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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 413 · 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.What is the average of all the whole numbers from 15 to 47? (a) 32 (b) 30 (c) 31 (d) 16
  2. 2.What is the average of all the whole numbers from 37 to 55? (a) 9 (b) 18 (c) 47 (d) 46
  3. 3.What is the average of all the whole numbers from 48 to 76? (a) 28 (b) 14 (c) 62 (d) 63
  4. 4.The average of 4 numbers is 36. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 75 (b) 27 (c) 36 (d) 28
  5. 5.The average of 5 numbers is 25. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 47 (b) 37 (c) 25 (d) 15
  6. 6.The average of 6 numbers is 22. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 42 (b) 12 (c) 22 (d) 32
  7. 7.A batter has an average of 58 runs in 5 matches. How many runs are needed in the next match to raise the average to 60? (a) 62 (b) 70 (c) 12 (d) 60
  8. 8.A batter has an average of 56 runs in 4 matches. How many runs are needed in the next match to raise the average to 58? (a) 10 (b) 60 (c) 66 (d) 58
  9. 9.A batter has an average of 31 runs in 5 matches. How many runs are needed in the next match to raise the average to 36? (a) 41 (b) 30 (c) 36 (d) 61
  10. 10.A batter has an average of 25 runs in 6 matches. How many runs are needed in the next match to raise the average to 32? (a) 39 (b) 32 (c) 74 (d) 49
  11. 11.What is the average of 81, 67, 66 and 70? (a) 73 (b) 71 (c) 72 (d) 70
  12. 12.What is the average of all the whole numbers from 15 to 33? (a) 9 (b) 24 (c) 18 (d) 25
  13. 13.What is the average of 25, 36, 46, 27, 24 and 64? (a) 36 (b) 39 (c) 37 (d) 38
  14. 14.The average of 4 numbers is 15. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 15 (b) 33 (c) 7 (d) 6
  15. 15.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 26? (a) 26 (b) 12 (c) 29 (d) 35
  16. 16.A batter has an average of 22 runs in 9 matches. How many runs are needed in the next match to raise the average to 26? (a) 30 (b) 26 (c) 40 (d) 62
  17. 17.The average of 7 numbers is 31. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 61 (b) 37 (c) 7 (d) 31
  18. 18.What is the average of 79, 65, 62, 81, 67 and 96? (a) 90 (b) 74 (c) 76 (d) 75
  19. 19.A batter has an average of 21 runs in 6 matches. How many runs are needed in the next match to raise the average to 29? (a) 29 (b) 37 (c) 56 (d) 77
  20. 20.The average of 8 numbers is 48. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 55 (b) 8 (c) 48 (d) 95
  21. 21.The average of 4 numbers is 27. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 27 (b) 13 (c) 59 (d) 12
  22. 22.The average of 8 numbers is 45. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 45 (b) 89 (c) 52 (d) 8
  23. 23.What is the average of 49, 42, 57 and 64? (a) 52 (b) 54 (c) 53 (d) 55
  24. 24.A batter has an average of 29 runs in 7 matches. How many runs are needed in the next match to raise the average to 31? (a) 31 (b) 16 (c) 33 (d) 45
  25. 25.What is the average of 40, 26, 24, 29, 37 and 24? (a) 29 (b) 36 (c) 31 (d) 30
  26. 26.What is the average of 72, 62, 66 and 108? (a) 76 (b) 78 (c) 79 (d) 77
  27. 27.What is the average of 41, 38, 23, 30 and 53? (a) 39 (b) 38 (c) 37 (d) 36
  28. 28.What is the average of 50, 47, 30, 36 and 57? (a) 45 (b) 55 (c) 44 (d) 43
  29. 29.What is the average of 62, 42, 48 and 60? (a) 55 (b) 52 (c) 54 (d) 53
  30. 30.What is the average of all the whole numbers from 13 to 39? (a) 27 (b) 13 (c) 26 (d) 25
  31. 31.What is the average of 72, 58, 62, 61, 63 and 26? (a) 59 (b) 58 (c) 57 (d) 56
  32. 32.What is the average of all the whole numbers from 11 to 41? (a) 30 (b) 26 (c) 15 (d) 27
  33. 33.What is the average of 30, 23, 37 and 46? (a) 36 (b) 35 (c) 34 (d) 33
  34. 34.What is the average of all the whole numbers from 32 to 60? (a) 46 (b) 14 (c) 47 (d) 28
  35. 35.What is the average of 13, 26, 43, 19 and 39? (a) 29 (b) 35 (c) 27 (d) 28
  36. 36.What is the average of all the whole numbers from 31 to 37? (a) 34 (b) 3 (c) 6 (d) 35
  37. 37.The average of 5 numbers is 24. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 40 (b) 44 (c) 24 (d) 20
  38. 38.What is the average of 44, 38, 25 and 9? (a) 28 (b) 29 (c) 31 (d) 30
  39. 39.What is the average of 45, 46, 61, 56 and 57? (a) 52 (b) 55 (c) 53 (d) 54
  40. 40.The average of 5 numbers is 36. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 36 (b) 74 (c) 28 (d) 29

Answer key

  1. 31
  2. 46
  3. 62
  4. 27
  5. 37
  6. 32
  7. 70
  8. 66
  9. 61
  10. 74
  11. 71
  12. 24
  13. 37
  14. 6
  15. 35
  16. 62
  17. 37
  18. 75
  19. 77
  20. 55
  21. 12
  22. 52
  23. 53
  24. 45
  25. 30
  26. 77
  27. 37
  28. 44
  29. 53
  30. 26
  31. 57
  32. 26
  33. 34
  34. 46
  35. 28
  36. 34
  37. 40
  38. 29
  39. 53
  40. 28

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