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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 74 · 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 4 numbers is 21. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 21 (b) 7 (c) 47 (d) 6
  2. 2.What is the average of 68, 69, 79, 65, 65 and 86? (a) 73 (b) 74 (c) 71 (d) 72
  3. 3.What is the average of all the whole numbers from 42 to 56? (a) 50 (b) 7 (c) 49 (d) 14
  4. 4.What is the average of all the whole numbers from 12 to 38? (a) 13 (b) 26 (c) 25 (d) 24
  5. 5.What is the average of 37, 43, 32, 29, 35 and 70? (a) 41 (b) 42 (c) 40 (d) 43
  6. 6.What is the average of all the whole numbers from 37 to 71? (a) 34 (b) 17 (c) 55 (d) 54
  7. 7.A batter has an average of 51 runs in 6 matches. How many runs are needed in the next match to raise the average to 59? (a) 59 (b) 56 (c) 67 (d) 107
  8. 8.What is the average of all the whole numbers from 5 to 35? (a) 21 (b) 15 (c) 30 (d) 20
  9. 9.The average of 7 numbers is 16. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 16 (b) 10 (c) 33 (d) 11
  10. 10.What is the average of 68, 85, 85, 91 and 66? (a) 80 (b) 81 (c) 78 (d) 79
  11. 11.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 31? (a) 31 (b) 39 (c) 48 (d) 71
  12. 12.What is the average of 48, 59, 30 and 39? (a) 44 (b) 45 (c) 46 (d) 43
  13. 13.The average of 6 numbers is 42. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 42 (b) 88 (c) 22 (d) 23
  14. 14.A batter has an average of 51 runs in 9 matches. How many runs are needed in the next match to raise the average to 55? (a) 40 (b) 55 (c) 91 (d) 59
  15. 15.A batter has an average of 59 runs in 6 matches. How many runs are needed in the next match to raise the average to 64? (a) 35 (b) 64 (c) 69 (d) 94
  16. 16.The average of 7 numbers is 50. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 56 (b) 7 (c) 99 (d) 50
  17. 17.A batter has an average of 55 runs in 3 matches. How many runs are needed in the next match to raise the average to 57? (a) 8 (b) 59 (c) 57 (d) 63
  18. 18.What is the average of 94, 67, 91, 93, 72 and 63? (a) 96 (b) 79 (c) 80 (d) 81
  19. 19.What is the average of all the whole numbers from 5 to 33? (a) 20 (b) 14 (c) 28 (d) 19
  20. 20.The average of 8 numbers is 49. When one number is taken away, the average of the rest is 54. Which number was taken away? (a) 14 (b) 49 (c) 103 (d) 15
  21. 21.The average of 4 numbers is 29. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 59 (b) 27 (c) 29 (d) 26
  22. 22.What is the average of all the whole numbers from 14 to 36? (a) 11 (b) 25 (c) 26 (d) 22
  23. 23.The average of 7 numbers is 26. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 14 (b) 50 (c) 38 (d) 26
  24. 24.What is the average of 45, 49, 65 and 77? (a) 61 (b) 60 (c) 58 (d) 59
  25. 25.The average of 4 numbers is 44. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 91 (b) 35 (c) 36 (d) 44
  26. 26.The average of 4 numbers is 11. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 25 (b) 11 (c) 2 (d) 3
  27. 27.What is the average of all the whole numbers from 37 to 77? (a) 20 (b) 57 (c) 58 (d) 40
  28. 28.A batter has an average of 32 runs in 3 matches. How many runs are needed in the next match to raise the average to 34? (a) 34 (b) 36 (c) 8 (d) 40
  29. 29.The average of 6 numbers is 22. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 22 (b) 2 (c) 3 (d) 48
  30. 30.The average of 8 numbers is 47. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 47 (b) 95 (c) 41 (d) 40
  31. 31.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 41? (a) 47 (b) 95 (c) 60 (d) 41
  32. 32.What is the average of all the whole numbers from 18 to 50? (a) 32 (b) 35 (c) 16 (d) 34
  33. 33.The average of 7 numbers is 44. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 26 (b) 44 (c) 91 (d) 27
  34. 34.What is the average of all the whole numbers from 59 to 75? (a) 8 (b) 68 (c) 16 (d) 67
  35. 35.What is the average of 58, 74, 51, 52 and 75? (a) 61 (b) 63 (c) 62 (d) 64
  36. 36.What is the average of 55, 60, 70, 59, 54 and 110? (a) 67 (b) 68 (c) 69 (d) 70
  37. 37.What is the average of 71, 78, 53 and 70? (a) 69 (b) 70 (c) 68 (d) 67
  38. 38.A batter has an average of 57 runs in 3 matches. How many runs are needed in the next match to raise the average to 62? (a) 62 (b) 67 (c) 20 (d) 77
  39. 39.What is the average of all the whole numbers from 56 to 62? (a) 3 (b) 60 (c) 6 (d) 59
  40. 40.The average of 4 numbers is 20. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 12 (b) 20 (c) 43 (d) 11

Answer key

  1. 6
  2. 72
  3. 49
  4. 25
  5. 41
  6. 54
  7. 107
  8. 20
  9. 10
  10. 79
  11. 71
  12. 44
  13. 22
  14. 91
  15. 94
  16. 56
  17. 63
  18. 80
  19. 19
  20. 14
  21. 26
  22. 25
  23. 38
  24. 59
  25. 35
  26. 2
  27. 57
  28. 40
  29. 2
  30. 40
  31. 95
  32. 34
  33. 26
  34. 67
  35. 62
  36. 68
  37. 68
  38. 77
  39. 59
  40. 11

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