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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 340 · 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 4 numbers is 39. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 76 (b) 8 (c) 39 (d) 45
  2. 2.The average of 6 numbers is 35. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 16 (b) 15 (c) 35 (d) 74
  3. 3.What is the average of all the whole numbers from 55 to 69? (a) 14 (b) 63 (c) 7 (d) 62
  4. 4.What is the average of 67, 61, 82 and 70? (a) 72 (b) 71 (c) 69 (d) 70
  5. 5.The average of 6 numbers is 30. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 57 (b) 18 (c) 45 (d) 30
  6. 6.What is the average of all the whole numbers from 10 to 48? (a) 19 (b) 29 (c) 38 (d) 30
  7. 7.A batter has an average of 38 runs in 8 matches. How many runs are needed in the next match to raise the average to 40? (a) 42 (b) 56 (c) 40 (d) 18
  8. 8.A batter has an average of 29 runs in 5 matches. How many runs are needed in the next match to raise the average to 35? (a) 35 (b) 65 (c) 41 (d) 36
  9. 9.The average of 6 numbers is 20. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 20 (b) 16 (c) 15 (d) 41
  10. 10.What is the average of 21, 13, 36, 16, 31 and 21? (a) 24 (b) 22 (c) 23 (d) 25
  11. 11.What is the average of 77, 61, 60 and 86? (a) 73 (b) 71 (c) 72 (d) 70
  12. 12.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) 87 (c) 26 (d) 27
  13. 13.What is the average of 35, 35, 51 and 39? (a) 39 (b) 42 (c) 41 (d) 40
  14. 14.What is the average of 30, 32, 27, 36, 25 and 30? (a) 29 (b) 30 (c) 36 (d) 31
  15. 15.The average of 5 numbers is 10. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 15 (b) 10 (c) 22 (d) 17
  16. 16.What is the average of all the whole numbers from 41 to 51? (a) 46 (b) 47 (c) 10 (d) 5
  17. 17.A batter has an average of 49 runs in 9 matches. How many runs are needed in the next match to raise the average to 56? (a) 70 (b) 63 (c) 56 (d) 119
  18. 18.What is the average of 19, 13, 33 and 31? (a) 25 (b) 32 (c) 24 (d) 23
  19. 19.What is the average of 53, 43, 51, 58, 43 and 88? (a) 58 (b) 57 (c) 56 (d) 55
  20. 20.What is the average of all the whole numbers from 57 to 95? (a) 38 (b) 77 (c) 19 (d) 76
  21. 21.A batter has an average of 58 runs in 4 matches. How many runs are needed in the next match to raise the average to 63? (a) 25 (b) 83 (c) 63 (d) 68
  22. 22.What is the average of all the whole numbers from 20 to 34? (a) 14 (b) 28 (c) 27 (d) 7
  23. 23.What is the average of all the whole numbers from 17 to 27? (a) 22 (b) 5 (c) 10 (d) 23
  24. 24.What is the average of all the whole numbers from 13 to 19? (a) 3 (b) 17 (c) 6 (d) 16
  25. 25.What is the average of 35, 22, 22, 29 and 72? (a) 36 (b) 45 (c) 37 (d) 35
  26. 26.What is the average of all the whole numbers from 47 to 57? (a) 5 (b) 10 (c) 53 (d) 52
  27. 27.What is the average of all the whole numbers from 44 to 54? (a) 10 (b) 50 (c) 49 (d) 5
  28. 28.What is the average of all the whole numbers from 7 to 37? (a) 30 (b) 15 (c) 23 (d) 22
  29. 29.The average of 7 numbers is 43. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 73 (b) 35 (c) 43 (d) 81
  30. 30.What is the average of 48, 65, 39, 57, 66 and 31? (a) 51 (b) 52 (c) 53 (d) 50
  31. 31.The average of 5 numbers is 39. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 39 (b) 31 (c) 32 (d) 80
  32. 32.What is the average of 64, 39, 65 and 32? (a) 51 (b) 50 (c) 49 (d) 52
  33. 33.The average of 5 numbers is 44. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 85 (b) 56 (c) 44 (d) 15
  34. 34.The average of 7 numbers is 28. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 60 (b) 4 (c) 28 (d) 5
  35. 35.What is the average of 71, 64, 53 and 76? (a) 88 (b) 66 (c) 67 (d) 65
  36. 36.A batter has an average of 44 runs in 4 matches. How many runs are needed in the next match to raise the average to 46? (a) 48 (b) 10 (c) 46 (d) 54
  37. 37.The average of 5 numbers is 21. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 43 (b) 17 (c) 18 (d) 21
  38. 38.The average of 5 numbers is 48. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 92 (b) 20 (c) 48 (d) 64
  39. 39.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) 25 (b) 43 (c) 24 (d) 44
  40. 40.What is the average of all the whole numbers from 19 to 27? (a) 24 (b) 4 (c) 8 (d) 23

Answer key

  1. 45
  2. 15
  3. 62
  4. 70
  5. 45
  6. 29
  7. 56
  8. 65
  9. 15
  10. 23
  11. 71
  12. 26
  13. 40
  14. 30
  15. 22
  16. 46
  17. 119
  18. 24
  19. 56
  20. 76
  21. 83
  22. 27
  23. 22
  24. 16
  25. 36
  26. 52
  27. 49
  28. 22
  29. 73
  30. 51
  31. 31
  32. 50
  33. 56
  34. 4
  35. 66
  36. 54
  37. 17
  38. 64
  39. 44
  40. 23

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