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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 819 · 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 6 numbers is 43. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 24 (b) 82 (c) 63 (d) 43
  2. 2.The average of 4 numbers is 22. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 37 (b) 39 (c) 22 (d) 20
  3. 3.What is the average of all the whole numbers from 60 to 86? (a) 13 (b) 74 (c) 26 (d) 73
  4. 4.What is the average of all the whole numbers from 9 to 17? (a) 14 (b) 13 (c) 4 (d) 8
  5. 5.What is the average of 52, 33, 52 and 51? (a) 48 (b) 47 (c) 49 (d) 46
  6. 6.A batter has an average of 30 runs in 3 matches. How many runs are needed in the next match to raise the average to 37? (a) 44 (b) 28 (c) 58 (d) 37
  7. 7.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 37? (a) 91 (b) 37 (c) 60 (d) 43
  8. 8.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) 52 (c) 20 (d) 36
  9. 9.The average of 8 numbers is 24. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 38 (b) 24 (c) 46 (d) 16
  10. 10.What is the average of all the whole numbers from 57 to 73? (a) 65 (b) 66 (c) 16 (d) 8
  11. 11.What is the average of 36, 19, 18 and 27? (a) 24 (b) 26 (c) 27 (d) 25
  12. 12.What is the average of 22, 48, 23, 36, 44 and 31? (a) 33 (b) 36 (c) 35 (d) 34
  13. 13.What is the average of 52, 61, 57, 72, 78 and 76? (a) 65 (b) 67 (c) 68 (d) 66
  14. 14.What is the average of all the whole numbers from 33 to 65? (a) 16 (b) 50 (c) 32 (d) 49
  15. 15.What is the average of all the whole numbers from 28 to 46? (a) 9 (b) 38 (c) 37 (d) 18
  16. 16.What is the average of all the whole numbers from 20 to 52? (a) 16 (b) 37 (c) 36 (d) 32
  17. 17.The average of 5 numbers is 46. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 46 (b) 20 (c) 88 (d) 62
  18. 18.What is the average of all the whole numbers from 15 to 29? (a) 14 (b) 22 (c) 7 (d) 23
  19. 19.What is the average of 38, 38, 64, 42 and 83? (a) 54 (b) 52 (c) 53 (d) 55
  20. 20.The average of 4 numbers is 16. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 16 (b) 12 (c) 25 (d) 29
  21. 21.A batter has an average of 40 runs in 4 matches. How many runs are needed in the next match to raise the average to 47? (a) 47 (b) 35 (c) 75 (d) 54
  22. 22.What is the average of 65, 57, 80 and 66? (a) 68 (b) 66 (c) 69 (d) 67
  23. 23.What is the average of all the whole numbers from 43 to 57? (a) 7 (b) 14 (c) 50 (d) 51
  24. 24.The average of 5 numbers is 26. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 38 (b) 26 (c) 15 (d) 49
  25. 25.The average of 5 numbers is 48. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 36 (b) 99 (c) 37 (d) 48
  26. 26.A batter has an average of 23 runs in 3 matches. How many runs are needed in the next match to raise the average to 31? (a) 39 (b) 32 (c) 55 (d) 31
  27. 27.A batter has an average of 24 runs in 3 matches. How many runs are needed in the next match to raise the average to 26? (a) 8 (b) 28 (c) 32 (d) 26
  28. 28.What is the average of 56, 63, 73, 49, 78 and 65? (a) 65 (b) 64 (c) 63 (d) 66
  29. 29.What is the average of 38, 50, 27, 35 and 30? (a) 35 (b) 36 (c) 37 (d) 45
  30. 30.What is the average of 49, 59, 72, 70 and 55? (a) 62 (b) 61 (c) 60 (d) 63
  31. 31.The average of 6 numbers is 47. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 42 (b) 47 (c) 95 (d) 43
  32. 32.What is the average of 69, 45, 66, 51 and 49? (a) 55 (b) 56 (c) 70 (d) 57
  33. 33.What is the average of 9, 11, 13, 7 and 70? (a) 21 (b) 24 (c) 23 (d) 22
  34. 34.What is the average of all the whole numbers from 27 to 47? (a) 20 (b) 37 (c) 38 (d) 10
  35. 35.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) 20 (b) 10 (c) 28 (d) 38
  36. 36.What is the average of 36, 29, 45 and 26? (a) 35 (b) 36 (c) 34 (d) 33
  37. 37.What is the average of all the whole numbers from 25 to 63? (a) 44 (b) 45 (c) 19 (d) 38
  38. 38.What is the average of all the whole numbers from 8 to 34? (a) 22 (b) 26 (c) 21 (d) 13
  39. 39.What is the average of 29, 39, 30 and 62? (a) 39 (b) 41 (c) 42 (d) 40
  40. 40.The average of 5 numbers is 16. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 16 (b) 28 (c) 20 (d) 32

Answer key

  1. 63
  2. 37
  3. 73
  4. 13
  5. 47
  6. 58
  7. 91
  8. 52
  9. 38
  10. 65
  11. 25
  12. 34
  13. 66
  14. 49
  15. 37
  16. 36
  17. 62
  18. 22
  19. 53
  20. 25
  21. 75
  22. 67
  23. 50
  24. 38
  25. 36
  26. 55
  27. 32
  28. 64
  29. 36
  30. 61
  31. 42
  32. 56
  33. 22
  34. 37
  35. 28
  36. 34
  37. 44
  38. 21
  39. 40
  40. 32

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