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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 426 · 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 12. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 7 (b) 12 (c) 25 (d) 6
  2. 2.The average of 4 numbers is 21. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 39 (b) 12 (c) 30 (d) 21
  3. 3.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) 11 (c) 29 (d) 10
  4. 4.What is the average of all the whole numbers from 25 to 35? (a) 5 (b) 10 (c) 31 (d) 30
  5. 5.The average of 7 numbers is 26. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 26 (b) 44 (c) 49 (d) 21
  6. 6.A batter has an average of 34 runs in 8 matches. How many runs are needed in the next match to raise the average to 38? (a) 36 (b) 38 (c) 42 (d) 70
  7. 7.A batter has an average of 51 runs in 6 matches. How many runs are needed in the next match to raise the average to 59? (a) 67 (b) 59 (c) 107 (d) 56
  8. 8.The average of 6 numbers is 11. When one number is taken away, the average of the rest is 6. Which number was taken away? (a) 30 (b) 36 (c) 17 (d) 11
  9. 9.A batter has an average of 60 runs in 5 matches. How many runs are needed in the next match to raise the average to 63? (a) 18 (b) 66 (c) 63 (d) 78
  10. 10.The average of 7 numbers is 29. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 55 (b) 29 (c) 47 (d) 21
  11. 11.What is the average of 53, 53, 80, 60 and 79? (a) 65 (b) 67 (c) 64 (d) 66
  12. 12.What is the average of all the whole numbers from 30 to 54? (a) 24 (b) 12 (c) 43 (d) 42
  13. 13.A batter has an average of 59 runs in 6 matches. How many runs are needed in the next match to raise the average to 66? (a) 108 (b) 49 (c) 73 (d) 66
  14. 14.What is the average of all the whole numbers from 8 to 48? (a) 40 (b) 29 (c) 28 (d) 20
  15. 15.What is the average of 33, 18, 19, 20, 35 and 61? (a) 30 (b) 32 (c) 33 (d) 31
  16. 16.What is the average of all the whole numbers from 31 to 47? (a) 8 (b) 40 (c) 16 (d) 39
  17. 17.A batter has an average of 58 runs in 5 matches. How many runs are needed in the next match to raise the average to 65? (a) 100 (b) 65 (c) 42 (d) 72
  18. 18.What is the average of 57, 54, 76, 81 and 67? (a) 66 (b) 69 (c) 67 (d) 68
  19. 19.A batter has an average of 34 runs in 5 matches. How many runs are needed in the next match to raise the average to 41? (a) 76 (b) 42 (c) 41 (d) 48
  20. 20.A batter has an average of 53 runs in 3 matches. How many runs are needed in the next match to raise the average to 59? (a) 77 (b) 65 (c) 24 (d) 59
  21. 21.What is the average of all the whole numbers from 20 to 28? (a) 25 (b) 4 (c) 8 (d) 24
  22. 22.The average of 4 numbers is 33. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 63 (b) 42 (c) 12 (d) 33
  23. 23.What is the average of 39, 45, 45 and 51? (a) 44 (b) 46 (c) 45 (d) 60
  24. 24.The average of 4 numbers is 48. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 46 (b) 97 (c) 48 (d) 45
  25. 25.What is the average of 74, 86, 78 and 82? (a) 82 (b) 80 (c) 81 (d) 79
  26. 26.A batter has an average of 35 runs in 4 matches. How many runs are needed in the next match to raise the average to 39? (a) 20 (b) 39 (c) 55 (d) 43
  27. 27.The average of 5 numbers is 46. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 26 (b) 97 (c) 46 (d) 27
  28. 28.What is the average of all the whole numbers from 30 to 52? (a) 11 (b) 42 (c) 22 (d) 41
  29. 29.What is the average of all the whole numbers from 49 to 85? (a) 36 (b) 68 (c) 67 (d) 18
  30. 30.The average of 8 numbers is 39. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 74 (b) 32 (c) 39 (d) 67
  31. 31.A batter has an average of 35 runs in 8 matches. How many runs are needed in the next match to raise the average to 39? (a) 36 (b) 43 (c) 39 (d) 71
  32. 32.The average of 4 numbers is 14. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 14 (b) 20 (c) 26 (d) 8
  33. 33.What is the average of all the whole numbers from 5 to 37? (a) 32 (b) 16 (c) 22 (d) 21
  34. 34.A batter has an average of 35 runs in 3 matches. How many runs are needed in the next match to raise the average to 38? (a) 41 (b) 38 (c) 12 (d) 47
  35. 35.A batter has an average of 52 runs in 6 matches. How many runs are needed in the next match to raise the average to 57? (a) 62 (b) 35 (c) 57 (d) 87
  36. 36.What is the average of 83, 61, 64, 79, 67 and 102? (a) 76 (b) 77 (c) 75 (d) 78
  37. 37.What is the average of all the whole numbers from 8 to 18? (a) 10 (b) 14 (c) 5 (d) 13
  38. 38.A batter has an average of 21 runs in 4 matches. How many runs are needed in the next match to raise the average to 23? (a) 31 (b) 23 (c) 25 (d) 10
  39. 39.A batter has an average of 25 runs in 4 matches. How many runs are needed in the next match to raise the average to 30? (a) 50 (b) 25 (c) 35 (d) 30
  40. 40.A batter has an average of 53 runs in 6 matches. How many runs are needed in the next match to raise the average to 57? (a) 81 (b) 28 (c) 61 (d) 57

Answer key

  1. 6
  2. 30
  3. 10
  4. 30
  5. 44
  6. 70
  7. 107
  8. 36
  9. 78
  10. 47
  11. 65
  12. 42
  13. 108
  14. 28
  15. 31
  16. 39
  17. 100
  18. 67
  19. 76
  20. 77
  21. 24
  22. 42
  23. 45
  24. 45
  25. 80
  26. 55
  27. 26
  28. 41
  29. 67
  30. 67
  31. 71
  32. 20
  33. 21
  34. 47
  35. 87
  36. 76
  37. 13
  38. 31
  39. 50
  40. 81

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