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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 3 · 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 21. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 5 (b) 6 (c) 46 (d) 21
  2. 2.What is the average of 64, 86, 77 and 65? (a) 73 (b) 74 (c) 75 (d) 72
  3. 3.A batter has an average of 36 runs in 4 matches. How many runs are needed in the next match to raise the average to 39? (a) 51 (b) 15 (c) 42 (d) 39
  4. 4.What is the average of 23, 10, 15, 24, 15 and 45? (a) 23 (b) 21 (c) 24 (d) 22
  5. 5.What is the average of 44, 21, 41 and 34? (a) 36 (b) 34 (c) 35 (d) 37
  6. 6.A batter has an average of 31 runs in 6 matches. How many runs are needed in the next match to raise the average to 37? (a) 73 (b) 37 (c) 43 (d) 42
  7. 7.A batter has an average of 51 runs in 7 matches. How many runs are needed in the next match to raise the average to 58? (a) 58 (b) 107 (c) 56 (d) 65
  8. 8.What is the average of all the whole numbers from 55 to 85? (a) 71 (b) 70 (c) 30 (d) 15
  9. 9.A batter has an average of 28 runs in 8 matches. How many runs are needed in the next match to raise the average to 32? (a) 64 (b) 32 (c) 36 (d) 65
  10. 10.What is the average of all the whole numbers from 18 to 28? (a) 5 (b) 23 (c) 24 (d) 10
  11. 11.What is the average of 43, 47, 40, 41, 45 and 48? (a) 43 (b) 44 (c) 45 (d) 46
  12. 12.The average of 6 numbers is 38. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 48 (b) 74 (c) 38 (d) 12
  13. 13.What is the average of 23, 27, 41, 18, 44 and 39? (a) 31 (b) 33 (c) 34 (d) 32
  14. 14.The average of 4 numbers is 15. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 31 (b) 15 (c) 12 (d) 13
  15. 15.What is the average of 44, 62, 56, 67, 46 and 55? (a) 66 (b) 55 (c) 56 (d) 54
  16. 16.A batter has an average of 23 runs in 9 matches. How many runs are needed in the next match to raise the average to 28? (a) 33 (b) 28 (c) 73 (d) 50
  17. 17.What is the average of all the whole numbers from 36 to 52? (a) 44 (b) 8 (c) 45 (d) 16
  18. 18.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 66? (a) 36 (b) 72 (c) 66 (d) 96
  19. 19.The average of 5 numbers is 45. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 89 (b) 5 (c) 45 (d) 49
  20. 20.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 60? (a) 67 (b) 60 (c) 88 (d) 35
  21. 21.What is the average of all the whole numbers from 38 to 72? (a) 56 (b) 17 (c) 55 (d) 34
  22. 22.The average of 4 numbers is 35. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 35 (b) 71 (c) 32 (d) 33
  23. 23.A batter has an average of 33 runs in 3 matches. How many runs are needed in the next match to raise the average to 37? (a) 37 (b) 16 (c) 41 (d) 49
  24. 24.What is the average of all the whole numbers from 31 to 59? (a) 45 (b) 28 (c) 46 (d) 14
  25. 25.What is the average of all the whole numbers from 53 to 91? (a) 73 (b) 72 (c) 38 (d) 19
  26. 26.A batter has an average of 39 runs in 5 matches. How many runs are needed in the next match to raise the average to 47? (a) 48 (b) 47 (c) 87 (d) 55
  27. 27.The average of 5 numbers is 47. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 95 (b) 47 (c) 44 (d) 43
  28. 28.What is the average of all the whole numbers from 46 to 52? (a) 3 (b) 50 (c) 6 (d) 49
  29. 29.What is the average of 50, 66, 60 and 32? (a) 52 (b) 53 (c) 51 (d) 54
  30. 30.What is the average of all the whole numbers from 23 to 29? (a) 26 (b) 6 (c) 27 (d) 3
  31. 31.What is the average of 35, 51, 42 and 20? (a) 36 (b) 39 (c) 37 (d) 38
  32. 32.What is the average of all the whole numbers from 43 to 71? (a) 14 (b) 57 (c) 58 (d) 28
  33. 33.What is the average of 84, 60, 70 and 86? (a) 76 (b) 75 (c) 74 (d) 100
  34. 34.The average of 4 numbers is 11. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 23 (b) 8 (c) 11 (d) 9
  35. 35.What is the average of all the whole numbers from 60 to 98? (a) 80 (b) 79 (c) 19 (d) 38
  36. 36.What is the average of all the whole numbers from 25 to 51? (a) 13 (b) 39 (c) 38 (d) 26
  37. 37.What is the average of 80, 64, 86, 75, 63 and 100? (a) 77 (b) 80 (c) 78 (d) 79
  38. 38.The average of 8 numbers is 32. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 32 (b) 40 (c) 67 (d) 59
  39. 39.The average of 4 numbers is 44. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 53 (b) 85 (c) 12 (d) 44
  40. 40.The average of 4 numbers is 28. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 28 (b) 31 (c) 55 (d) 4

Answer key

  1. 5
  2. 73
  3. 51
  4. 22
  5. 35
  6. 73
  7. 107
  8. 70
  9. 64
  10. 23
  11. 44
  12. 48
  13. 32
  14. 12
  15. 55
  16. 73
  17. 44
  18. 96
  19. 49
  20. 88
  21. 55
  22. 32
  23. 49
  24. 45
  25. 72
  26. 87
  27. 43
  28. 49
  29. 52
  30. 26
  31. 37
  32. 57
  33. 75
  34. 8
  35. 79
  36. 38
  37. 78
  38. 67
  39. 53
  40. 31

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