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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 403 · 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 23. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 41 (b) 58 (c) 23 (d) 40
  2. 2.The average of 6 numbers is 41. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 61 (b) 24 (c) 78 (d) 41
  3. 3.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) 28 (b) 33 (c) 73 (d) 50
  4. 4.The average of 7 numbers is 10. When one number is taken away, the average of the rest is 6. Which number was taken away? (a) 28 (b) 34 (c) 16 (d) 10
  5. 5.What is the average of 68, 54, 78, 52 and 68? (a) 65 (b) 63 (c) 64 (d) 80
  6. 6.What is the average of 52, 27, 35 and 54? (a) 42 (b) 43 (c) 41 (d) 56
  7. 7.What is the average of all the whole numbers from 48 to 66? (a) 9 (b) 18 (c) 57 (d) 58
  8. 8.What is the average of 74, 55, 76, 83 and 62? (a) 72 (b) 70 (c) 71 (d) 69
  9. 9.What is the average of all the whole numbers from 8 to 34? (a) 21 (b) 13 (c) 22 (d) 26
  10. 10.The average of 4 numbers is 44. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 50 (b) 44 (c) 86 (d) 8
  11. 11.What is the average of all the whole numbers from 43 to 73? (a) 59 (b) 15 (c) 58 (d) 30
  12. 12.The average of 4 numbers is 40. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 38 (b) 81 (c) 37 (d) 40
  13. 13.The average of 5 numbers is 45. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 88 (b) 53 (c) 45 (d) 10
  14. 14.What is the average of 73, 71, 82 and 82? (a) 76 (b) 79 (c) 78 (d) 77
  15. 15.What is the average of all the whole numbers from 34 to 64? (a) 50 (b) 30 (c) 49 (d) 15
  16. 16.The average of 7 numbers is 24. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 47 (b) 30 (c) 7 (d) 24
  17. 17.A batter has an average of 33 runs in 8 matches. How many runs are needed in the next match to raise the average to 41? (a) 49 (b) 72 (c) 105 (d) 41
  18. 18.What is the average of 42, 27, 20 and 23? (a) 29 (b) 30 (c) 27 (d) 28
  19. 19.What is the average of 34, 35, 34 and 17? (a) 29 (b) 40 (c) 31 (d) 30
  20. 20.What is the average of all the whole numbers from 16 to 34? (a) 25 (b) 9 (c) 18 (d) 26
  21. 21.The average of 8 numbers is 25. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 16 (b) 25 (c) 48 (d) 39
  22. 22.A batter has an average of 38 runs in 7 matches. How many runs are needed in the next match to raise the average to 41? (a) 62 (b) 44 (c) 41 (d) 24
  23. 23.What is the average of 19, 37, 10, 8 and 36? (a) 24 (b) 22 (c) 21 (d) 23
  24. 24.What is the average of 41, 50, 56, 41 and 67? (a) 52 (b) 50 (c) 51 (d) 53
  25. 25.What is the average of 54, 37, 54 and 39? (a) 47 (b) 48 (c) 45 (d) 46
  26. 26.The average of 4 numbers is 36. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 8 (b) 36 (c) 70 (d) 42
  27. 27.A batter has an average of 24 runs in 7 matches. How many runs are needed in the next match to raise the average to 28? (a) 57 (b) 56 (c) 28 (d) 32
  28. 28.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) 84 (d) 36
  29. 29.A batter has an average of 49 runs in 8 matches. How many runs are needed in the next match to raise the average to 55? (a) 54 (b) 55 (c) 103 (d) 61
  30. 30.What is the average of 59, 85, 79, 61 and 71? (a) 72 (b) 73 (c) 71 (d) 70
  31. 31.The average of 6 numbers is 22. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 42 (b) 32 (c) 12 (d) 22
  32. 32.A batter has an average of 46 runs in 3 matches. How many runs are needed in the next match to raise the average to 54? (a) 62 (b) 78 (c) 32 (d) 54
  33. 33.What is the average of all the whole numbers from 10 to 48? (a) 29 (b) 38 (c) 19 (d) 30
  34. 34.A batter has an average of 32 runs in 3 matches. How many runs are needed in the next match to raise the average to 40? (a) 64 (b) 32 (c) 40 (d) 48
  35. 35.What is the average of all the whole numbers from 24 to 52? (a) 38 (b) 28 (c) 14 (d) 39
  36. 36.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 29? (a) 29 (b) 40 (c) 61 (d) 37
  37. 37.What is the average of all the whole numbers from 12 to 38? (a) 26 (b) 24 (c) 25 (d) 13
  38. 38.What is the average of all the whole numbers from 59 to 69? (a) 65 (b) 10 (c) 64 (d) 5
  39. 39.What is the average of all the whole numbers from 30 to 56? (a) 43 (b) 44 (c) 13 (d) 26
  40. 40.What is the average of all the whole numbers from 23 to 35? (a) 30 (b) 29 (c) 6 (d) 12

Answer key

  1. 58
  2. 61
  3. 73
  4. 34
  5. 64
  6. 42
  7. 57
  8. 70
  9. 21
  10. 50
  11. 58
  12. 37
  13. 53
  14. 77
  15. 49
  16. 30
  17. 105
  18. 28
  19. 30
  20. 25
  21. 39
  22. 62
  23. 22
  24. 51
  25. 46
  26. 42
  27. 56
  28. 84
  29. 103
  30. 71
  31. 32
  32. 78
  33. 29
  34. 64
  35. 38
  36. 61
  37. 25
  38. 64
  39. 43
  40. 29

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