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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 687 · 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 51, 38, 51, 55, 47 and 58? (a) 51 (b) 49 (c) 50 (d) 60
  2. 2.The average of 6 numbers is 25. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 35 (b) 12 (c) 25 (d) 48
  3. 3.The average of 5 numbers is 38. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 20 (b) 72 (c) 54 (d) 38
  4. 4.What is the average of all the whole numbers from 37 to 55? (a) 18 (b) 47 (c) 9 (d) 46
  5. 5.What is the average of 34, 35, 39 and 84? (a) 49 (b) 47 (c) 48 (d) 64
  6. 6.A batter has an average of 24 runs in 5 matches. How many runs are needed in the next match to raise the average to 32? (a) 32 (b) 48 (c) 40 (d) 72
  7. 7.What is the average of 67, 63, 54 and 24? (a) 52 (b) 54 (c) 51 (d) 53
  8. 8.A batter has an average of 45 runs in 4 matches. How many runs are needed in the next match to raise the average to 51? (a) 57 (b) 51 (c) 75 (d) 30
  9. 9.A batter has an average of 22 runs in 8 matches. How many runs are needed in the next match to raise the average to 30? (a) 30 (b) 38 (c) 94 (d) 72
  10. 10.What is the average of all the whole numbers from 42 to 60? (a) 52 (b) 51 (c) 18 (d) 9
  11. 11.A batter has an average of 22 runs in 4 matches. How many runs are needed in the next match to raise the average to 26? (a) 20 (b) 30 (c) 26 (d) 42
  12. 12.What is the average of all the whole numbers from 23 to 45? (a) 34 (b) 35 (c) 22 (d) 11
  13. 13.What is the average of 68, 62, 43, 57 and 45? (a) 56 (b) 57 (c) 54 (d) 55
  14. 14.What is the average of all the whole numbers from 50 to 60? (a) 55 (b) 10 (c) 56 (d) 5
  15. 15.A batter has an average of 57 runs in 7 matches. How many runs are needed in the next match to raise the average to 59? (a) 61 (b) 73 (c) 59 (d) 16
  16. 16.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 27? (a) 24 (b) 31 (c) 27 (d) 47
  17. 17.The average of 5 numbers is 15. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 15 (b) 10 (c) 23 (d) 28
  18. 18.The average of 5 numbers is 45. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 49 (b) 89 (c) 5 (d) 45
  19. 19.What is the average of 27, 18, 26 and 57? (a) 33 (b) 34 (c) 32 (d) 31
  20. 20.A batter has an average of 47 runs in 9 matches. How many runs are needed in the next match to raise the average to 55? (a) 63 (b) 80 (c) 55 (d) 127
  21. 21.What is the average of 34, 34, 36 and 20? (a) 32 (b) 33 (c) 30 (d) 31
  22. 22.The average of 4 numbers is 25. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 25 (b) 52 (c) 20 (d) 19
  23. 23.What is the average of 72, 86, 87, 85, 83 and 55? (a) 77 (b) 78 (c) 79 (d) 80
  24. 24.A batter has an average of 20 runs in 3 matches. How many runs are needed in the next match to raise the average to 28? (a) 28 (b) 36 (c) 32 (d) 52
  25. 25.What is the average of all the whole numbers from 54 to 88? (a) 17 (b) 72 (c) 71 (d) 34
  26. 26.What is the average of all the whole numbers from 22 to 54? (a) 39 (b) 16 (c) 38 (d) 32
  27. 27.The average of 5 numbers is 41. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 45 (b) 41 (c) 5 (d) 81
  28. 28.What is the average of 51, 60, 36 and 49? (a) 51 (b) 50 (c) 48 (d) 49
  29. 29.What is the average of 44, 21, 16 and 35? (a) 29 (b) 28 (c) 30 (d) 31
  30. 30.The average of 4 numbers is 46. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 46 (b) 38 (c) 37 (d) 95
  31. 31.The average of 8 numbers is 34. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 34 (b) 71 (c) 14 (d) 13
  32. 32.A batter has an average of 52 runs in 5 matches. How many runs are needed in the next match to raise the average to 57? (a) 62 (b) 82 (c) 30 (d) 57
  33. 33.What is the average of all the whole numbers from 19 to 49? (a) 30 (b) 34 (c) 35 (d) 15
  34. 34.What is the average of all the whole numbers from 6 to 32? (a) 20 (b) 26 (c) 13 (d) 19
  35. 35.A batter has an average of 58 runs in 6 matches. How many runs are needed in the next match to raise the average to 64? (a) 42 (b) 100 (c) 70 (d) 64
  36. 36.A batter has an average of 46 runs in 5 matches. How many runs are needed in the next match to raise the average to 48? (a) 48 (b) 50 (c) 58 (d) 12
  37. 37.A batter has an average of 31 runs in 3 matches. How many runs are needed in the next match to raise the average to 36? (a) 41 (b) 51 (c) 36 (d) 20
  38. 38.A batter has an average of 20 runs in 6 matches. How many runs are needed in the next match to raise the average to 23? (a) 41 (b) 21 (c) 26 (d) 23
  39. 39.A batter has an average of 35 runs in 7 matches. How many runs are needed in the next match to raise the average to 43? (a) 43 (b) 51 (c) 99 (d) 64
  40. 40.What is the average of 41, 34, 31 and 14? (a) 29 (b) 40 (c) 31 (d) 30

Answer key

  1. 50
  2. 35
  3. 54
  4. 46
  5. 48
  6. 72
  7. 52
  8. 75
  9. 94
  10. 51
  11. 42
  12. 34
  13. 55
  14. 55
  15. 73
  16. 47
  17. 23
  18. 49
  19. 32
  20. 127
  21. 31
  22. 19
  23. 78
  24. 52
  25. 71
  26. 38
  27. 45
  28. 49
  29. 29
  30. 37
  31. 13
  32. 82
  33. 34
  34. 19
  35. 100
  36. 58
  37. 51
  38. 41
  39. 99
  40. 30

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