is taken away, the average of the rest is 50. Which number was taken away? (a) 49 (b) 99 (c) 45 (d) 46
  15. 15.What is the average of all the whole numbers from 16 to 44? (a) 28 (b) 14 (c) 30 (d) 31
  16. 16.What is the average of 53, 73, 73, 75 and 61? (a) 67 (b) 68 (c) 66 (d) 69
  17. 17.What is the average of 54, 74, 50 and 58? (a) 59 (b) 60 (c) 58 (d) 61
  18. 18.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 30? (a) 30 (b) 18 (c) 33 (d) 45
  19. 19.What is the average of 74, 63, 82, 66 and 90? (a) 74 (b) 75 (c) 77 (d) 76
  20. 20.What is the average of all the whole numbers from 35 to 53? (a) 45 (b) 9 (c) 18 (d) 44
  21. 21.What is the average of all the whole numbers from 6 to 42? (a) 25 (b) 36 (c) 24 (d) 18
  22. 22.The average of 7 numbers is 35. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 35 (b) 75 (c) 5 (d) 6
  23. 23.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) 12 (b) 32 (c) 24 (d) 22
  24. 24.The average of 4 numbers is 24. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 36 (b) 24 (c) 16 (d) 44
  25. 25.What is the average of 78, 51, 59, 67 and 60? (a) 62 (b) 63 (c) 64 (d) 65
  26. 26.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
  27. 27.What is the average of 28, 29, 27 and 24? (a) 36 (b) 27 (c) 28 (d) 26
  28. 28.What is the average of all the whole numbers from 51 to 63? (a) 12 (b) 6 (c) 58 (d) 57
  29. 29.The average of 7 numbers is 46. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 40 (b) 46 (c) 93 (d) 41
  30. 30.The average of 8 numbers is 32. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 32 (b) 4 (c) 68 (d) 5
  31. 31.The average of 5 numbers is 35. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 35 (b) 28 (c) 72 (d) 27
  32. 32.What is the average of 72, 94, 95 and 59? (a) 80 (b) 79 (c) 82 (d) 81
  33. 33.What is the average of all the whole numbers from 39 to 73? (a) 34 (b) 56 (c) 57 (d) 17
  34. 34.A batter has an average of 58 runs in 9 matches. How many runs are needed in the next match to raise the average to 61? (a) 30 (b) 61 (c) 64 (d) 88
  35. 35.A batter has an average of 44 runs in 9 matches. How many runs are needed in the next match to raise the average to 47? (a) 50 (b) 74 (c) 30 (d) 47
  36. 36.What is the average of all the whole numbers from 8 to 46? (a) 38 (b) 19 (c) 27 (d) 28
  37. 37.A batter has an average of 41 runs in 3 matches. How many runs are needed in the next match to raise the average to 43? (a) 45 (b) 43 (c) 8 (d) 49
  38. 38.What is the average of 64, 60, 55 and 65? (a) 63 (b) 60 (c) 61 (d) 62
  39. 39.What is the average of all the whole numbers from 20 to 56? (a) 36 (b) 18 (c) 38 (d) 39
  40. 40.What is the average of all the whole numbers from 8 to 20? (a) 15 (b) 12 (c) 14 (d) 6

Answer key

  1. 49
  2. 19
  3. 14
  4. 16
  5. 77
  6. 88
  7. 53
  8. 13
  9. 78
  10. 78
  11. 52
  12. 78
  13. 41
  14. 45
  15. 30
  16. 67
  17. 59
  18. 45
  19. 75
  20. 44
  21. 24
  22. 5
  23. 32
  24. 36
  25. 63
  26. 61
  27. 27
  28. 57
  29. 40
  30. 4
  31. 27
  32. 80
  33. 56
  34. 88
  35. 74
  36. 27
  37. 49
  38. 61
  39. 38
  40. 14

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