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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 763 · 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 49. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 93 (b) 49 (c) 84 (d) 40
  2. 2.What is the average of 29, 46, 53, 56 and 26? (a) 43 (b) 44 (c) 42 (d) 41
  3. 3.What is the average of all the whole numbers from 48 to 76? (a) 28 (b) 63 (c) 62 (d) 14
  4. 4.A batter has an average of 47 runs in 5 matches. How many runs are needed in the next match to raise the average to 52? (a) 57 (b) 30 (c) 77 (d) 52
  5. 5.What is the average of all the whole numbers from 23 to 35? (a) 29 (b) 12 (c) 6 (d) 30
  6. 6.What is the average of all the whole numbers from 45 to 71? (a) 59 (b) 13 (c) 58 (d) 26
  7. 7.What is the average of 71, 78, 68 and 39? (a) 64 (b) 63 (c) 66 (d) 65
  8. 8.A batter has an average of 55 runs in 5 matches. How many runs are needed in the next match to raise the average to 63? (a) 63 (b) 71 (c) 103 (d) 48
  9. 9.The average of 4 numbers is 20. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 34 (b) 36 (c) 35 (d) 20
  10. 10.The average of 7 numbers is 41. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 14 (b) 53 (c) 80 (d) 41
  11. 11.A batter has an average of 24 runs in 6 matches. How many runs are needed in the next match to raise the average to 30? (a) 36 (b) 42 (c) 30 (d) 66
  12. 12.The average of 7 numbers is 13. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 13 (b) 25 (c) 7 (d) 19
  13. 13.The average of 8 numbers is 17. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 32 (b) 31 (c) 16 (d) 17
  14. 14.The average of 4 numbers is 15. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 24 (b) 15 (c) 27 (d) 12
  15. 15.A batter has an average of 51 runs in 3 matches. How many runs are needed in the next match to raise the average to 58? (a) 79 (b) 58 (c) 65 (d) 28
  16. 16.What is the average of 30, 43, 35, 18, 48 and 24? (a) 34 (b) 32 (c) 35 (d) 33
  17. 17.The average of 7 numbers is 50. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 62 (b) 14 (c) 98 (d) 50
  18. 18.The average of 4 numbers is 28. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 28 (b) 31 (c) 4 (d) 55
  19. 19.The average of 7 numbers is 19. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 41 (b) 19 (c) 2 (d) 1
  20. 20.What is the average of 24, 31, 37 and 40? (a) 44 (b) 34 (c) 32 (d) 33
  21. 21.What is the average of all the whole numbers from 8 to 30? (a) 19 (b) 11 (c) 20 (d) 22
  22. 22.What is the average of all the whole numbers from 23 to 55? (a) 16 (b) 40 (c) 39 (d) 32
  23. 23.What is the average of 69, 77, 76, 79, 83 and 96? (a) 81 (b) 79 (c) 80 (d) 96
  24. 24.What is the average of 82, 58, 84, 55 and 71? (a) 72 (b) 69 (c) 70 (d) 71
  25. 25.The average of 7 numbers is 37. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 67 (b) 35 (c) 37 (d) 69
  26. 26.The average of 8 numbers is 14. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 26 (b) 28 (c) 16 (d) 14
  27. 27.A batter has an average of 38 runs in 4 matches. How many runs are needed in the next match to raise the average to 40? (a) 40 (b) 10 (c) 42 (d) 48
  28. 28.The average of 7 numbers is 43. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 43 (b) 89 (c) 26 (d) 25
  29. 29.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 42? (a) 24 (b) 48 (c) 42 (d) 60
  30. 30.What is the average of 79, 61, 64 and 56? (a) 67 (b) 64 (c) 65 (d) 66
  31. 31.What is the average of all the whole numbers from 9 to 33? (a) 24 (b) 21 (c) 22 (d) 12
  32. 32.What is the average of 18, 19, 24, 45, 23 and 69? (a) 33 (b) 34 (c) 35 (d) 32
  33. 33.A batter has an average of 51 runs in 3 matches. How many runs are needed in the next match to raise the average to 54? (a) 54 (b) 12 (c) 63 (d) 57
  34. 34.The average of 6 numbers is 20. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 39 (b) 6 (c) 20 (d) 25
  35. 35.The average of 8 numbers is 41. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 14 (b) 86 (c) 13 (d) 41
  36. 36.The average of 8 numbers is 15. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 25 (b) 40 (c) 15 (d) 50
  37. 37.What is the average of all the whole numbers from 14 to 52? (a) 33 (b) 38 (c) 34 (d) 19
  38. 38.What is the average of all the whole numbers from 45 to 85? (a) 20 (b) 65 (c) 40 (d) 66
  39. 39.The average of 6 numbers is 34. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 69 (b) 30 (c) 34 (d) 29
  40. 40.The average of 8 numbers is 26. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 47 (b) 40 (c) 26 (d) 61

Answer key

  1. 84
  2. 42
  3. 62
  4. 77
  5. 29
  6. 58
  7. 64
  8. 103
  9. 35
  10. 53
  11. 66
  12. 19
  13. 31
  14. 24
  15. 79
  16. 33
  17. 62
  18. 31
  19. 1
  20. 33
  21. 19
  22. 39
  23. 80
  24. 70
  25. 67
  26. 28
  27. 48
  28. 25
  29. 60
  30. 65
  31. 21
  32. 33
  33. 63
  34. 25
  35. 13
  36. 50
  37. 33
  38. 65
  39. 29
  40. 61

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