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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 286 · 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 8 numbers is 49. When one number is taken away, the average of the rest is 54. Which number was taken away? (a) 49 (b) 15 (c) 103 (d) 14
  2. 2.The average of 7 numbers is 38. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 26 (b) 78 (c) 27 (d) 38
  3. 3.What is the average of all the whole numbers from 34 to 58? (a) 24 (b) 47 (c) 12 (d) 46
  4. 4.The average of 4 numbers is 35. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 72 (b) 29 (c) 30 (d) 35
  5. 5.What is the average of all the whole numbers from 13 to 41? (a) 14 (b) 28 (c) 26 (d) 27
  6. 6.What is the average of 78, 72, 78, 83, 80 and 71? (a) 78 (b) 76 (c) 77 (d) 79
  7. 7.What is the average of all the whole numbers from 22 to 28? (a) 3 (b) 26 (c) 25 (d) 6
  8. 8.A batter has an average of 41 runs in 4 matches. How many runs are needed in the next match to raise the average to 46? (a) 25 (b) 66 (c) 46 (d) 51
  9. 9.What is the average of 57, 53, 71, 70, 63 and 64? (a) 64 (b) 62 (c) 63 (d) 65
  10. 10.A batter has an average of 55 runs in 4 matches. How many runs are needed in the next match to raise the average to 59? (a) 20 (b) 59 (c) 75 (d) 63
  11. 11.What is the average of all the whole numbers from 15 to 29? (a) 14 (b) 7 (c) 23 (d) 22
  12. 12.What is the average of all the whole numbers from 6 to 36? (a) 21 (b) 30 (c) 15 (d) 22
  13. 13.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 28? (a) 31 (b) 24 (c) 49 (d) 28
  14. 14.A batter has an average of 29 runs in 6 matches. How many runs are needed in the next match to raise the average to 33? (a) 33 (b) 57 (c) 28 (d) 37
  15. 15.What is the average of 67, 74, 57, 84 and 73? (a) 72 (b) 73 (c) 70 (d) 71
  16. 16.The average of 5 numbers is 28. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 28 (b) 52 (c) 44 (d) 20
  17. 17.What is the average of 33, 28, 55, 43, 40 and 41? (a) 41 (b) 39 (c) 40 (d) 48
  18. 18.The average of 4 numbers is 43. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 81 (b) 58 (c) 20 (d) 43
  19. 19.The average of 7 numbers is 17. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 17 (b) 6 (c) 36 (d) 5
  20. 20.What is the average of 64, 57, 65 and 90? (a) 70 (b) 92 (c) 69 (d) 68
  21. 21.What is the average of 55, 52, 49, 36 and 53? (a) 51 (b) 49 (c) 50 (d) 48
  22. 22.The average of 7 numbers is 19. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 8 (b) 40 (c) 7 (d) 19
  23. 23.A batter has an average of 56 runs in 3 matches. How many runs are needed in the next match to raise the average to 58? (a) 58 (b) 8 (c) 60 (d) 64
  24. 24.What is the average of all the whole numbers from 60 to 68? (a) 4 (b) 8 (c) 65 (d) 64
  25. 25.The average of 8 numbers is 47. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 47 (b) 40 (c) 41 (d) 95
  26. 26.The average of 4 numbers is 34. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 34 (b) 23 (c) 72 (d) 22
  27. 27.What is the average of 62, 57, 66, 59, 58 and 106? (a) 67 (b) 70 (c) 68 (d) 69
  28. 28.A batter has an average of 29 runs in 8 matches. How many runs are needed in the next match to raise the average to 36? (a) 43 (b) 63 (c) 92 (d) 36
  29. 29.What is the average of 23, 23, 26, 26, 23 and 101? (a) 37 (b) 36 (c) 38 (d) 39
  30. 30.What is the average of all the whole numbers from 33 to 71? (a) 52 (b) 38 (c) 53 (d) 19
  31. 31.A batter has an average of 35 runs in 5 matches. How many runs are needed in the next match to raise the average to 41? (a) 71 (b) 47 (c) 36 (d) 41
  32. 32.The average of 8 numbers is 22. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 43 (b) 41 (c) 24 (d) 22
  33. 33.A batter has an average of 20 runs in 8 matches. How many runs are needed in the next match to raise the average to 28? (a) 92 (b) 28 (c) 72 (d) 36
  34. 34.A batter has an average of 46 runs in 5 matches. How many runs are needed in the next match to raise the average to 50? (a) 50 (b) 24 (c) 70 (d) 54
  35. 35.What is the average of 19, 34, 41, 18, 15 and 35? (a) 26 (b) 27 (c) 29 (d) 28
  36. 36.What is the average of 66, 53, 59, 58 and 94? (a) 68 (b) 66 (c) 67 (d) 65
  37. 37.The average of 4 numbers is 45. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 8 (b) 88 (c) 45 (d) 51
  38. 38.The average of 5 numbers is 19. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 8 (b) 41 (c) 7 (d) 19
  39. 39.The average of 7 numbers is 11. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 35 (b) 28 (c) 18 (d) 11
  40. 40.What is the average of all the whole numbers from 38 to 78? (a) 20 (b) 58 (c) 40 (d) 59

Answer key

  1. 14
  2. 26
  3. 46
  4. 29
  5. 27
  6. 77
  7. 25
  8. 66
  9. 63
  10. 75
  11. 22
  12. 21
  13. 49
  14. 57
  15. 71
  16. 44
  17. 40
  18. 58
  19. 5
  20. 69
  21. 49
  22. 7
  23. 64
  24. 64
  25. 40
  26. 22
  27. 68
  28. 92
  29. 37
  30. 52
  31. 71
  32. 43
  33. 92
  34. 70
  35. 27
  36. 66
  37. 51
  38. 7
  39. 35
  40. 58

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