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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 103 · 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 8 numbers is 50. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 50 (b) 40 (c) 85 (d) 95
  2. 2.What is the average of 79, 62, 67 and 96? (a) 77 (b) 76 (c) 78 (d) 75
  3. 3.The average of 4 numbers is 19. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 37 (b) 4 (c) 22 (d) 19
  4. 4.What is the average of all the whole numbers from 43 to 53? (a) 49 (b) 10 (c) 48 (d) 5
  5. 5.The average of 5 numbers is 21. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 44 (b) 14 (c) 13 (d) 21
  6. 6.A batter has an average of 31 runs in 4 matches. How many runs are needed in the next match to raise the average to 36? (a) 36 (b) 56 (c) 25 (d) 41
  7. 7.A batter has an average of 52 runs in 7 matches. How many runs are needed in the next match to raise the average to 56? (a) 60 (b) 32 (c) 56 (d) 84
  8. 8.The average of 5 numbers is 39. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 20 (b) 74 (c) 39 (d) 55
  9. 9.A batter has an average of 54 runs in 9 matches. How many runs are needed in the next match to raise the average to 60? (a) 115 (b) 66 (c) 114 (d) 60
  10. 10.A batter has an average of 60 runs in 4 matches. How many runs are needed in the next match to raise the average to 64? (a) 64 (b) 80 (c) 20 (d) 68
  11. 11.What is the average of 46, 24, 43 and 27? (a) 35 (b) 36 (c) 37 (d) 34
  12. 12.What is the average of all the whole numbers from 24 to 64? (a) 40 (b) 20 (c) 45 (d) 44
  13. 13.The average of 5 numbers is 30. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 38 (b) 10 (c) 58 (d) 30
  14. 14.A batter has an average of 60 runs in 3 matches. How many runs are needed in the next match to raise the average to 62? (a) 64 (b) 8 (c) 62 (d) 68
  15. 15.The average of 8 numbers is 27. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 27 (b) 40 (c) 49 (d) 62
  16. 16.What is the average of all the whole numbers from 36 to 76? (a) 20 (b) 40 (c) 57 (d) 56
  17. 17.What is the average of 46, 42, 50, 43 and 59? (a) 47 (b) 48 (c) 60 (d) 49
  18. 18.What is the average of all the whole numbers from 10 to 24? (a) 14 (b) 7 (c) 17 (d) 18
  19. 19.What is the average of all the whole numbers from 56 to 88? (a) 73 (b) 16 (c) 72 (d) 32
  20. 20.What is the average of 44, 55, 40, 37 and 24? (a) 50 (b) 39 (c) 41 (d) 40
  21. 21.A batter has an average of 20 runs in 7 matches. How many runs are needed in the next match to raise the average to 28? (a) 28 (b) 64 (c) 36 (d) 84
  22. 22.The average of 4 numbers is 19. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 19 (b) 31 (c) 16 (d) 34
  23. 23.What is the average of 37, 22, 37 and 40? (a) 34 (b) 33 (c) 36 (d) 35
  24. 24.A batter has an average of 53 runs in 8 matches. How many runs are needed in the next match to raise the average to 56? (a) 27 (b) 56 (c) 59 (d) 80
  25. 25.What is the average of all the whole numbers from 25 to 63? (a) 19 (b) 44 (c) 38 (d) 45
  26. 26.What is the average of 81, 81, 75, 62 and 56? (a) 72 (b) 70 (c) 71 (d) 73
  27. 27.The average of 4 numbers is 34. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 63 (b) 49 (c) 20 (d) 34
  28. 28.A batter has an average of 29 runs in 5 matches. How many runs are needed in the next match to raise the average to 35? (a) 36 (b) 65 (c) 35 (d) 41
  29. 29.The average of 6 numbers is 29. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 29 (b) 59 (c) 25 (d) 24
  30. 30.A batter has an average of 22 runs in 4 matches. How many runs are needed in the next match to raise the average to 26? (a) 20 (b) 42 (c) 30 (d) 26
  31. 31.What is the average of 48, 61, 66, 57, 52 and 22? (a) 52 (b) 51 (c) 50 (d) 53
  32. 32.What is the average of all the whole numbers from 12 to 34? (a) 23 (b) 22 (c) 11 (d) 24
  33. 33.What is the average of 61, 56, 50, 47 and 56? (a) 53 (b) 54 (c) 55 (d) 56
  34. 34.What is the average of all the whole numbers from 54 to 80? (a) 13 (b) 26 (c) 68 (d) 67
  35. 35.What is the average of 49, 43, 56, 44 and 98? (a) 59 (b) 57 (c) 60 (d) 58
  36. 36.What is the average of all the whole numbers from 25 to 57? (a) 32 (b) 16 (c) 41 (d) 42
  37. 37.The average of 7 numbers is 41. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 41 (b) 23 (c) 24 (d) 85
  38. 38.The average of 6 numbers is 43. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 43 (b) 91 (c) 18 (d) 19
  39. 39.What is the average of all the whole numbers from 31 to 57? (a) 26 (b) 44 (c) 13 (d) 45
  40. 40.The average of 4 numbers is 21. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 43 (b) 19 (c) 18 (d) 21

Answer key

  1. 85
  2. 76
  3. 22
  4. 48
  5. 13
  6. 56
  7. 84
  8. 55
  9. 114
  10. 80
  11. 35
  12. 44
  13. 38
  14. 68
  15. 62
  16. 56
  17. 48
  18. 17
  19. 72
  20. 40
  21. 84
  22. 31
  23. 34
  24. 80
  25. 44
  26. 71
  27. 49
  28. 65
  29. 24
  30. 42
  31. 51
  32. 23
  33. 54
  34. 67
  35. 58
  36. 41
  37. 23
  38. 18
  39. 44
  40. 18

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