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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 89 · 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 36. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 70 (b) 36 (c) 42 (d) 8
  2. 2.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 62? (a) 25 (b) 62 (c) 67 (d) 82
  3. 3.What is the average of all the whole numbers from 15 to 33? (a) 9 (b) 25 (c) 18 (d) 24
  4. 4.A batter has an average of 24 runs in 5 matches. How many runs are needed in the next match to raise the average to 30? (a) 36 (b) 61 (c) 30 (d) 60
  5. 5.What is the average of 45, 49, 26 and 36? (a) 40 (b) 38 (c) 39 (d) 52
  6. 6.What is the average of 43, 37, 22, 40 and 18? (a) 33 (b) 31 (c) 32 (d) 40
  7. 7.What is the average of 57, 57, 81 and 77? (a) 70 (b) 67 (c) 68 (d) 69
  8. 8.What is the average of all the whole numbers from 6 to 38? (a) 16 (b) 32 (c) 22 (d) 23
  9. 9.The average of 8 numbers is 21. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 8 (b) 7 (c) 21 (d) 44
  10. 10.What is the average of 63, 66, 67 and 28? (a) 55 (b) 57 (c) 56 (d) 58
  11. 11.A batter has an average of 55 runs in 3 matches. How many runs are needed in the next match to raise the average to 60? (a) 20 (b) 60 (c) 75 (d) 65
  12. 12.What is the average of all the whole numbers from 19 to 43? (a) 12 (b) 24 (c) 31 (d) 32
  13. 13.What is the average of all the whole numbers from 52 to 64? (a) 6 (b) 58 (c) 59 (d) 12
  14. 14.The average of 6 numbers is 40. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 65 (b) 75 (c) 30 (d) 40
  15. 15.What is the average of 63, 71, 63 and 111? (a) 78 (b) 76 (c) 79 (d) 77
  16. 16.A batter has an average of 46 runs in 7 matches. How many runs are needed in the next match to raise the average to 50? (a) 78 (b) 32 (c) 50 (d) 54
  17. 17.What is the average of 56, 76, 64, 66 and 58? (a) 63 (b) 64 (c) 65 (d) 80
  18. 18.A batter has an average of 24 runs in 5 matches. How many runs are needed in the next match to raise the average to 27? (a) 27 (b) 18 (c) 42 (d) 30
  19. 19.A batter has an average of 31 runs in 4 matches. How many runs are needed in the next match to raise the average to 33? (a) 35 (b) 33 (c) 10 (d) 41
  20. 20.The average of 7 numbers is 29. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 35 (b) 29 (c) 57 (d) 7
  21. 21.A batter has an average of 47 runs in 9 matches. How many runs are needed in the next match to raise the average to 53? (a) 53 (b) 107 (c) 60 (d) 59
  22. 22.The average of 8 numbers is 49. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 97 (b) 8 (c) 49 (d) 56
  23. 23.A batter has an average of 51 runs in 5 matches. How many runs are needed in the next match to raise the average to 55? (a) 24 (b) 75 (c) 59 (d) 55
  24. 24.What is the average of all the whole numbers from 21 to 35? (a) 14 (b) 29 (c) 7 (d) 28
  25. 25.What is the average of all the whole numbers from 53 to 83? (a) 15 (b) 30 (c) 69 (d) 68
  26. 26.What is the average of all the whole numbers from 5 to 15? (a) 5 (b) 9 (c) 11 (d) 10
  27. 27.What is the average of 24, 27, 33, 6, 23 and 7? (a) 19 (b) 20 (c) 21 (d) 24
  28. 28.What is the average of 63, 42, 45, 61, 61 and 46? (a) 53 (b) 54 (c) 52 (d) 55
  29. 29.What is the average of 24, 25, 12 and 35? (a) 23 (b) 32 (c) 25 (d) 24
  30. 30.A batter has an average of 27 runs in 8 matches. How many runs are needed in the next match to raise the average to 29? (a) 31 (b) 45 (c) 18 (d) 29
  31. 31.A batter has an average of 38 runs in 4 matches. How many runs are needed in the next match to raise the average to 42? (a) 46 (b) 58 (c) 20 (d) 42
  32. 32.What is the average of 78, 60, 71 and 91? (a) 76 (b) 74 (c) 100 (d) 75
  33. 33.What is the average of 56, 81, 82, 55 and 76? (a) 71 (b) 69 (c) 72 (d) 70
  34. 34.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 48? (a) 55 (b) 35 (c) 76 (d) 48
  35. 35.The average of 4 numbers is 19. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 33 (b) 19 (c) 20 (d) 34
  36. 36.What is the average of 34, 24, 35, 24 and 63? (a) 35 (b) 37 (c) 36 (d) 45
  37. 37.The average of 6 numbers is 11. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 18 (b) 26 (c) 19 (d) 11
  38. 38.What is the average of all the whole numbers from 55 to 61? (a) 59 (b) 58 (c) 3 (d) 6
  39. 39.The average of 4 numbers is 27. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 27 (b) 16 (c) 39 (d) 50
  40. 40.What is the average of 25, 33, 40, 33 and 44? (a) 36 (b) 34 (c) 37 (d) 35

Answer key

  1. 42
  2. 82
  3. 24
  4. 60
  5. 39
  6. 32
  7. 68
  8. 22
  9. 7
  10. 56
  11. 75
  12. 31
  13. 58
  14. 65
  15. 77
  16. 78
  17. 64
  18. 42
  19. 41
  20. 35
  21. 107
  22. 56
  23. 75
  24. 28
  25. 68
  26. 10
  27. 20
  28. 53
  29. 24
  30. 45
  31. 58
  32. 75
  33. 70
  34. 76
  35. 34
  36. 36
  37. 26
  38. 58
  39. 39
  40. 35

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