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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 700 · 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.A batter has an average of 22 runs in 8 matches. How many runs are needed in the next match to raise the average to 28? (a) 34 (b) 76 (c) 54 (d) 28
  2. 2.What is the average of 18, 33, 11, 14 and 49? (a) 26 (b) 27 (c) 25 (d) 24
  3. 3.The average of 7 numbers is 23. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 6 (b) 23 (c) 49 (d) 5
  4. 4.What is the average of 85, 81, 91 and 47? (a) 78 (b) 76 (c) 77 (d) 75
  5. 5.A batter has an average of 50 runs in 3 matches. How many runs are needed in the next match to raise the average to 52? (a) 58 (b) 8 (c) 52 (d) 54
  6. 6.The average of 5 numbers is 37. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 71 (b) 15 (c) 49 (d) 37
  7. 7.What is the average of 48, 52, 57, 61, 47 and 83? (a) 60 (b) 57 (c) 58 (d) 59
  8. 8.What is the average of all the whole numbers from 54 to 92? (a) 73 (b) 38 (c) 19 (d) 74
  9. 9.What is the average of 63, 49, 53 and 83? (a) 64 (b) 63 (c) 61 (d) 62
  10. 10.What is the average of all the whole numbers from 8 to 46? (a) 28 (b) 27 (c) 19 (d) 38
  11. 11.The average of 6 numbers is 24. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 9 (b) 24 (c) 51 (d) 10
  12. 12.The average of 8 numbers is 41. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 41 (b) 69 (c) 32 (d) 78
  13. 13.A batter has an average of 45 runs in 7 matches. How many runs are needed in the next match to raise the average to 53? (a) 109 (b) 53 (c) 61 (d) 64
  14. 14.What is the average of 9, 39, 28 and 20? (a) 25 (b) 24 (c) 32 (d) 23
  15. 15.What is the average of all the whole numbers from 14 to 28? (a) 7 (b) 21 (c) 22 (d) 14
  16. 16.What is the average of all the whole numbers from 48 to 56? (a) 52 (b) 8 (c) 53 (d) 4
  17. 17.What is the average of 86, 81, 87 and 62? (a) 80 (b) 79 (c) 78 (d) 81
  18. 18.The average of 6 numbers is 12. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 37 (b) 12 (c) 30 (d) 19
  19. 19.What is the average of 30, 14, 36, 36 and 29? (a) 30 (b) 31 (c) 28 (d) 29
  20. 20.A batter has an average of 31 runs in 7 matches. How many runs are needed in the next match to raise the average to 34? (a) 55 (b) 24 (c) 34 (d) 37
  21. 21.A batter has an average of 25 runs in 6 matches. How many runs are needed in the next match to raise the average to 29? (a) 33 (b) 28 (c) 29 (d) 53
  22. 22.What is the average of all the whole numbers from 33 to 47? (a) 7 (b) 41 (c) 40 (d) 14
  23. 23.What is the average of 36, 30, 57 and 53? (a) 46 (b) 45 (c) 44 (d) 43
  24. 24.The average of 6 numbers is 21. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 11 (b) 44 (c) 12 (d) 21
  25. 25.A batter has an average of 38 runs in 8 matches. How many runs are needed in the next match to raise the average to 44? (a) 50 (b) 54 (c) 92 (d) 44
  26. 26.The average of 7 numbers is 32. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 3 (b) 69 (c) 2 (d) 32
  27. 27.What is the average of 72, 65, 49 and 58? (a) 60 (b) 63 (c) 62 (d) 61
  28. 28.What is the average of 48, 48, 53 and 99? (a) 62 (b) 64 (c) 63 (d) 61
  29. 29.What is the average of all the whole numbers from 36 to 56? (a) 20 (b) 47 (c) 10 (d) 46
  30. 30.What is the average of 42, 32, 28, 57, 31 and 68? (a) 45 (b) 44 (c) 42 (d) 43
  31. 31.What is the average of 24, 19, 14, 36 and 42? (a) 29 (b) 28 (c) 26 (d) 27
  32. 32.The average of 7 numbers is 44. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 14 (b) 86 (c) 44 (d) 56
  33. 33.A batter has an average of 32 runs in 6 matches. How many runs are needed in the next match to raise the average to 38? (a) 74 (b) 44 (c) 42 (d) 38
  34. 34.The average of 8 numbers is 25. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 52 (b) 11 (c) 25 (d) 12
  35. 35.What is the average of 39, 37, 29 and 39? (a) 48 (b) 37 (c) 35 (d) 36
  36. 36.A batter has an average of 43 runs in 7 matches. How many runs are needed in the next match to raise the average to 51? (a) 59 (b) 107 (c) 51 (d) 64
  37. 37.The average of 7 numbers is 10. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 5 (b) 4 (c) 21 (d) 10
  38. 38.The average of 5 numbers is 46. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 46 (b) 90 (c) 54 (d) 10
  39. 39.The average of 7 numbers is 36. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 36 (b) 6 (c) 7 (d) 77
  40. 40.What is the average of all the whole numbers from 47 to 83? (a) 36 (b) 18 (c) 66 (d) 65

Answer key

  1. 76
  2. 25
  3. 5
  4. 76
  5. 58
  6. 49
  7. 58
  8. 73
  9. 62
  10. 27
  11. 9
  12. 69
  13. 109
  14. 24
  15. 21
  16. 52
  17. 79
  18. 37
  19. 29
  20. 55
  21. 53
  22. 40
  23. 44
  24. 11
  25. 92
  26. 2
  27. 61
  28. 62
  29. 46
  30. 43
  31. 27
  32. 56
  33. 74
  34. 11
  35. 36
  36. 107
  37. 4
  38. 54
  39. 6
  40. 65

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