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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 299 · 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 5 numbers is 13. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 27 (b) 9 (c) 13 (d) 10
  2. 2.The average of 8 numbers is 40. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 61 (b) 40 (c) 77 (d) 24
  3. 3.What is the average of all the whole numbers from 29 to 57? (a) 44 (b) 28 (c) 43 (d) 14
  4. 4.The average of 8 numbers is 41. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 13 (b) 14 (c) 41 (d) 86
  5. 5.What is the average of 26, 37, 48, 43 and 31? (a) 36 (b) 39 (c) 38 (d) 37
  6. 6.The average of 7 numbers is 44. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 14 (b) 44 (c) 86 (d) 56
  7. 7.What is the average of all the whole numbers from 29 to 65? (a) 36 (b) 48 (c) 18 (d) 47
  8. 8.What is the average of all the whole numbers from 17 to 29? (a) 6 (b) 23 (c) 24 (d) 12
  9. 9.What is the average of all the whole numbers from 5 to 29? (a) 24 (b) 18 (c) 12 (d) 17
  10. 10.What is the average of all the whole numbers from 32 to 42? (a) 38 (b) 5 (c) 10 (d) 37
  11. 11.What is the average of all the whole numbers from 31 to 43? (a) 12 (b) 37 (c) 38 (d) 6
  12. 12.A batter has an average of 42 runs in 9 matches. How many runs are needed in the next match to raise the average to 44? (a) 20 (b) 46 (c) 44 (d) 62
  13. 13.The average of 4 numbers is 24. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 43 (b) 24 (c) 39 (d) 20
  14. 14.What is the average of 53, 42, 58, 62, 36 and 31? (a) 47 (b) 48 (c) 46 (d) 49
  15. 15.A batter has an average of 33 runs in 7 matches. How many runs are needed in the next match to raise the average to 40? (a) 89 (b) 40 (c) 47 (d) 56
  16. 16.What is the average of all the whole numbers from 13 to 51? (a) 38 (b) 32 (c) 33 (d) 19
  17. 17.A batter has an average of 32 runs in 7 matches. How many runs are needed in the next match to raise the average to 39? (a) 39 (b) 46 (c) 56 (d) 88
  18. 18.A batter has an average of 29 runs in 7 matches. How many runs are needed in the next match to raise the average to 32? (a) 32 (b) 24 (c) 35 (d) 53
  19. 19.What is the average of 45, 30, 38, 40, 19 and 8? (a) 29 (b) 31 (c) 30 (d) 36
  20. 20.The average of 8 numbers is 17. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 16 (b) 17 (c) 31 (d) 32
  21. 21.A batter has an average of 35 runs in 9 matches. How many runs are needed in the next match to raise the average to 37? (a) 39 (b) 55 (c) 37 (d) 20
  22. 22.The average of 6 numbers is 41. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 85 (b) 26 (c) 27 (d) 41
  23. 23.The average of 4 numbers is 46. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 41 (b) 94 (c) 40 (d) 46
  24. 24.What is the average of all the whole numbers from 47 to 83? (a) 18 (b) 66 (c) 65 (d) 36
  25. 25.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 36? (a) 35 (b) 36 (c) 64 (d) 43
  26. 26.What is the average of 62, 67, 72 and 55? (a) 63 (b) 65 (c) 66 (d) 64
  27. 27.The average of 6 numbers is 30. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 45 (b) 57 (c) 18 (d) 30
  28. 28.What is the average of 53, 79, 74 and 50? (a) 65 (b) 66 (c) 64 (d) 63
  29. 29.What is the average of all the whole numbers from 51 to 79? (a) 66 (b) 14 (c) 65 (d) 28
  30. 30.The average of 4 numbers is 31. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 26 (b) 64 (c) 25 (d) 31
  31. 31.A batter has an average of 39 runs in 8 matches. How many runs are needed in the next match to raise the average to 44? (a) 44 (b) 49 (c) 84 (d) 45
  32. 32.A batter has an average of 43 runs in 6 matches. How many runs are needed in the next match to raise the average to 49? (a) 49 (b) 55 (c) 85 (d) 42
  33. 33.The average of 7 numbers is 46. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 16 (b) 97 (c) 46 (d) 17
  34. 34.What is the average of all the whole numbers from 46 to 72? (a) 26 (b) 60 (c) 13 (d) 59
  35. 35.The average of 5 numbers is 40. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 48 (b) 78 (c) 40 (d) 10
  36. 36.What is the average of 56, 51, 52, 62 and 94? (a) 64 (b) 63 (c) 65 (d) 62
  37. 37.What is the average of 53, 80, 74, 83, 77 and 41? (a) 70 (b) 69 (c) 68 (d) 67
  38. 38.The average of 8 numbers is 39. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 40 (b) 39 (c) 73 (d) 74
  39. 39.What is the average of all the whole numbers from 52 to 58? (a) 3 (b) 55 (c) 56 (d) 6
  40. 40.What is the average of 53, 64, 66, 48 and 79? (a) 64 (b) 61 (c) 63 (d) 62

Answer key

  1. 9
  2. 61
  3. 43
  4. 13
  5. 37
  6. 56
  7. 47
  8. 23
  9. 17
  10. 37
  11. 37
  12. 62
  13. 39
  14. 47
  15. 89
  16. 32
  17. 88
  18. 53
  19. 30
  20. 31
  21. 55
  22. 26
  23. 40
  24. 65
  25. 64
  26. 64
  27. 45
  28. 64
  29. 65
  30. 25
  31. 84
  32. 85
  33. 16
  34. 59
  35. 48
  36. 63
  37. 68
  38. 74
  39. 55
  40. 62

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