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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 862 · 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 8 numbers is 31. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 18 (b) 17 (c) 64 (d) 31
  2. 2.A batter has an average of 33 runs in 3 matches. How many runs are needed in the next match to raise the average to 38? (a) 53 (b) 38 (c) 43 (d) 20
  3. 3.What is the average of all the whole numbers from 40 to 66? (a) 13 (b) 26 (c) 53 (d) 54
  4. 4.The average of 4 numbers is 35. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 4 (b) 69 (c) 35 (d) 38
  5. 5.What is the average of 62, 34, 64, 50 and 35? (a) 51 (b) 49 (c) 48 (d) 50
  6. 6.The average of 7 numbers is 36. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 66 (b) 35 (c) 36 (d) 67
  7. 7.A batter has an average of 53 runs in 8 matches. How many runs are needed in the next match to raise the average to 60? (a) 116 (b) 67 (c) 60 (d) 63
  8. 8.A batter has an average of 33 runs in 5 matches. How many runs are needed in the next match to raise the average to 35? (a) 35 (b) 12 (c) 45 (d) 37
  9. 9.The average of 6 numbers is 49. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 96 (b) 12 (c) 49 (d) 59
  10. 10.What is the average of all the whole numbers from 21 to 27? (a) 25 (b) 6 (c) 24 (d) 3
  11. 11.What is the average of 21, 12, 14 and 37? (a) 28 (b) 21 (c) 20 (d) 22
  12. 12.The average of 8 numbers is 41. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 41 (b) 20 (c) 21 (d) 85
  13. 13.What is the average of 61, 64, 79, 57 and 69? (a) 65 (b) 66 (c) 67 (d) 68
  14. 14.The average of 5 numbers is 38. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 38 (b) 18 (c) 81 (d) 19
  15. 15.What is the average of 18, 35, 30 and 13? (a) 24 (b) 23 (c) 32 (d) 25
  16. 16.What is the average of all the whole numbers from 21 to 55? (a) 17 (b) 39 (c) 34 (d) 38
  17. 17.What is the average of 34, 10, 7, 12 and 47? (a) 24 (b) 23 (c) 21 (d) 22
  18. 18.The average of 6 numbers is 12. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 23 (b) 12 (c) 17 (d) 6
  19. 19.What is the average of 46, 43, 45, 38 and 73? (a) 50 (b) 49 (c) 51 (d) 48
  20. 20.The average of 6 numbers is 23. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 48 (b) 23 (c) 14 (d) 13
  21. 21.What is the average of 50, 41, 50, 70 and 69? (a) 70 (b) 57 (c) 56 (d) 55
  22. 22.A batter has an average of 59 runs in 4 matches. How many runs are needed in the next match to raise the average to 61? (a) 10 (b) 63 (c) 69 (d) 61
  23. 23.A batter has an average of 23 runs in 6 matches. How many runs are needed in the next match to raise the average to 28? (a) 28 (b) 33 (c) 58 (d) 35
  24. 24.What is the average of all the whole numbers from 14 to 38? (a) 12 (b) 24 (c) 27 (d) 26
  25. 25.What is the average of all the whole numbers from 12 to 34? (a) 22 (b) 23 (c) 24 (d) 11
  26. 26.What is the average of 17, 12, 20 and 59? (a) 27 (b) 28 (c) 36 (d) 26
  27. 27.A batter has an average of 49 runs in 5 matches. How many runs are needed in the next match to raise the average to 51? (a) 12 (b) 51 (c) 61 (d) 53
  28. 28.The average of 8 numbers is 18. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 32 (b) 46 (c) 18 (d) 47
  29. 29.What is the average of all the whole numbers from 19 to 29? (a) 5 (b) 10 (c) 25 (d) 24
  30. 30.A batter has an average of 52 runs in 4 matches. How many runs are needed in the next match to raise the average to 57? (a) 25 (b) 62 (c) 57 (d) 77
  31. 31.A batter has an average of 40 runs in 7 matches. How many runs are needed in the next match to raise the average to 45? (a) 40 (b) 45 (c) 50 (d) 80
  32. 32.The average of 8 numbers is 47. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 12 (b) 13 (c) 99 (d) 47
  33. 33.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) 12 (c) 26 (d) 16
  34. 34.A batter has an average of 54 runs in 6 matches. How many runs are needed in the next match to raise the average to 59? (a) 35 (b) 64 (c) 89 (d) 59
  35. 35.The average of 5 numbers is 28. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 25 (b) 48 (c) 28 (d) 51
  36. 36.What is the average of 57, 55, 72 and 68? (a) 62 (b) 63 (c) 84 (d) 64
  37. 37.What is the average of all the whole numbers from 31 to 67? (a) 49 (b) 18 (c) 50 (d) 36
  38. 38.What is the average of 45, 61, 40 and 46? (a) 64 (b) 49 (c) 47 (d) 48
  39. 39.The average of 5 numbers is 48. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 10 (b) 56 (c) 48 (d) 94
  40. 40.What is the average of all the whole numbers from 21 to 47? (a) 26 (b) 34 (c) 35 (d) 13

Answer key

  1. 17
  2. 53
  3. 53
  4. 38
  5. 49
  6. 66
  7. 116
  8. 45
  9. 59
  10. 24
  11. 21
  12. 20
  13. 66
  14. 18
  15. 24
  16. 38
  17. 22
  18. 17
  19. 49
  20. 13
  21. 56
  22. 69
  23. 58
  24. 26
  25. 23
  26. 27
  27. 61
  28. 46
  29. 24
  30. 77
  31. 80
  32. 12
  33. 26
  34. 89
  35. 48
  36. 63
  37. 49
  38. 48
  39. 56
  40. 34

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