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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 781 · 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.The average of 7 numbers is 29. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 59 (b) 35 (c) 53 (d) 29
  2. 2.What is the average of 25, 19, 23 and 21? (a) 22 (b) 21 (c) 23 (d) 24
  3. 3.What is the average of 47, 46, 44, 32 and 11? (a) 37 (b) 45 (c) 36 (d) 35
  4. 4.A batter has an average of 53 runs in 9 matches. How many runs are needed in the next match to raise the average to 59? (a) 113 (b) 65 (c) 60 (d) 59
  5. 5.What is the average of 88, 77, 82, 70, 65 and 56? (a) 74 (b) 75 (c) 73 (d) 72
  6. 6.What is the average of 55, 70, 61, 58 and 71? (a) 64 (b) 63 (c) 65 (d) 62
  7. 7.What is the average of all the whole numbers from 8 to 38? (a) 30 (b) 24 (c) 15 (d) 23
  8. 8.What is the average of 23, 31, 21 and 49? (a) 31 (b) 30 (c) 32 (d) 33
  9. 9.What is the average of all the whole numbers from 59 to 97? (a) 19 (b) 79 (c) 38 (d) 78
  10. 10.The average of 4 numbers is 34. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 29 (b) 28 (c) 34 (d) 70
  11. 11.What is the average of all the whole numbers from 17 to 35? (a) 27 (b) 9 (c) 18 (d) 26
  12. 12.A batter has an average of 20 runs in 3 matches. How many runs are needed in the next match to raise the average to 28? (a) 32 (b) 36 (c) 28 (d) 52
  13. 13.What is the average of all the whole numbers from 13 to 29? (a) 21 (b) 16 (c) 22 (d) 8
  14. 14.What is the average of 28, 35, 16 and 25? (a) 26 (b) 25 (c) 28 (d) 27
  15. 15.The average of 6 numbers is 17. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 7 (b) 17 (c) 8 (d) 36
  16. 16.The average of 6 numbers is 41. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 30 (b) 66 (c) 77 (d) 41
  17. 17.The average of 7 numbers is 47. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 53 (b) 93 (c) 7 (d) 47
  18. 18.The average of 5 numbers is 24. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 24 (b) 47 (c) 28 (d) 5
  19. 19.What is the average of 48, 63, 37, 40 and 52? (a) 47 (b) 49 (c) 60 (d) 48
  20. 20.The average of 6 numbers is 23. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 23 (b) 8 (c) 9 (d) 49
  21. 21.What is the average of all the whole numbers from 38 to 56? (a) 47 (b) 48 (c) 18 (d) 9
  22. 22.What is the average of all the whole numbers from 50 to 76? (a) 64 (b) 63 (c) 26 (d) 13
  23. 23.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) 38 (c) 65 (d) 6
  24. 24.What is the average of 51, 46, 47, 50 and 51? (a) 51 (b) 48 (c) 50 (d) 49
  25. 25.What is the average of all the whole numbers from 19 to 49? (a) 34 (b) 35 (c) 30 (d) 15
  26. 26.The average of 7 numbers is 12. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 12 (b) 20 (c) 36 (d) 28
  27. 27.What is the average of all the whole numbers from 39 to 77? (a) 59 (b) 19 (c) 58 (d) 38
  28. 28.What is the average of all the whole numbers from 35 to 71? (a) 54 (b) 18 (c) 36 (d) 53
  29. 29.What is the average of 47, 42, 66, 41, 40 and 70? (a) 53 (b) 51 (c) 50 (d) 52
  30. 30.The average of 7 numbers is 48. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 35 (b) 91 (c) 78 (d) 48
  31. 31.The average of 5 numbers is 24. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 24 (b) 43 (c) 25 (d) 44
  32. 32.The average of 8 numbers is 36. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 29 (b) 36 (c) 73 (d) 30
  33. 33.What is the average of 24, 36, 16, 26 and 8? (a) 23 (b) 21 (c) 24 (d) 22
  34. 34.What is the average of all the whole numbers from 48 to 74? (a) 13 (b) 26 (c) 61 (d) 62
  35. 35.What is the average of 13, 20, 13, 42 and 47? (a) 28 (b) 29 (c) 27 (d) 26
  36. 36.What is the average of all the whole numbers from 14 to 28? (a) 22 (b) 7 (c) 21 (d) 14
  37. 37.What is the average of all the whole numbers from 44 to 76? (a) 32 (b) 16 (c) 61 (d) 60
  38. 38.The average of 6 numbers is 11. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 16 (b) 11 (c) 21 (d) 6
  39. 39.What is the average of all the whole numbers from 46 to 62? (a) 54 (b) 55 (c) 16 (d) 8
  40. 40.What is the average of 51, 41, 42, 65 and 71? (a) 56 (b) 53 (c) 54 (d) 55

Answer key

  1. 59
  2. 22
  3. 36
  4. 113
  5. 73
  6. 63
  7. 23
  8. 31
  9. 78
  10. 28
  11. 26
  12. 52
  13. 21
  14. 26
  15. 7
  16. 66
  17. 53
  18. 28
  19. 48
  20. 8
  21. 47
  22. 63
  23. 38
  24. 49
  25. 34
  26. 36
  27. 58
  28. 53
  29. 51
  30. 78
  31. 44
  32. 29
  33. 22
  34. 61
  35. 27
  36. 21
  37. 60
  38. 16
  39. 54
  40. 54

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