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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 483 · 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 7 numbers is 36. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 60 (b) 36 (c) 28 (d) 68
  2. 2.The average of 7 numbers is 31. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 31 (b) 63 (c) 25 (d) 26
  3. 3.What is the average of 60, 53, 37, 57 and 53? (a) 52 (b) 65 (c) 53 (d) 51
  4. 4.What is the average of all the whole numbers from 52 to 58? (a) 55 (b) 3 (c) 6 (d) 56
  5. 5.What is the average of 32, 9, 15, 24, 33 and 7? (a) 24 (b) 21 (c) 19 (d) 20
  6. 6.What is the average of all the whole numbers from 47 to 83? (a) 18 (b) 65 (c) 66 (d) 36
  7. 7.The average of 5 numbers is 24. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 12 (b) 51 (c) 24 (d) 13
  8. 8.A batter has an average of 50 runs in 6 matches. How many runs are needed in the next match to raise the average to 57? (a) 64 (b) 99 (c) 57 (d) 49
  9. 9.A batter has an average of 31 runs in 9 matches. How many runs are needed in the next match to raise the average to 33? (a) 51 (b) 33 (c) 35 (d) 20
  10. 10.What is the average of 65, 66, 79 and 70? (a) 72 (b) 69 (c) 70 (d) 71
  11. 11.What is the average of 70, 62, 65, 78 and 70? (a) 71 (b) 68 (c) 69 (d) 70
  12. 12.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 43? (a) 78 (b) 48 (c) 43 (d) 40
  13. 13.A batter has an average of 25 runs in 9 matches. How many runs are needed in the next match to raise the average to 28? (a) 30 (b) 55 (c) 31 (d) 28
  14. 14.What is the average of 59, 65, 78 and 70? (a) 69 (b) 67 (c) 70 (d) 68
  15. 15.The average of 5 numbers is 15. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 15 (b) 8 (c) 7 (d) 32
  16. 16.A batter has an average of 53 runs in 7 matches. How many runs are needed in the next match to raise the average to 56? (a) 59 (b) 56 (c) 24 (d) 77
  17. 17.What is the average of 31, 21, 38, 30 and 50? (a) 33 (b) 36 (c) 35 (d) 34
  18. 18.The average of 5 numbers is 10. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 17 (b) 18 (c) 10 (d) 19
  19. 19.The average of 8 numbers is 50. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 50 (b) 16 (c) 64 (d) 98
  20. 20.What is the average of 65, 76, 72, 73, 75 and 71? (a) 72 (b) 74 (c) 71 (d) 73
  21. 21.What is the average of 33, 13, 26 and 28? (a) 26 (b) 24 (c) 25 (d) 27
  22. 22.The average of 4 numbers is 40. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 55 (b) 75 (c) 40 (d) 20
  23. 23.What is the average of 40, 37, 39, 41 and 3? (a) 31 (b) 40 (c) 32 (d) 33
  24. 24.What is the average of 29, 49, 33 and 33? (a) 48 (b) 37 (c) 36 (d) 35
  25. 25.What is the average of all the whole numbers from 7 to 27? (a) 10 (b) 17 (c) 18 (d) 20
  26. 26.What is the average of 71, 56, 76, 58 and 84? (a) 71 (b) 69 (c) 70 (d) 68
  27. 27.What is the average of all the whole numbers from 26 to 32? (a) 29 (b) 6 (c) 30 (d) 3
  28. 28.The average of 7 numbers is 13. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 7 (b) 25 (c) 13 (d) 19
  29. 29.What is the average of 8, 24, 16 and 44? (a) 24 (b) 23 (c) 25 (d) 22
  30. 30.What is the average of 54, 42, 59, 53 and 72? (a) 57 (b) 55 (c) 56 (d) 70
  31. 31.What is the average of all the whole numbers from 58 to 66? (a) 63 (b) 62 (c) 8 (d) 4
  32. 32.What is the average of all the whole numbers from 41 to 81? (a) 62 (b) 40 (c) 61 (d) 20
  33. 33.The average of 8 numbers is 42. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 42 (b) 86 (c) 28 (d) 29
  34. 34.What is the average of 22, 37, 30, 45, 42 and 46? (a) 38 (b) 36 (c) 39 (d) 37
  35. 35.What is the average of 59, 36, 39 and 66? (a) 49 (b) 50 (c) 52 (d) 51
  36. 36.The average of 6 numbers is 34. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 19 (b) 34 (c) 20 (d) 71
  37. 37.What is the average of 48, 53, 36, 46, 51 and 36? (a) 44 (b) 45 (c) 54 (d) 46
  38. 38.The average of 5 numbers is 42. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 31 (b) 42 (c) 30 (d) 87
  39. 39.The average of 4 numbers is 44. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 30 (b) 29 (c) 44 (d) 93
  40. 40.What is the average of 27, 43, 39, 42, 23 and 54? (a) 38 (b) 39 (c) 37 (d) 40

Answer key

  1. 60
  2. 25
  3. 52
  4. 55
  5. 20
  6. 65
  7. 12
  8. 99
  9. 51
  10. 70
  11. 69
  12. 78
  13. 55
  14. 68
  15. 7
  16. 77
  17. 34
  18. 18
  19. 64
  20. 72
  21. 25
  22. 55
  23. 32
  24. 36
  25. 17
  26. 69
  27. 29
  28. 19
  29. 23
  30. 56
  31. 62
  32. 61
  33. 28
  34. 37
  35. 50
  36. 19
  37. 45
  38. 30
  39. 29
  40. 38

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