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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 742 · 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 6 numbers is 15. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 31 (b) 11 (c) 15 (d) 10
  2. 2.The average of 4 numbers is 19. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 25 (b) 8 (c) 19 (d) 36
  3. 3.The average of 5 numbers is 16. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 16 (b) 12 (c) 13 (d) 33
  4. 4.What is the average of all the whole numbers from 34 to 40? (a) 38 (b) 3 (c) 37 (d) 6
  5. 5.What is the average of 71, 62, 76, 80, 76 and 73? (a) 72 (b) 73 (c) 75 (d) 74
  6. 6.A batter has an average of 37 runs in 6 matches. How many runs are needed in the next match to raise the average to 45? (a) 45 (b) 93 (c) 56 (d) 53
  7. 7.What is the average of 64, 46, 70 and 64? (a) 61 (b) 63 (c) 60 (d) 62
  8. 8.The average of 5 numbers is 48. When one number is taken away, the average of the rest is 50. Which number was taken away? (a) 98 (b) 41 (c) 48 (d) 40
  9. 9.What is the average of all the whole numbers from 52 to 62? (a) 57 (b) 10 (c) 58 (d) 5
  10. 10.What is the average of all the whole numbers from 29 to 65? (a) 36 (b) 47 (c) 48 (d) 18
  11. 11.The average of 6 numbers is 39. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 35 (b) 34 (c) 79 (d) 39
  12. 12.What is the average of all the whole numbers from 31 to 37? (a) 6 (b) 3 (c) 34 (d) 35
  13. 13.The average of 7 numbers is 33. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 33 (b) 35 (c) 61 (d) 63
  14. 14.The average of 8 numbers is 33. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 62 (b) 61 (c) 33 (d) 32
  15. 15.What is the average of all the whole numbers from 7 to 45? (a) 19 (b) 26 (c) 38 (d) 27
  16. 16.The average of 5 numbers is 48. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 97 (b) 48 (c) 45 (d) 44
  17. 17.What is the average of all the whole numbers from 56 to 62? (a) 60 (b) 6 (c) 3 (d) 59
  18. 18.What is the average of 47, 52, 61 and 64? (a) 55 (b) 57 (c) 56 (d) 58
  19. 19.A batter has an average of 24 runs in 5 matches. How many runs are needed in the next match to raise the average to 26? (a) 28 (b) 26 (c) 36 (d) 12
  20. 20.The average of 6 numbers is 31. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 16 (b) 31 (c) 17 (d) 65
  21. 21.What is the average of all the whole numbers from 46 to 78? (a) 32 (b) 16 (c) 62 (d) 63
  22. 22.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
  23. 23.The average of 4 numbers is 23. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 48 (b) 17 (c) 18 (d) 23
  24. 24.The average of 6 numbers is 42. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 85 (b) 38 (c) 42 (d) 37
  25. 25.What is the average of all the whole numbers from 48 to 66? (a) 9 (b) 18 (c) 58 (d) 57
  26. 26.What is the average of 80, 57, 62 and 81? (a) 72 (b) 69 (c) 71 (d) 70
  27. 27.A batter has an average of 52 runs in 5 matches. How many runs are needed in the next match to raise the average to 54? (a) 54 (b) 64 (c) 12 (d) 56
  28. 28.What is the average of all the whole numbers from 9 to 15? (a) 6 (b) 12 (c) 3 (d) 13
  29. 29.A batter has an average of 58 runs in 5 matches. How many runs are needed in the next match to raise the average to 64? (a) 36 (b) 64 (c) 94 (d) 70
  30. 30.What is the average of 7, 18, 23, 14 and 43? (a) 23 (b) 22 (c) 20 (d) 21
  31. 31.What is the average of 41, 55, 41 and 63? (a) 51 (b) 49 (c) 50 (d) 52
  32. 32.What is the average of all the whole numbers from 7 to 27? (a) 18 (b) 10 (c) 20 (d) 17
  33. 33.A batter has an average of 23 runs in 3 matches. How many runs are needed in the next match to raise the average to 28? (a) 20 (b) 33 (c) 43 (d) 28
  34. 34.The average of 4 numbers is 15. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 4 (b) 34 (c) 3 (d) 15
  35. 35.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 55? (a) 71 (b) 57 (c) 18 (d) 55
  36. 36.What is the average of 38, 25, 43, 44 and 50? (a) 41 (b) 50 (c) 39 (d) 40
  37. 37.What is the average of all the whole numbers from 18 to 44? (a) 32 (b) 13 (c) 26 (d) 31
  38. 38.What is the average of all the whole numbers from 43 to 75? (a) 32 (b) 60 (c) 16 (d) 59
  39. 39.What is the average of 54, 45, 39, 45, 65 and 64? (a) 51 (b) 54 (c) 52 (d) 53
  40. 40.What is the average of all the whole numbers from 30 to 42? (a) 37 (b) 12 (c) 36 (d) 6

Answer key

  1. 10
  2. 25
  3. 12
  4. 37
  5. 73
  6. 93
  7. 61
  8. 40
  9. 57
  10. 47
  11. 34
  12. 34
  13. 63
  14. 61
  15. 26
  16. 44
  17. 59
  18. 56
  19. 36
  20. 16
  21. 62
  22. 6
  23. 17
  24. 37
  25. 57
  26. 70
  27. 64
  28. 12
  29. 94
  30. 21
  31. 50
  32. 17
  33. 43
  34. 3
  35. 71
  36. 40
  37. 31
  38. 59
  39. 52
  40. 36

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