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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 106 · 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.What is the average of all the whole numbers from 36 to 52? (a) 16 (b) 44 (c) 8 (d) 45
  2. 2.What is the average of all the whole numbers from 5 to 17? (a) 12 (b) 10 (c) 6 (d) 11
  3. 3.A batter has an average of 42 runs in 5 matches. How many runs are needed in the next match to raise the average to 44? (a) 44 (b) 12 (c) 46 (d) 54
  4. 4.What is the average of all the whole numbers from 22 to 32? (a) 28 (b) 10 (c) 27 (d) 5
  5. 5.What is the average of all the whole numbers from 24 to 52? (a) 38 (b) 28 (c) 14 (d) 39
  6. 6.A batter has an average of 31 runs in 5 matches. How many runs are needed in the next match to raise the average to 34? (a) 18 (b) 37 (c) 49 (d) 34
  7. 7.The average of 7 numbers is 25. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 25 (b) 52 (c) 14 (d) 13
  8. 8.What is the average of 52, 46, 63, 64, 43 and 74? (a) 56 (b) 58 (c) 59 (d) 57
  9. 9.What is the average of 49, 35, 36 and 36? (a) 38 (b) 39 (c) 52 (d) 40
  10. 10.What is the average of 52, 30, 36 and 62? (a) 60 (b) 44 (c) 45 (d) 46
  11. 11.What is the average of 36, 46, 52 and 38? (a) 42 (b) 43 (c) 44 (d) 45
  12. 12.What is the average of all the whole numbers from 34 to 56? (a) 46 (b) 22 (c) 11 (d) 45
  13. 13.What is the average of 19, 37, 38, 9 and 12? (a) 25 (b) 23 (c) 24 (d) 22
  14. 14.What is the average of 24, 23, 24 and 65? (a) 33 (b) 35 (c) 34 (d) 36
  15. 15.The average of 8 numbers is 38. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 73 (b) 71 (c) 40 (d) 38
  16. 16.The average of 7 numbers is 47. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 93 (b) 7 (c) 47 (d) 53
  17. 17.What is the average of all the whole numbers from 56 to 72? (a) 16 (b) 8 (c) 64 (d) 65
  18. 18.What is the average of 34, 40, 31, 57 and 63? (a) 45 (b) 47 (c) 44 (d) 46
  19. 19.The average of 5 numbers is 46. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 42 (b) 43 (c) 46 (d) 93
  20. 20.The average of 8 numbers is 36. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 75 (b) 16 (c) 15 (d) 36
  21. 21.What is the average of 91, 71, 76, 71, 89 and 58? (a) 77 (b) 78 (c) 75 (d) 76
  22. 22.The average of 4 numbers is 43. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 43 (b) 90 (c) 32 (d) 31
  23. 23.The average of 6 numbers is 27. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 27 (b) 37 (c) 12 (d) 52
  24. 24.What is the average of 39, 54, 66, 46 and 50? (a) 50 (b) 52 (c) 53 (d) 51
  25. 25.What is the average of 82, 72, 80, 53 and 48? (a) 69 (b) 67 (c) 66 (d) 68
  26. 26.The average of 5 numbers is 22. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 6 (b) 7 (c) 48 (d) 22
  27. 27.The average of 5 numbers is 43. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 43 (b) 36 (c) 88 (d) 35
  28. 28.The average of 4 numbers is 34. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 34 (b) 31 (c) 32 (d) 69
  29. 29.What is the average of 25, 46, 25 and 44? (a) 35 (b) 34 (c) 36 (d) 37
  30. 30.A batter has an average of 38 runs in 6 matches. How many runs are needed in the next match to raise the average to 41? (a) 59 (b) 44 (c) 41 (d) 21
  31. 31.The average of 6 numbers is 17. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 13 (b) 35 (c) 12 (d) 17
  32. 32.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 26? (a) 25 (b) 26 (c) 46 (d) 31
  33. 33.The average of 4 numbers is 13. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 30 (b) 1 (c) 13 (d) 2
  34. 34.What is the average of 78, 81, 81 and 28? (a) 67 (b) 68 (c) 69 (d) 66
  35. 35.The average of 6 numbers is 33. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 43 (b) 12 (c) 64 (d) 33
  36. 36.What is the average of 14, 31, 15, 15 and 60? (a) 28 (b) 29 (c) 27 (d) 26
  37. 37.What is the average of 78, 60, 77, 63 and 42? (a) 65 (b) 80 (c) 64 (d) 63
  38. 38.A batter has an average of 27 runs in 7 matches. How many runs are needed in the next match to raise the average to 30? (a) 51 (b) 24 (c) 33 (d) 30
  39. 39.A batter has an average of 22 runs in 5 matches. How many runs are needed in the next match to raise the average to 26? (a) 24 (b) 30 (c) 46 (d) 26
  40. 40.The average of 5 numbers is 20. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 35 (b) 36 (c) 20 (d) 37

Answer key

  1. 44
  2. 11
  3. 54
  4. 27
  5. 38
  6. 49
  7. 13
  8. 57
  9. 39
  10. 45
  11. 43
  12. 45
  13. 23
  14. 34
  15. 73
  16. 53
  17. 64
  18. 45
  19. 42
  20. 15
  21. 76
  22. 31
  23. 37
  24. 51
  25. 67
  26. 6
  27. 35
  28. 31
  29. 35
  30. 59
  31. 12
  32. 46
  33. 1
  34. 67
  35. 43
  36. 27
  37. 64
  38. 51
  39. 46
  40. 36

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