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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 971 · 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 52, 51, 52, 65, 54 and 110? (a) 64 (b) 66 (c) 63 (d) 65
  2. 2.The average of 6 numbers is 48. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 58 (b) 12 (c) 94 (d) 48
  3. 3.The average of 7 numbers is 23. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 41 (b) 35 (c) 53 (d) 23
  4. 4.What is the average of all the whole numbers from 9 to 31? (a) 11 (b) 21 (c) 22 (d) 20
  5. 5.A batter has an average of 26 runs in 3 matches. How many runs are needed in the next match to raise the average to 28? (a) 8 (b) 34 (c) 28 (d) 30
  6. 6.What is the average of 34, 32, 45, 27 and 47? (a) 37 (b) 39 (c) 38 (d) 36
  7. 7.The average of 6 numbers is 37. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 78 (b) 17 (c) 18 (d) 37
  8. 8.What is the average of 73, 65, 87 and 87? (a) 79 (b) 78 (c) 77 (d) 104
  9. 9.What is the average of 56, 61, 49, 72, 72 and 74? (a) 66 (b) 63 (c) 64 (d) 65
  10. 10.What is the average of 40, 43, 37 and 20? (a) 37 (b) 36 (c) 35 (d) 34
  11. 11.The average of 8 numbers is 36. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 70 (b) 16 (c) 50 (d) 36
  12. 12.What is the average of 50, 71, 56 and 59? (a) 59 (b) 60 (c) 58 (d) 61
  13. 13.The average of 4 numbers is 29. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 8 (b) 56 (c) 29 (d) 35
  14. 14.What is the average of 82, 61, 53, 75 and 69? (a) 69 (b) 67 (c) 68 (d) 85
  15. 15.What is the average of 41, 61, 59 and 59? (a) 56 (b) 55 (c) 57 (d) 54
  16. 16.The average of 8 numbers is 42. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 42 (b) 80 (c) 32 (d) 70
  17. 17.The average of 6 numbers is 42. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 85 (b) 37 (c) 42 (d) 38
  18. 18.What is the average of all the whole numbers from 16 to 52? (a) 35 (b) 18 (c) 36 (d) 34
  19. 19.What is the average of 65, 52, 42, 40, 55 and 70? (a) 56 (b) 53 (c) 54 (d) 55
  20. 20.The average of 4 numbers is 32. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 32 (b) 69 (c) 18 (d) 17
  21. 21.What is the average of 22, 37, 21, 25, 36 and 45? (a) 31 (b) 33 (c) 32 (d) 30
  22. 22.What is the average of 40, 56, 56, 66, 45 and 67? (a) 56 (b) 55 (c) 66 (d) 54
  23. 23.What is the average of all the whole numbers from 42 to 60? (a) 51 (b) 52 (c) 18 (d) 9
  24. 24.The average of 4 numbers is 44. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 83 (b) 44 (c) 59 (d) 20
  25. 25.What is the average of all the whole numbers from 59 to 67? (a) 8 (b) 64 (c) 63 (d) 4
  26. 26.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) 16 (b) 24 (c) 36 (d) 44
  27. 27.A batter has an average of 27 runs in 7 matches. How many runs are needed in the next match to raise the average to 33? (a) 33 (b) 75 (c) 48 (d) 39
  28. 28.What is the average of all the whole numbers from 15 to 23? (a) 8 (b) 4 (c) 20 (d) 19
  29. 29.The average of 8 numbers is 24. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 11 (b) 50 (c) 10 (d) 24
  30. 30.What is the average of all the whole numbers from 29 to 65? (a) 47 (b) 18 (c) 48 (d) 36
  31. 31.What is the average of 48, 38, 50 and 32? (a) 56 (b) 41 (c) 43 (d) 42
  32. 32.What is the average of 60, 47, 58, 57, 59 and 85? (a) 60 (b) 62 (c) 63 (d) 61
  33. 33.The average of 5 numbers is 17. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 5 (b) 6 (c) 17 (d) 37
  34. 34.The average of 5 numbers is 19. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 25 (b) 33 (c) 39 (d) 19
  35. 35.What is the average of all the whole numbers from 24 to 32? (a) 29 (b) 8 (c) 28 (d) 4
  36. 36.The average of 5 numbers is 38. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 38 (b) 50 (c) 15 (d) 73
  37. 37.What is the average of all the whole numbers from 39 to 45? (a) 43 (b) 42 (c) 6 (d) 3
  38. 38.What is the average of all the whole numbers from 7 to 43? (a) 18 (b) 36 (c) 26 (d) 25
  39. 39.A batter has an average of 50 runs in 6 matches. How many runs are needed in the next match to raise the average to 55? (a) 35 (b) 55 (c) 60 (d) 85
  40. 40.What is the average of 19, 31, 31, 23, 43 and 33? (a) 30 (b) 36 (c) 31 (d) 29

Answer key

  1. 64
  2. 58
  3. 53
  4. 20
  5. 34
  6. 37
  7. 17
  8. 78
  9. 64
  10. 35
  11. 50
  12. 59
  13. 35
  14. 68
  15. 55
  16. 70
  17. 37
  18. 34
  19. 54
  20. 17
  21. 31
  22. 55
  23. 51
  24. 59
  25. 63
  26. 36
  27. 75
  28. 19
  29. 10
  30. 47
  31. 42
  32. 61
  33. 5
  34. 39
  35. 28
  36. 50
  37. 42
  38. 25
  39. 85
  40. 30

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