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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 246 · 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 35. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 35 (b) 72 (c) 30 (d) 29
  2. 2.What is the average of 45, 47, 45, 56, 44 and 57? (a) 51 (b) 50 (c) 49 (d) 48
  3. 3.The average of 6 numbers is 37. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 73 (b) 42 (c) 37 (d) 6
  4. 4.A batter has an average of 57 runs in 4 matches. How many runs are needed in the next match to raise the average to 65? (a) 40 (b) 65 (c) 73 (d) 97
  5. 5.The average of 8 numbers is 44. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 8 (b) 87 (c) 44 (d) 51
  6. 6.What is the average of all the whole numbers from 46 to 58? (a) 52 (b) 12 (c) 6 (d) 53
  7. 7.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
  8. 8.What is the average of all the whole numbers from 48 to 72? (a) 24 (b) 12 (c) 61 (d) 60
  9. 9.What is the average of all the whole numbers from 60 to 98? (a) 80 (b) 79 (c) 38 (d) 19
  10. 10.What is the average of 70, 93, 83, 70 and 74? (a) 79 (b) 78 (c) 80 (d) 77
  11. 11.What is the average of all the whole numbers from 41 to 51? (a) 47 (b) 10 (c) 46 (d) 5
  12. 12.The average of 8 numbers is 50. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 64 (b) 16 (c) 98 (d) 50
  13. 13.What is the average of 48, 66, 67, 52 and 67? (a) 61 (b) 60 (c) 59 (d) 75
  14. 14.What is the average of all the whole numbers from 5 to 37? (a) 22 (b) 16 (c) 21 (d) 32
  15. 15.What is the average of 20, 39, 19 and 38? (a) 28 (b) 31 (c) 30 (d) 29
  16. 16.What is the average of all the whole numbers from 12 to 48? (a) 30 (b) 18 (c) 36 (d) 31
  17. 17.A batter has an average of 39 runs in 3 matches. How many runs are needed in the next match to raise the average to 45? (a) 45 (b) 51 (c) 24 (d) 63
  18. 18.The average of 6 numbers is 11. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 31 (b) 24 (c) 11 (d) 18
  19. 19.A batter has an average of 53 runs in 4 matches. How many runs are needed in the next match to raise the average to 57? (a) 57 (b) 73 (c) 61 (d) 20
  20. 20.What is the average of 47, 58, 58, 55, 64 and 72? (a) 61 (b) 59 (c) 58 (d) 60
  21. 21.A batter has an average of 59 runs in 8 matches. How many runs are needed in the next match to raise the average to 63? (a) 63 (b) 95 (c) 36 (d) 67
  22. 22.What is the average of all the whole numbers from 48 to 82? (a) 65 (b) 66 (c) 17 (d) 34
  23. 23.What is the average of 17, 18, 27, 21, 28 and 9? (a) 20 (b) 21 (c) 24 (d) 19
  24. 24.The average of 5 numbers is 29. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 15 (b) 29 (c) 41 (d) 55
  25. 25.What is the average of 30, 48, 39, 33 and 70? (a) 45 (b) 44 (c) 55 (d) 43
  26. 26.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 27? (a) 32 (b) 72 (c) 50 (d) 27
  27. 27.A batter has an average of 23 runs in 6 matches. How many runs are needed in the next match to raise the average to 29? (a) 29 (b) 42 (c) 65 (d) 35
  28. 28.What is the average of all the whole numbers from 23 to 59? (a) 42 (b) 18 (c) 36 (d) 41
  29. 29.The average of 4 numbers is 39. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 83 (b) 24 (c) 39 (d) 25
  30. 30.What is the average of 47, 64, 58 and 67? (a) 61 (b) 59 (c) 60 (d) 58
  31. 31.A batter has an average of 20 runs in 9 matches. How many runs are needed in the next match to raise the average to 26? (a) 60 (b) 32 (c) 80 (d) 26
  32. 32.The average of 4 numbers is 42. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 48 (b) 42 (c) 8 (d) 82
  33. 33.A batter has an average of 37 runs in 8 matches. How many runs are needed in the next match to raise the average to 39? (a) 41 (b) 18 (c) 55 (d) 39
  34. 34.The average of 5 numbers is 14. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 14 (b) 29 (c) 11 (d) 10
  35. 35.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) 15 (b) 3 (c) 34 (d) 4
  36. 36.What is the average of 37, 59, 47, 32, 47 and 54? (a) 46 (b) 47 (c) 45 (d) 48
  37. 37.What is the average of all the whole numbers from 34 to 62? (a) 49 (b) 14 (c) 48 (d) 28
  38. 38.The average of 4 numbers is 31. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 31 (b) 60 (c) 8 (d) 37
  39. 39.The average of 8 numbers is 34. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 40 (b) 34 (c) 63 (d) 69
  40. 40.What is the average of all the whole numbers from 37 to 71? (a) 34 (b) 54 (c) 17 (d) 55

Answer key

  1. 29
  2. 49
  3. 42
  4. 97
  5. 51
  6. 52
  7. 7
  8. 60
  9. 79
  10. 78
  11. 46
  12. 64
  13. 60
  14. 21
  15. 29
  16. 30
  17. 63
  18. 31
  19. 73
  20. 59
  21. 95
  22. 65
  23. 20
  24. 41
  25. 44
  26. 72
  27. 65
  28. 41
  29. 24
  30. 59
  31. 80
  32. 48
  33. 55
  34. 10
  35. 3
  36. 46
  37. 48
  38. 37
  39. 69
  40. 54

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