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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 398 · 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 26 runs in 9 matches. How many runs are needed in the next match to raise the average to 30? (a) 30 (b) 66 (c) 40 (d) 34
  2. 2.The average of 6 numbers is 48. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 94 (b) 12 (c) 58 (d) 48
  3. 3.The average of 7 numbers is 11. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 21 (b) 11 (c) 17 (d) 7
  4. 4.The average of 6 numbers is 13. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 13 (b) 9 (c) 8 (d) 27
  5. 5.What is the average of 55, 53, 39 and 25? (a) 42 (b) 45 (c) 44 (d) 43
  6. 6.A batter has an average of 58 runs in 9 matches. How many runs are needed in the next match to raise the average to 62? (a) 62 (b) 66 (c) 40 (d) 98
  7. 7.What is the average of 59, 42, 64 and 63? (a) 76 (b) 58 (c) 56 (d) 57
  8. 8.What is the average of 6, 14, 14, 26, 14 and 46? (a) 21 (b) 20 (c) 24 (d) 19
  9. 9.What is the average of 75, 72, 71, 56 and 76? (a) 70 (b) 72 (c) 71 (d) 69
  10. 10.The average of 7 numbers is 22. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 7 (b) 28 (c) 43 (d) 22
  11. 11.What is the average of all the whole numbers from 38 to 54? (a) 46 (b) 47 (c) 8 (d) 16
  12. 12.What is the average of 68, 70, 71 and 91? (a) 76 (b) 75 (c) 74 (d) 100
  13. 13.The average of 5 numbers is 20. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 28 (b) 20 (c) 38 (d) 10
  14. 14.What is the average of all the whole numbers from 23 to 31? (a) 27 (b) 8 (c) 28 (d) 4
  15. 15.What is the average of 22, 10, 6, 26, 25 and 37? (a) 23 (b) 20 (c) 22 (d) 21
  16. 16.The average of 7 numbers is 22. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 46 (b) 28 (c) 40 (d) 22
  17. 17.What is the average of 75, 86, 73, 82, 63 and 83? (a) 76 (b) 77 (c) 79 (d) 78
  18. 18.What is the average of all the whole numbers from 50 to 66? (a) 8 (b) 58 (c) 59 (d) 16
  19. 19.The average of 4 numbers is 35. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 35 (b) 29 (c) 30 (d) 72
  20. 20.The average of 5 numbers is 43. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 24 (b) 23 (c) 43 (d) 91
  21. 21.What is the average of 22, 29, 52, 30, 23 and 66? (a) 38 (b) 36 (c) 37 (d) 39
  22. 22.The average of 8 numbers is 24. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 4 (b) 51 (c) 24 (d) 3
  23. 23.A batter has an average of 44 runs in 3 matches. How many runs are needed in the next match to raise the average to 46? (a) 52 (b) 46 (c) 8 (d) 48
  24. 24.The average of 7 numbers is 33. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 51 (b) 21 (c) 33 (d) 63
  25. 25.The average of 4 numbers is 18. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 41 (b) 4 (c) 3 (d) 18
  26. 26.The average of 5 numbers is 19. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 15 (b) 31 (c) 35 (d) 19
  27. 27.What is the average of 67, 57, 58, 66, 59 and 23? (a) 55 (b) 56 (c) 66 (d) 54
  28. 28.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) 18 (b) 17 (c) 48 (d) 23
  29. 29.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 43? (a) 115 (b) 80 (c) 43 (d) 51
  30. 30.A batter has an average of 21 runs in 8 matches. How many runs are needed in the next match to raise the average to 25? (a) 36 (b) 25 (c) 29 (d) 57
  31. 31.What is the average of 32, 41, 35, 11 and 11? (a) 27 (b) 28 (c) 26 (d) 25
  32. 32.The average of 5 numbers is 26. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 46 (b) 47 (c) 25 (d) 26
  33. 33.The average of 5 numbers is 42. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 25 (b) 42 (c) 62 (d) 79
  34. 34.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 25? (a) 41 (b) 29 (c) 25 (d) 20
  35. 35.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 42? (a) 47 (b) 72 (c) 42 (d) 35
  36. 36.What is the average of all the whole numbers from 29 to 65? (a) 18 (b) 36 (c) 48 (d) 47
  37. 37.The average of 5 numbers is 17. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 36 (b) 9 (c) 10 (d) 17
  38. 38.What is the average of all the whole numbers from 8 to 32? (a) 21 (b) 12 (c) 24 (d) 20
  39. 39.The average of 6 numbers is 42. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 81 (b) 42 (c) 57 (d) 18
  40. 40.What is the average of all the whole numbers from 31 to 65? (a) 49 (b) 34 (c) 48 (d) 17

Answer key

  1. 66
  2. 58
  3. 17
  4. 8
  5. 43
  6. 98
  7. 57
  8. 20
  9. 70
  10. 28
  11. 46
  12. 75
  13. 28
  14. 27
  15. 21
  16. 46
  17. 77
  18. 58
  19. 29
  20. 23
  21. 37
  22. 3
  23. 52
  24. 51
  25. 3
  26. 31
  27. 55
  28. 17
  29. 115
  30. 57
  31. 26
  32. 46
  33. 62
  34. 41
  35. 72
  36. 47
  37. 9
  38. 20
  39. 57
  40. 48

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