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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 230 · 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 5 numbers is 18. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 33 (b) 15 (c) 18 (d) 30
  2. 2.What is the average of 29, 18, 16, 29, 30 and 58? (a) 36 (b) 31 (c) 30 (d) 29
  3. 3.The average of 4 numbers is 47. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 47 (b) 90 (c) 59 (d) 16
  4. 4.The average of 8 numbers is 12. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 47 (b) 19 (c) 40 (d) 12
  5. 5.What is the average of 43, 42, 45, 50, 51 and 111? (a) 59 (b) 57 (c) 58 (d) 56
  6. 6.The average of 7 numbers is 27. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 9 (b) 57 (c) 10 (d) 27
  7. 7.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 41? (a) 44 (b) 15 (c) 53 (d) 41
  8. 8.What is the average of all the whole numbers from 16 to 46? (a) 30 (b) 32 (c) 15 (d) 31
  9. 9.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) 6 (b) 37 (c) 42 (d) 73
  10. 10.A batter has an average of 52 runs in 3 matches. How many runs are needed in the next match to raise the average to 58? (a) 64 (b) 76 (c) 58 (d) 24
  11. 11.What is the average of 67, 75, 81, 92 and 70? (a) 76 (b) 79 (c) 78 (d) 77
  12. 12.A batter has an average of 34 runs in 7 matches. How many runs are needed in the next match to raise the average to 42? (a) 64 (b) 42 (c) 98 (d) 50
  13. 13.What is the average of all the whole numbers from 47 to 55? (a) 51 (b) 4 (c) 8 (d) 52
  14. 14.The average of 4 numbers is 21. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 21 (b) 24 (c) 4 (d) 41
  15. 15.A batter has an average of 31 runs in 9 matches. How many runs are needed in the next match to raise the average to 34? (a) 61 (b) 34 (c) 37 (d) 30
  16. 16.The average of 5 numbers is 43. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 5 (b) 43 (c) 47 (d) 85
  17. 17.A batter has an average of 53 runs in 9 matches. How many runs are needed in the next match to raise the average to 56? (a) 56 (b) 59 (c) 83 (d) 30
  18. 18.What is the average of 41, 41, 51, 31 and 66? (a) 45 (b) 47 (c) 48 (d) 46
  19. 19.A batter has an average of 32 runs in 9 matches. How many runs are needed in the next match to raise the average to 34? (a) 34 (b) 20 (c) 36 (d) 52
  20. 20.What is the average of 40, 33, 15, 17 and 40? (a) 31 (b) 28 (c) 30 (d) 29
  21. 21.What is the average of 32, 20, 27, 39 and 42? (a) 31 (b) 32 (c) 33 (d) 40
  22. 22.What is the average of 45, 22, 21, 23, 29 and 70? (a) 36 (b) 35 (c) 42 (d) 34
  23. 23.What is the average of all the whole numbers from 13 to 53? (a) 40 (b) 33 (c) 20 (d) 34
  24. 24.The average of 5 numbers is 38. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 38 (b) 19 (c) 18 (d) 81
  25. 25.What is the average of all the whole numbers from 42 to 50? (a) 8 (b) 47 (c) 4 (d) 46
  26. 26.What is the average of 32, 54, 49, 46, 31 and 58? (a) 54 (b) 44 (c) 46 (d) 45
  27. 27.What is the average of all the whole numbers from 33 to 45? (a) 40 (b) 6 (c) 12 (d) 39
  28. 28.A batter has an average of 40 runs in 9 matches. How many runs are needed in the next match to raise the average to 44? (a) 40 (b) 80 (c) 44 (d) 48
  29. 29.The average of 6 numbers is 37. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 18 (b) 78 (c) 17 (d) 37
  30. 30.What is the average of 25, 47, 38, 20 and 45? (a) 35 (b) 34 (c) 36 (d) 37
  31. 31.The average of 5 numbers is 20. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 13 (b) 20 (c) 12 (d) 42
  32. 32.What is the average of 49, 58, 48, 71, 52 and 70? (a) 57 (b) 59 (c) 58 (d) 60
  33. 33.What is the average of 52, 41, 29 and 46? (a) 56 (b) 41 (c) 43 (d) 42
  34. 34.The average of 8 numbers is 36. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 2 (b) 77 (c) 1 (d) 36
  35. 35.A batter has an average of 22 runs in 7 matches. How many runs are needed in the next match to raise the average to 29? (a) 56 (b) 78 (c) 36 (d) 29
  36. 36.A batter has an average of 56 runs in 8 matches. How many runs are needed in the next match to raise the average to 63? (a) 119 (b) 63 (c) 70 (d) 120
  37. 37.What is the average of all the whole numbers from 40 to 74? (a) 34 (b) 57 (c) 17 (d) 58
  38. 38.What is the average of all the whole numbers from 10 to 20? (a) 5 (b) 16 (c) 10 (d) 15
  39. 39.The average of 7 numbers is 38. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 38 (b) 20 (c) 21 (d) 79
  40. 40.What is the average of all the whole numbers from 19 to 39? (a) 10 (b) 29 (c) 30 (d) 20

Answer key

  1. 30
  2. 30
  3. 59
  4. 47
  5. 57
  6. 9
  7. 53
  8. 31
  9. 42
  10. 76
  11. 77
  12. 98
  13. 51
  14. 24
  15. 61
  16. 47
  17. 83
  18. 46
  19. 52
  20. 29
  21. 32
  22. 35
  23. 33
  24. 18
  25. 46
  26. 45
  27. 39
  28. 80
  29. 17
  30. 35
  31. 12
  32. 58
  33. 42
  34. 1
  35. 78
  36. 119
  37. 57
  38. 15
  39. 20
  40. 29

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