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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 771 · 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 38. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 38 (b) 77 (c) 32 (d) 33
  2. 2.What is the average of all the whole numbers from 18 to 28? (a) 23 (b) 10 (c) 24 (d) 5
  3. 3.The average of 7 numbers is 33. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 70 (b) 33 (c) 10 (d) 9
  4. 4.A batter has an average of 37 runs in 4 matches. How many runs are needed in the next match to raise the average to 43? (a) 30 (b) 49 (c) 43 (d) 67
  5. 5.A batter has an average of 36 runs in 6 matches. How many runs are needed in the next match to raise the average to 40? (a) 28 (b) 44 (c) 64 (d) 40
  6. 6.A batter has an average of 40 runs in 4 matches. How many runs are needed in the next match to raise the average to 48? (a) 48 (b) 40 (c) 56 (d) 80
  7. 7.What is the average of all the whole numbers from 43 to 57? (a) 7 (b) 14 (c) 51 (d) 50
  8. 8.What is the average of 13, 12, 38 and 29? (a) 23 (b) 24 (c) 22 (d) 25
  9. 9.The average of 5 numbers is 21. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 38 (b) 37 (c) 21 (d) 20
  10. 10.The average of 4 numbers is 39. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 37 (b) 36 (c) 39 (d) 79
  11. 11.What is the average of 20, 27, 19 and 18? (a) 20 (b) 22 (c) 28 (d) 21
  12. 12.What is the average of 37, 42, 30, 23, 42 and 36? (a) 36 (b) 42 (c) 34 (d) 35
  13. 13.A batter has an average of 60 runs in 9 matches. How many runs are needed in the next match to raise the average to 68? (a) 140 (b) 68 (c) 76 (d) 80
  14. 14.What is the average of all the whole numbers from 29 to 43? (a) 7 (b) 36 (c) 14 (d) 37
  15. 15.The average of 7 numbers is 26. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 51 (b) 32 (c) 26 (d) 7
  16. 16.What is the average of all the whole numbers from 58 to 84? (a) 71 (b) 13 (c) 26 (d) 72
  17. 17.A batter has an average of 53 runs in 3 matches. How many runs are needed in the next match to raise the average to 56? (a) 12 (b) 65 (c) 56 (d) 59
  18. 18.The average of 4 numbers is 25. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 25 (b) 8 (c) 31 (d) 48
  19. 19.What is the average of 55, 53, 35, 53 and 44? (a) 47 (b) 49 (c) 48 (d) 60
  20. 20.The average of 5 numbers is 43. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 25 (b) 81 (c) 43 (d) 63
  21. 21.A batter has an average of 28 runs in 9 matches. How many runs are needed in the next match to raise the average to 31? (a) 31 (b) 34 (c) 30 (d) 58
  22. 22.The average of 8 numbers is 44. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 44 (b) 85 (c) 24 (d) 65
  23. 23.A batter has an average of 42 runs in 6 matches. How many runs are needed in the next match to raise the average to 44? (a) 14 (b) 46 (c) 56 (d) 44
  24. 24.A batter has an average of 36 runs in 3 matches. How many runs are needed in the next match to raise the average to 38? (a) 8 (b) 44 (c) 40 (d) 38
  25. 25.The average of 5 numbers is 16. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 35 (b) 16 (c) 4 (d) 5
  26. 26.What is the average of all the whole numbers from 19 to 29? (a) 5 (b) 24 (c) 10 (d) 25
  27. 27.The average of 5 numbers is 20. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 20 (b) 36 (c) 35 (d) 37
  28. 28.What is the average of all the whole numbers from 54 to 88? (a) 72 (b) 34 (c) 71 (d) 17
  29. 29.The average of 6 numbers is 44. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 44 (b) 54 (c) 86 (d) 12
  30. 30.What is the average of 32, 44, 31, 29, 29 and 87? (a) 42 (b) 43 (c) 44 (d) 41
  31. 31.A batter has an average of 28 runs in 9 matches. How many runs are needed in the next match to raise the average to 30? (a) 48 (b) 20 (c) 30 (d) 32
  32. 32.A batter has an average of 56 runs in 7 matches. How many runs are needed in the next match to raise the average to 60? (a) 64 (b) 88 (c) 60 (d) 32
  33. 33.A batter has an average of 48 runs in 4 matches. How many runs are needed in the next match to raise the average to 54? (a) 60 (b) 54 (c) 78 (d) 30
  34. 34.What is the average of 87, 86, 72, 67, 72 and 96? (a) 96 (b) 79 (c) 80 (d) 81
  35. 35.A batter has an average of 42 runs in 5 matches. How many runs are needed in the next match to raise the average to 47? (a) 30 (b) 47 (c) 52 (d) 72
  36. 36.What is the average of 57, 60, 76, 68, 57 and 72? (a) 64 (b) 66 (c) 65 (d) 78
  37. 37.The average of 6 numbers is 46. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 94 (b) 36 (c) 46 (d) 37
  38. 38.The average of 8 numbers is 41. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 27 (b) 41 (c) 28 (d) 84
  39. 39.What is the average of 47, 28, 28 and 37? (a) 34 (b) 35 (c) 36 (d) 37
  40. 40.What is the average of 20, 23, 28 and 69? (a) 37 (b) 34 (c) 36 (d) 35

Answer key

  1. 32
  2. 23
  3. 9
  4. 67
  5. 64
  6. 80
  7. 50
  8. 23
  9. 37
  10. 36
  11. 21
  12. 35
  13. 140
  14. 36
  15. 32
  16. 71
  17. 65
  18. 31
  19. 48
  20. 63
  21. 58
  22. 65
  23. 56
  24. 44
  25. 4
  26. 24
  27. 36
  28. 71
  29. 54
  30. 42
  31. 48
  32. 88
  33. 78
  34. 80
  35. 72
  36. 65
  37. 36
  38. 27
  39. 35
  40. 35

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