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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 629 · 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 9 to 43? (a) 26 (b) 27 (c) 17 (d) 34
  2. 2.The average of 4 numbers is 20. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 6 (b) 5 (c) 45 (d) 20
  3. 3.What is the average of 74, 61, 62, 63, 70 and 102? (a) 72 (b) 74 (c) 71 (d) 73
  4. 4.A batter has an average of 39 runs in 7 matches. How many runs are needed in the next match to raise the average to 47? (a) 47 (b) 64 (c) 103 (d) 55
  5. 5.What is the average of 30, 17, 25 and 40? (a) 29 (b) 27 (c) 28 (d) 30
  6. 6.The average of 4 numbers is 40. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 40 (b) 82 (c) 34 (d) 35
  7. 7.The average of 6 numbers is 22. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 22 (b) 6 (c) 27 (d) 43
  8. 8.The average of 8 numbers is 31. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 11 (b) 31 (c) 65 (d) 10
  9. 9.What is the average of 26, 12, 12 and 34? (a) 20 (b) 28 (c) 22 (d) 21
  10. 10.What is the average of 47, 25, 25, 22 and 41? (a) 40 (b) 32 (c) 33 (d) 31
  11. 11.A batter has an average of 56 runs in 4 matches. How many runs are needed in the next match to raise the average to 59? (a) 15 (b) 62 (c) 59 (d) 71
  12. 12.The average of 4 numbers is 32. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 8 (b) 38 (c) 32 (d) 62
  13. 13.What is the average of 23, 40, 46, 18, 32 and 33? (a) 32 (b) 34 (c) 33 (d) 31
  14. 14.The average of 7 numbers is 14. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 21 (b) 32 (c) 25 (d) 14
  15. 15.What is the average of 66, 54, 73, 57, 65 and 51? (a) 62 (b) 63 (c) 61 (d) 60
  16. 16.The average of 6 numbers is 49. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 100 (b) 40 (c) 39 (d) 49
  17. 17.What is the average of 57, 43, 31, 36 and 43? (a) 41 (b) 44 (c) 43 (d) 42
  18. 18.The average of 5 numbers is 11. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 8 (b) 23 (c) 7 (d) 11
  19. 19.What is the average of all the whole numbers from 15 to 55? (a) 35 (b) 36 (c) 20 (d) 40
  20. 20.The average of 6 numbers is 46. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 21 (b) 97 (c) 22 (d) 46
  21. 21.The average of 7 numbers is 29. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 29 (b) 56 (c) 14 (d) 41
  22. 22.What is the average of 76, 75, 77 and 36? (a) 65 (b) 67 (c) 66 (d) 88
  23. 23.A batter has an average of 48 runs in 5 matches. How many runs are needed in the next match to raise the average to 51? (a) 54 (b) 66 (c) 51 (d) 18
  24. 24.The average of 5 numbers is 37. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 73 (b) 41 (c) 37 (d) 5
  25. 25.What is the average of all the whole numbers from 40 to 70? (a) 15 (b) 30 (c) 55 (d) 56
  26. 26.A batter has an average of 24 runs in 9 matches. How many runs are needed in the next match to raise the average to 28? (a) 64 (b) 28 (c) 32 (d) 40
  27. 27.What is the average of all the whole numbers from 16 to 52? (a) 18 (b) 36 (c) 34 (d) 35
  28. 28.What is the average of 59, 59, 63, 73, 63 and 97? (a) 69 (b) 70 (c) 68 (d) 71
  29. 29.The average of 8 numbers is 34. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 27 (b) 28 (c) 69 (d) 34
  30. 30.What is the average of all the whole numbers from 49 to 55? (a) 53 (b) 52 (c) 6 (d) 3
  31. 31.What is the average of all the whole numbers from 6 to 12? (a) 3 (b) 9 (c) 10 (d) 6
  32. 32.What is the average of all the whole numbers from 35 to 57? (a) 22 (b) 46 (c) 11 (d) 47
  33. 33.A batter has an average of 25 runs in 7 matches. How many runs are needed in the next match to raise the average to 32? (a) 56 (b) 32 (c) 81 (d) 39
  34. 34.What is the average of all the whole numbers from 17 to 49? (a) 16 (b) 34 (c) 32 (d) 33
  35. 35.A batter has an average of 51 runs in 3 matches. How many runs are needed in the next match to raise the average to 55? (a) 59 (b) 16 (c) 55 (d) 67
  36. 36.What is the average of all the whole numbers from 14 to 54? (a) 20 (b) 40 (c) 35 (d) 34
  37. 37.What is the average of all the whole numbers from 52 to 76? (a) 65 (b) 64 (c) 24 (d) 12
  38. 38.The average of 8 numbers is 33. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 20 (b) 33 (c) 68 (d) 19
  39. 39.What is the average of all the whole numbers from 54 to 62? (a) 8 (b) 4 (c) 58 (d) 59
  40. 40.A batter has an average of 47 runs in 4 matches. How many runs are needed in the next match to raise the average to 55? (a) 87 (b) 55 (c) 63 (d) 40

Answer key

  1. 26
  2. 5
  3. 72
  4. 103
  5. 28
  6. 34
  7. 27
  8. 10
  9. 21
  10. 32
  11. 71
  12. 38
  13. 32
  14. 32
  15. 61
  16. 39
  17. 42
  18. 7
  19. 35
  20. 21
  21. 41
  22. 66
  23. 66
  24. 41
  25. 55
  26. 64
  27. 34
  28. 69
  29. 27
  30. 52
  31. 9
  32. 46
  33. 81
  34. 33
  35. 67
  36. 34
  37. 64
  38. 19
  39. 58
  40. 87

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