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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 261 · 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 49. When one number is taken away, the average of the rest is 54. Which number was taken away? (a) 49 (b) 34 (c) 103 (d) 35
  2. 2.What is the average of 49, 38, 43, 37, 59 and 68? (a) 51 (b) 49 (c) 50 (d) 48
  3. 3.What is the average of all the whole numbers from 12 to 34? (a) 24 (b) 23 (c) 11 (d) 22
  4. 4.A batter has an average of 48 runs in 3 matches. How many runs are needed in the next match to raise the average to 54? (a) 60 (b) 54 (c) 24 (d) 72
  5. 5.What is the average of 80, 58, 75, 77 and 60? (a) 69 (b) 71 (c) 72 (d) 70
  6. 6.A batter has an average of 23 runs in 4 matches. How many runs are needed in the next match to raise the average to 31? (a) 31 (b) 39 (c) 40 (d) 63
  7. 7.What is the average of all the whole numbers from 46 to 60? (a) 54 (b) 53 (c) 14 (d) 7
  8. 8.What is the average of 27, 16, 21, 29 and 22? (a) 23 (b) 22 (c) 25 (d) 24
  9. 9.A batter has an average of 51 runs in 4 matches. How many runs are needed in the next match to raise the average to 56? (a) 61 (b) 25 (c) 76 (d) 56
  10. 10.The average of 4 numbers is 10. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 16 (b) 10 (c) 18 (d) 8
  11. 11.A batter has an average of 21 runs in 9 matches. How many runs are needed in the next match to raise the average to 27? (a) 27 (b) 60 (c) 33 (d) 81
  12. 12.What is the average of all the whole numbers from 34 to 44? (a) 10 (b) 40 (c) 5 (d) 39
  13. 13.The average of 5 numbers is 34. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 42 (b) 10 (c) 66 (d) 34
  14. 14.The average of 7 numbers is 28. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 46 (b) 53 (c) 28 (d) 21
  15. 15.The average of 7 numbers is 44. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 44 (b) 91 (c) 27 (d) 26
  16. 16.What is the average of all the whole numbers from 16 to 28? (a) 12 (b) 6 (c) 23 (d) 22
  17. 17.The average of 5 numbers is 23. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 23 (b) 25 (c) 41 (d) 43
  18. 18.What is the average of 48, 61, 52, 56 and 88? (a) 63 (b) 61 (c) 60 (d) 62
  19. 19.What is the average of 49, 37, 42, 36 and 66? (a) 47 (b) 48 (c) 46 (d) 45
  20. 20.The average of 7 numbers is 26. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 50 (b) 48 (c) 28 (d) 26
  21. 21.The average of 4 numbers is 15. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 3 (b) 4 (c) 34 (d) 15
  22. 22.What is the average of all the whole numbers from 47 to 53? (a) 6 (b) 50 (c) 51 (d) 3
  23. 23.The average of 5 numbers is 31. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 63 (b) 28 (c) 27 (d) 31
  24. 24.What is the average of all the whole numbers from 41 to 73? (a) 58 (b) 16 (c) 32 (d) 57
  25. 25.The average of 6 numbers is 32. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 30 (b) 59 (c) 57 (d) 32
  26. 26.A batter has an average of 50 runs in 4 matches. How many runs are needed in the next match to raise the average to 54? (a) 58 (b) 70 (c) 20 (d) 54
  27. 27.The average of 8 numbers is 43. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 32 (b) 43 (c) 71 (d) 82
  28. 28.What is the average of 47, 39, 47, 50 and 27? (a) 41 (b) 43 (c) 42 (d) 44
  29. 29.A batter has an average of 48 runs in 4 matches. How many runs are needed in the next match to raise the average to 52? (a) 68 (b) 56 (c) 52 (d) 20
  30. 30.A batter has an average of 55 runs in 7 matches. How many runs are needed in the next match to raise the average to 57? (a) 71 (b) 16 (c) 57 (d) 59
  31. 31.What is the average of 37, 47, 56, 39, 55 and 42? (a) 47 (b) 45 (c) 48 (d) 46
  32. 32.A batter has an average of 57 runs in 7 matches. How many runs are needed in the next match to raise the average to 61? (a) 61 (b) 32 (c) 89 (d) 65
  33. 33.What is the average of 26, 41, 29, 36 and 8? (a) 35 (b) 28 (c) 29 (d) 27
  34. 34.The average of 4 numbers is 12. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 12 (b) 19 (c) 20 (d) 27
  35. 35.The average of 5 numbers is 31. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 61 (b) 31 (c) 5 (d) 35
  36. 36.The average of 5 numbers is 18. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 38 (b) 18 (c) 11 (d) 10
  37. 37.What is the average of 58, 76, 47 and 67? (a) 63 (b) 64 (c) 61 (d) 62
  38. 38.The average of 8 numbers is 39. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 39 (b) 8 (c) 77 (d) 46
  39. 39.A batter has an average of 22 runs in 9 matches. How many runs are needed in the next match to raise the average to 25? (a) 25 (b) 52 (c) 30 (d) 28
  40. 40.The average of 4 numbers is 18. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 37 (b) 16 (c) 15 (d) 18

Answer key

  1. 34
  2. 49
  3. 23
  4. 72
  5. 70
  6. 63
  7. 53
  8. 23
  9. 76
  10. 16
  11. 81
  12. 39
  13. 42
  14. 46
  15. 26
  16. 22
  17. 43
  18. 61
  19. 46
  20. 50
  21. 3
  22. 50
  23. 27
  24. 57
  25. 57
  26. 70
  27. 71
  28. 42
  29. 68
  30. 71
  31. 46
  32. 89
  33. 28
  34. 27
  35. 35
  36. 10
  37. 62
  38. 46
  39. 52
  40. 15

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