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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 760 · 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 15. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 31 (b) 10 (c) 15 (d) 11
  2. 2.What is the average of all the whole numbers from 22 to 34? (a) 12 (b) 6 (c) 28 (d) 29
  3. 3.A batter has an average of 43 runs in 6 matches. How many runs are needed in the next match to raise the average to 49? (a) 49 (b) 55 (c) 42 (d) 85
  4. 4.What is the average of 17, 34, 18 and 43? (a) 27 (b) 29 (c) 28 (d) 30
  5. 5.What is the average of 63, 44, 46, 53 and 64? (a) 53 (b) 54 (c) 56 (d) 55
  6. 6.A batter has an average of 41 runs in 9 matches. How many runs are needed in the next match to raise the average to 48? (a) 70 (b) 48 (c) 111 (d) 55
  7. 7.The average of 7 numbers is 29. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 29 (b) 53 (c) 54 (d) 28
  8. 8.What is the average of all the whole numbers from 41 to 57? (a) 16 (b) 8 (c) 50 (d) 49
  9. 9.The average of 6 numbers is 17. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 29 (b) 30 (c) 42 (d) 17
  10. 10.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 59? (a) 59 (b) 35 (c) 66 (d) 87
  11. 11.What is the average of 56, 54, 62, 46, 40 and 54? (a) 54 (b) 51 (c) 52 (d) 53
  12. 12.What is the average of all the whole numbers from 43 to 55? (a) 12 (b) 49 (c) 50 (d) 6
  13. 13.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) 89 (b) 5 (c) 49 (d) 45
  14. 14.The average of 4 numbers is 20. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 18 (b) 20 (c) 41 (d) 17
  15. 15.A batter has an average of 31 runs in 4 matches. How many runs are needed in the next match to raise the average to 35? (a) 35 (b) 20 (c) 39 (d) 51
  16. 16.What is the average of 62, 61, 56, 45 and 61? (a) 56 (b) 59 (c) 58 (d) 57
  17. 17.A batter has an average of 56 runs in 9 matches. How many runs are needed in the next match to raise the average to 62? (a) 60 (b) 68 (c) 116 (d) 62
  18. 18.The average of 6 numbers is 36. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 36 (b) 70 (c) 46 (d) 12
  19. 19.The average of 5 numbers is 23. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 23 (b) 15 (c) 35 (d) 43
  20. 20.A batter has an average of 41 runs in 4 matches. How many runs are needed in the next match to raise the average to 44? (a) 15 (b) 44 (c) 47 (d) 56
  21. 21.The average of 4 numbers is 47. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 47 (b) 89 (c) 20 (d) 62
  22. 22.What is the average of 23, 39, 22 and 52? (a) 35 (b) 36 (c) 33 (d) 34
  23. 23.A batter has an average of 40 runs in 6 matches. How many runs are needed in the next match to raise the average to 43? (a) 43 (b) 21 (c) 61 (d) 46
  24. 24.What is the average of all the whole numbers from 28 to 48? (a) 20 (b) 39 (c) 10 (d) 38
  25. 25.A batter has an average of 41 runs in 7 matches. How many runs are needed in the next match to raise the average to 48? (a) 55 (b) 56 (c) 97 (d) 48
  26. 26.The average of 5 numbers is 10. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 10 (b) 6 (c) 7 (d) 21
  27. 27.What is the average of all the whole numbers from 30 to 36? (a) 6 (b) 34 (c) 33 (d) 3
  28. 28.The average of 7 numbers is 44. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 44 (b) 21 (c) 85 (d) 62
  29. 29.The average of 7 numbers is 46. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 46 (b) 95 (c) 28 (d) 29
  30. 30.A batter has an average of 28 runs in 3 matches. How many runs are needed in the next match to raise the average to 31? (a) 40 (b) 12 (c) 34 (d) 31
  31. 31.What is the average of all the whole numbers from 20 to 26? (a) 23 (b) 3 (c) 6 (d) 24
  32. 32.What is the average of all the whole numbers from 16 to 36? (a) 27 (b) 26 (c) 20 (d) 10
  33. 33.The average of 6 numbers is 46. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 46 (b) 95 (c) 31 (d) 32
  34. 34.What is the average of 18, 26, 27, 36 and 13? (a) 30 (b) 23 (c) 25 (d) 24
  35. 35.The average of 5 numbers is 25. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 5 (b) 6 (c) 25 (d) 55
  36. 36.A batter has an average of 30 runs in 5 matches. How many runs are needed in the next match to raise the average to 37? (a) 37 (b) 72 (c) 44 (d) 42
  37. 37.What is the average of all the whole numbers from 10 to 20? (a) 10 (b) 5 (c) 16 (d) 15
  38. 38.The average of 4 numbers is 26. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 26 (b) 50 (c) 32 (d) 8
  39. 39.What is the average of all the whole numbers from 42 to 54? (a) 49 (b) 48 (c) 6 (d) 12
  40. 40.What is the average of 75, 80, 68, 64, 69 and 106? (a) 76 (b) 78 (c) 79 (d) 77

Answer key

  1. 10
  2. 28
  3. 85
  4. 28
  5. 54
  6. 111
  7. 53
  8. 49
  9. 42
  10. 87
  11. 52
  12. 49
  13. 49
  14. 17
  15. 51
  16. 57
  17. 116
  18. 46
  19. 35
  20. 56
  21. 62
  22. 34
  23. 61
  24. 38
  25. 97
  26. 6
  27. 33
  28. 62
  29. 28
  30. 40
  31. 23
  32. 26
  33. 31
  34. 24
  35. 5
  36. 72
  37. 15
  38. 32
  39. 48
  40. 77

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