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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 8 · 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 7 numbers is 50. When one number is taken away, the average of the rest is 53. Which number was taken away? (a) 32 (b) 33 (c) 50 (d) 103
  2. 2.The average of 7 numbers is 16. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 40 (b) 16 (c) 41 (d) 28
  3. 3.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 53? (a) 88 (b) 42 (c) 53 (d) 60
  4. 4.The average of 8 numbers is 18. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 25 (b) 18 (c) 8 (d) 35
  5. 5.The average of 6 numbers is 46. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 21 (b) 22 (c) 97 (d) 46
  6. 6.What is the average of all the whole numbers from 14 to 30? (a) 8 (b) 22 (c) 16 (d) 23
  7. 7.A batter has an average of 29 runs in 3 matches. How many runs are needed in the next match to raise the average to 33? (a) 33 (b) 16 (c) 45 (d) 37
  8. 8.The average of 6 numbers is 27. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 32 (b) 27 (c) 6 (d) 53
  9. 9.What is the average of 93, 88, 79 and 60? (a) 82 (b) 80 (c) 79 (d) 81
  10. 10.A batter has an average of 56 runs in 3 matches. How many runs are needed in the next match to raise the average to 61? (a) 61 (b) 66 (c) 76 (d) 20
  11. 11.What is the average of all the whole numbers from 16 to 52? (a) 36 (b) 35 (c) 34 (d) 18
  12. 12.A batter has an average of 21 runs in 7 matches. How many runs are needed in the next match to raise the average to 23? (a) 16 (b) 37 (c) 25 (d) 23
  13. 13.What is the average of all the whole numbers from 42 to 52? (a) 48 (b) 10 (c) 47 (d) 5
  14. 14.The average of 6 numbers is 19. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 39 (b) 15 (c) 14 (d) 19
  15. 15.What is the average of all the whole numbers from 25 to 51? (a) 38 (b) 13 (c) 39 (d) 26
  16. 16.The average of 4 numbers is 14. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 14 (b) 8 (c) 30 (d) 9
  17. 17.The average of 5 numbers is 29. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 29 (b) 37 (c) 56 (d) 10
  18. 18.A batter has an average of 26 runs in 7 matches. How many runs are needed in the next match to raise the average to 32? (a) 32 (b) 38 (c) 74 (d) 48
  19. 19.What is the average of 75, 76, 64 and 93? (a) 79 (b) 78 (c) 77 (d) 76
  20. 20.What is the average of 59, 56, 54, 57 and 119? (a) 70 (b) 69 (c) 71 (d) 68
  21. 21.What is the average of 11, 26, 31, 18 and 44? (a) 27 (b) 25 (c) 28 (d) 26
  22. 22.What is the average of 39, 40, 17 and 4? (a) 27 (b) 24 (c) 26 (d) 25
  23. 23.What is the average of all the whole numbers from 14 to 46? (a) 31 (b) 16 (c) 32 (d) 30
  24. 24.The average of 4 numbers is 23. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 16 (b) 42 (c) 35 (d) 23
  25. 25.A batter has an average of 27 runs in 4 matches. How many runs are needed in the next match to raise the average to 34? (a) 35 (b) 62 (c) 41 (d) 34
  26. 26.What is the average of 21, 9, 11, 31, 25 and 41? (a) 22 (b) 25 (c) 24 (d) 23
  27. 27.The average of 4 numbers is 14. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 14 (b) 4 (c) 17 (d) 27
  28. 28.What is the average of 38, 32, 30, 33 and 47? (a) 36 (b) 35 (c) 45 (d) 37
  29. 29.What is the average of all the whole numbers from 41 to 57? (a) 8 (b) 49 (c) 16 (d) 50
  30. 30.The average of 4 numbers is 22. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 22 (b) 47 (c) 14 (d) 13
  31. 31.What is the average of 33, 27, 23 and 53? (a) 33 (b) 35 (c) 36 (d) 34
  32. 32.What is the average of 34, 13, 38 and 7? (a) 23 (b) 25 (c) 24 (d) 22
  33. 33.What is the average of 77, 67, 58 and 90? (a) 74 (b) 75 (c) 72 (d) 73
  34. 34.What is the average of 70, 72, 85, 65, 83 and 69? (a) 76 (b) 75 (c) 73 (d) 74
  35. 35.A batter has an average of 28 runs in 5 matches. How many runs are needed in the next match to raise the average to 33? (a) 33 (b) 30 (c) 58 (d) 38
  36. 36.What is the average of all the whole numbers from 21 to 37? (a) 8 (b) 29 (c) 30 (d) 16
  37. 37.The average of 6 numbers is 29. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 29 (b) 53 (c) 54 (d) 30
  38. 38.The average of 4 numbers is 14. When one number is taken away, the average of the rest is 9. Which number was taken away? (a) 20 (b) 23 (c) 14 (d) 29
  39. 39.What is the average of all the whole numbers from 10 to 16? (a) 6 (b) 13 (c) 3 (d) 14
  40. 40.What is the average of all the whole numbers from 5 to 19? (a) 13 (b) 12 (c) 7 (d) 14

Answer key

  1. 32
  2. 40
  3. 88
  4. 25
  5. 21
  6. 22
  7. 45
  8. 32
  9. 80
  10. 76
  11. 34
  12. 37
  13. 47
  14. 14
  15. 38
  16. 8
  17. 37
  18. 74
  19. 77
  20. 69
  21. 26
  22. 25
  23. 30
  24. 35
  25. 62
  26. 23
  27. 17
  28. 36
  29. 49
  30. 13
  31. 34
  32. 23
  33. 73
  34. 74
  35. 58
  36. 29
  37. 54
  38. 29
  39. 13
  40. 12

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