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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 746 · 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 54 runs in 5 matches. How many runs are needed in the next match to raise the average to 58? (a) 58 (b) 78 (c) 24 (d) 62
  2. 2.A batter has an average of 43 runs in 3 matches. How many runs are needed in the next match to raise the average to 50? (a) 71 (b) 50 (c) 28 (d) 57
  3. 3.What is the average of all the whole numbers from 55 to 71? (a) 63 (b) 8 (c) 16 (d) 64
  4. 4.What is the average of 36, 41, 30 and 73? (a) 44 (b) 60 (c) 46 (d) 45
  5. 5.The average of 6 numbers is 14. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 9 (b) 29 (c) 14 (d) 10
  6. 6.What is the average of 70, 81, 57 and 76? (a) 72 (b) 71 (c) 73 (d) 70
  7. 7.What is the average of 33, 42, 42 and 43? (a) 42 (b) 40 (c) 41 (d) 39
  8. 8.A batter has an average of 23 runs in 5 matches. How many runs are needed in the next match to raise the average to 30? (a) 42 (b) 37 (c) 30 (d) 65
  9. 9.The average of 5 numbers is 10. When one number is taken away, the average of the rest is 6. Which number was taken away? (a) 10 (b) 20 (c) 26 (d) 16
  10. 10.What is the average of 59, 54, 31 and 36? (a) 60 (b) 46 (c) 44 (d) 45
  11. 11.What is the average of 42, 24, 21, 36, 26 and 31? (a) 29 (b) 36 (c) 31 (d) 30
  12. 12.What is the average of all the whole numbers from 55 to 89? (a) 73 (b) 17 (c) 34 (d) 72
  13. 13.The average of 8 numbers is 38. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 32 (b) 77 (c) 38 (d) 31
  14. 14.What is the average of 34, 36, 47 and 67? (a) 47 (b) 45 (c) 48 (d) 46
  15. 15.What is the average of 59, 48, 43 and 42? (a) 64 (b) 47 (c) 49 (d) 48
  16. 16.What is the average of all the whole numbers from 22 to 62? (a) 42 (b) 20 (c) 43 (d) 40
  17. 17.The average of 5 numbers is 13. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 21 (b) 33 (c) 13 (d) 25
  18. 18.What is the average of 79, 74, 60, 87, 60 and 78? (a) 72 (b) 75 (c) 74 (d) 73
  19. 19.What is the average of 10, 15, 21, 39 and 35? (a) 25 (b) 30 (c) 23 (d) 24
  20. 20.The average of 5 numbers is 22. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 22 (b) 25 (c) 39 (d) 42
  21. 21.What is the average of 38, 43, 36, 34 and 84? (a) 46 (b) 48 (c) 49 (d) 47
  22. 22.The average of 5 numbers is 24. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 24 (b) 5 (c) 53 (d) 4
  23. 23.What is the average of all the whole numbers from 14 to 20? (a) 18 (b) 3 (c) 6 (d) 17
  24. 24.The average of 4 numbers is 29. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 24 (b) 60 (c) 23 (d) 29
  25. 25.What is the average of 14, 35, 9, 33 and 14? (a) 23 (b) 22 (c) 21 (d) 20
  26. 26.The average of 6 numbers is 16. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 30 (b) 26 (c) 16 (d) 12
  27. 27.What is the average of 55, 53, 62, 66, 50 and 20? (a) 53 (b) 50 (c) 52 (d) 51
  28. 28.A batter has an average of 56 runs in 6 matches. How many runs are needed in the next match to raise the average to 58? (a) 58 (b) 60 (c) 70 (d) 14
  29. 29.What is the average of 36, 35, 38 and 47? (a) 39 (b) 40 (c) 38 (d) 52
  30. 30.The average of 7 numbers is 24. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 47 (b) 24 (c) 7 (d) 30
  31. 31.What is the average of all the whole numbers from 50 to 60? (a) 5 (b) 55 (c) 10 (d) 56
  32. 32.What is the average of all the whole numbers from 23 to 33? (a) 5 (b) 28 (c) 10 (d) 29
  33. 33.What is the average of 45, 22, 23, 24 and 61? (a) 37 (b) 34 (c) 36 (d) 35
  34. 34.The average of 7 numbers is 28. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 16 (b) 28 (c) 58 (d) 17
  35. 35.The average of 5 numbers is 21. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 20 (b) 37 (c) 21 (d) 38
  36. 36.What is the average of 28, 14, 20, 33 and 25? (a) 30 (b) 25 (c) 23 (d) 24
  37. 37.What is the average of 68, 82, 67 and 87? (a) 75 (b) 76 (c) 77 (d) 78
  38. 38.What is the average of all the whole numbers from 15 to 21? (a) 6 (b) 3 (c) 18 (d) 19
  39. 39.What is the average of all the whole numbers from 27 to 53? (a) 26 (b) 13 (c) 40 (d) 41
  40. 40.What is the average of all the whole numbers from 37 to 51? (a) 44 (b) 45 (c) 7 (d) 14

Answer key

  1. 78
  2. 71
  3. 63
  4. 45
  5. 9
  6. 71
  7. 40
  8. 65
  9. 26
  10. 45
  11. 30
  12. 72
  13. 31
  14. 46
  15. 48
  16. 42
  17. 33
  18. 73
  19. 24
  20. 42
  21. 47
  22. 4
  23. 17
  24. 23
  25. 21
  26. 26
  27. 51
  28. 70
  29. 39
  30. 30
  31. 55
  32. 28
  33. 35
  34. 16
  35. 37
  36. 24
  37. 76
  38. 18
  39. 40
  40. 44

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