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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 270 · 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 47, 64, 46 and 63? (a) 56 (b) 55 (c) 57 (d) 54
  2. 2.What is the average of 31, 42, 31 and 8? (a) 28 (b) 30 (c) 27 (d) 29
  3. 3.The average of 6 numbers is 45. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 45 (b) 85 (c) 30 (d) 70
  4. 4.The average of 4 numbers is 18. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 18 (b) 9 (c) 39 (d) 10
  5. 5.A batter has an average of 47 runs in 3 matches. How many runs are needed in the next match to raise the average to 53? (a) 71 (b) 59 (c) 24 (d) 53
  6. 6.A batter has an average of 45 runs in 6 matches. How many runs are needed in the next match to raise the average to 52? (a) 94 (b) 59 (c) 49 (d) 52
  7. 7.What is the average of 70, 63, 59 and 100? (a) 74 (b) 72 (c) 73 (d) 75
  8. 8.The average of 8 numbers is 17. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 38 (b) 24 (c) 31 (d) 17
  9. 9.The average of 5 numbers is 30. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 42 (b) 57 (c) 15 (d) 30
  10. 10.The average of 5 numbers is 43. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 51 (b) 10 (c) 84 (d) 43
  11. 11.What is the average of all the whole numbers from 30 to 62? (a) 46 (b) 16 (c) 47 (d) 32
  12. 12.What is the average of 65, 70, 61 and 68? (a) 67 (b) 66 (c) 88 (d) 65
  13. 13.What is the average of all the whole numbers from 36 to 60? (a) 49 (b) 12 (c) 48 (d) 24
  14. 14.A batter has an average of 47 runs in 5 matches. How many runs are needed in the next match to raise the average to 50? (a) 50 (b) 18 (c) 65 (d) 53
  15. 15.What is the average of 63, 66, 65, 85 and 96? (a) 76 (b) 77 (c) 75 (d) 74
  16. 16.What is the average of all the whole numbers from 19 to 39? (a) 29 (b) 30 (c) 20 (d) 10
  17. 17.A batter has an average of 26 runs in 5 matches. How many runs are needed in the next match to raise the average to 32? (a) 36 (b) 32 (c) 62 (d) 38
  18. 18.What is the average of 26, 26, 38, 30, 38 and 52? (a) 35 (b) 42 (c) 36 (d) 34
  19. 19.What is the average of all the whole numbers from 43 to 77? (a) 34 (b) 17 (c) 60 (d) 61
  20. 20.What is the average of all the whole numbers from 36 to 42? (a) 40 (b) 6 (c) 39 (d) 3
  21. 21.What is the average of 40, 26, 54 and 36? (a) 52 (b) 39 (c) 38 (d) 40
  22. 22.What is the average of all the whole numbers from 13 to 33? (a) 10 (b) 24 (c) 23 (d) 20
  23. 23.What is the average of all the whole numbers from 43 to 79? (a) 18 (b) 61 (c) 36 (d) 62
  24. 24.What is the average of all the whole numbers from 20 to 46? (a) 26 (b) 33 (c) 13 (d) 34
  25. 25.A batter has an average of 37 runs in 8 matches. How many runs are needed in the next match to raise the average to 44? (a) 44 (b) 51 (c) 100 (d) 63
  26. 26.A batter has an average of 29 runs in 4 matches. How many runs are needed in the next match to raise the average to 33? (a) 33 (b) 20 (c) 37 (d) 49
  27. 27.What is the average of all the whole numbers from 40 to 76? (a) 36 (b) 59 (c) 58 (d) 18
  28. 28.The average of 5 numbers is 11. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 11 (b) 24 (c) 3 (d) 4
  29. 29.What is the average of 31, 28, 51, 24, 52 and 48? (a) 40 (b) 41 (c) 38 (d) 39
  30. 30.What is the average of all the whole numbers from 30 to 60? (a) 15 (b) 45 (c) 30 (d) 46
  31. 31.The average of 5 numbers is 16. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 16 (b) 31 (c) 20 (d) 5
  32. 32.What is the average of 29, 22, 50 and 43? (a) 36 (b) 35 (c) 48 (d) 37
  33. 33.What is the average of all the whole numbers from 14 to 42? (a) 28 (b) 14 (c) 29 (d) 27
  34. 34.What is the average of 60, 59, 68 and 85? (a) 67 (b) 69 (c) 68 (d) 70
  35. 35.The average of 5 numbers is 31. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 15 (b) 43 (c) 31 (d) 59
  36. 36.What is the average of 17, 42, 43, 30 and 8? (a) 35 (b) 29 (c) 28 (d) 27
  37. 37.The average of 7 numbers is 19. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 13 (b) 14 (c) 19 (d) 39
  38. 38.What is the average of 10, 24, 36, 18, 8 and 30? (a) 20 (b) 21 (c) 23 (d) 22
  39. 39.The average of 7 numbers is 31. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 31 (b) 58 (c) 55 (d) 28
  40. 40.The average of 8 numbers is 15. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 29 (b) 15 (c) 22 (d) 8

Answer key

  1. 55
  2. 28
  3. 70
  4. 9
  5. 71
  6. 94
  7. 73
  8. 38
  9. 42
  10. 51
  11. 46
  12. 66
  13. 48
  14. 65
  15. 75
  16. 29
  17. 62
  18. 35
  19. 60
  20. 39
  21. 39
  22. 23
  23. 61
  24. 33
  25. 100
  26. 49
  27. 58
  28. 3
  29. 39
  30. 45
  31. 20
  32. 36
  33. 28
  34. 68
  35. 43
  36. 28
  37. 13
  38. 21
  39. 55
  40. 22

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