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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 266 · 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.A batter has an average of 57 runs in 4 matches. How many runs are needed in the next match to raise the average to 59? (a) 61 (b) 59 (c) 67 (d) 10
  2. 2.A batter has an average of 51 runs in 6 matches. How many runs are needed in the next match to raise the average to 58? (a) 65 (b) 100 (c) 58 (d) 49
  3. 3.A batter has an average of 54 runs in 5 matches. How many runs are needed in the next match to raise the average to 58? (a) 24 (b) 62 (c) 78 (d) 58
  4. 4.The average of 8 numbers is 46. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 26 (b) 95 (c) 25 (d) 46
  5. 5.The average of 4 numbers is 48. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 48 (b) 63 (c) 20 (d) 91
  6. 6.What is the average of 45, 54, 35, 33, 56 and 29? (a) 44 (b) 43 (c) 42 (d) 41
  7. 7.The average of 7 numbers is 48. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 43 (b) 97 (c) 48 (d) 42
  8. 8.What is the average of 42, 37, 23 and 38? (a) 35 (b) 34 (c) 37 (d) 36
  9. 9.The average of 5 numbers is 49. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 95 (b) 49 (c) 61 (d) 15
  10. 10.What is the average of all the whole numbers from 55 to 93? (a) 74 (b) 38 (c) 75 (d) 19
  11. 11.The average of 8 numbers is 10. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 4 (b) 3 (c) 21 (d) 10
  12. 12.A batter has an average of 46 runs in 8 matches. How many runs are needed in the next match to raise the average to 49? (a) 73 (b) 27 (c) 49 (d) 52
  13. 13.What is the average of all the whole numbers from 48 to 78? (a) 15 (b) 64 (c) 63 (d) 30
  14. 14.The average of 7 numbers is 30. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 7 (b) 59 (c) 36 (d) 30
  15. 15.What is the average of all the whole numbers from 57 to 67? (a) 62 (b) 5 (c) 10 (d) 63
  16. 16.What is the average of 32, 19, 24, 36, 43 and 20? (a) 28 (b) 31 (c) 29 (d) 30
  17. 17.The average of 5 numbers is 36. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 68 (b) 36 (c) 20 (d) 52
  18. 18.What is the average of all the whole numbers from 33 to 57? (a) 45 (b) 24 (c) 46 (d) 12
  19. 19.What is the average of all the whole numbers from 9 to 41? (a) 16 (b) 26 (c) 25 (d) 32
  20. 20.The average of 6 numbers is 20. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 5 (b) 6 (c) 43 (d) 20
  21. 21.The average of 8 numbers is 46. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 46 (b) 32 (c) 88 (d) 74
  22. 22.The average of 6 numbers is 47. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 23 (b) 22 (c) 47 (d) 99
  23. 23.The average of 7 numbers is 49. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 94 (b) 28 (c) 49 (d) 73
  24. 24.The average of 5 numbers is 25. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 33 (b) 25 (c) 48 (d) 10
  25. 25.What is the average of 82, 78, 73, 62 and 50? (a) 69 (b) 71 (c) 68 (d) 70
  26. 26.What is the average of 77, 52, 51 and 84? (a) 67 (b) 66 (c) 88 (d) 65
  27. 27.What is the average of 69, 63, 59 and 25? (a) 55 (b) 72 (c) 53 (d) 54
  28. 28.What is the average of 42, 54, 31, 47, 48 and 24? (a) 41 (b) 40 (c) 43 (d) 42
  29. 29.What is the average of all the whole numbers from 10 to 20? (a) 5 (b) 16 (c) 10 (d) 15
  30. 30.The average of 4 numbers is 12. When one number is taken away, the average of the rest is 9. Which number was taken away? (a) 12 (b) 21 (c) 22 (d) 20
  31. 31.The average of 7 numbers is 35. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 64 (b) 35 (c) 66 (d) 65
  32. 32.The average of 6 numbers is 30. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 30 (b) 63 (c) 15 (d) 16
  33. 33.What is the average of 33, 51, 55, 40, 48 and 19? (a) 40 (b) 42 (c) 41 (d) 43
  34. 34.What is the average of 77, 84, 83, 59 and 47? (a) 69 (b) 71 (c) 70 (d) 72
  35. 35.What is the average of 62, 79, 77, 84, 55 and 63? (a) 69 (b) 84 (c) 71 (d) 70
  36. 36.The average of 7 numbers is 20. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 20 (b) 38 (c) 21 (d) 37
  37. 37.The average of 5 numbers is 42. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 10 (b) 42 (c) 82 (d) 50
  38. 38.A batter has an average of 28 runs in 4 matches. How many runs are needed in the next match to raise the average to 35? (a) 63 (b) 42 (c) 64 (d) 35
  39. 39.The average of 8 numbers is 29. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 57 (b) 8 (c) 36 (d) 29
  40. 40.The average of 7 numbers is 19. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 28 (b) 34 (c) 43 (d) 19

Answer key

  1. 67
  2. 100
  3. 78
  4. 25
  5. 63
  6. 42
  7. 42
  8. 35
  9. 61
  10. 74
  11. 3
  12. 73
  13. 63
  14. 36
  15. 62
  16. 29
  17. 52
  18. 45
  19. 25
  20. 5
  21. 74
  22. 22
  23. 73
  24. 33
  25. 69
  26. 66
  27. 54
  28. 41
  29. 15
  30. 21
  31. 65
  32. 15
  33. 41
  34. 70
  35. 70
  36. 38
  37. 50
  38. 63
  39. 36
  40. 43

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