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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 615 · 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 17. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 17 (b) 23 (c) 33 (d) 7
  2. 2.The average of 4 numbers is 29. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 29 (b) 62 (c) 18 (d) 17
  3. 3.A batter has an average of 54 runs in 5 matches. How many runs are needed in the next match to raise the average to 56? (a) 56 (b) 12 (c) 58 (d) 66
  4. 4.What is the average of all the whole numbers from 17 to 25? (a) 21 (b) 4 (c) 22 (d) 8
  5. 5.What is the average of all the whole numbers from 27 to 41? (a) 7 (b) 35 (c) 34 (d) 14
  6. 6.What is the average of 58, 57, 74 and 91? (a) 72 (b) 70 (c) 69 (d) 71
  7. 7.What is the average of all the whole numbers from 46 to 52? (a) 3 (b) 6 (c) 50 (d) 49
  8. 8.What is the average of 56, 56, 53, 60 and 115? (a) 85 (b) 68 (c) 69 (d) 67
  9. 9.A batter has an average of 47 runs in 4 matches. How many runs are needed in the next match to raise the average to 50? (a) 62 (b) 50 (c) 15 (d) 53
  10. 10.The average of 8 numbers is 25. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 25 (b) 16 (c) 39 (d) 48
  11. 11.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) 11 (b) 31 (c) 10 (d) 15
  12. 12.What is the average of 47, 30, 39, 43 and 56? (a) 44 (b) 43 (c) 45 (d) 42
  13. 13.A batter has an average of 51 runs in 6 matches. How many runs are needed in the next match to raise the average to 55? (a) 55 (b) 28 (c) 79 (d) 59
  14. 14.The average of 5 numbers is 49. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 49 (b) 25 (c) 69 (d) 93
  15. 15.What is the average of 54, 41, 51, 52, 39 and 69? (a) 51 (b) 52 (c) 50 (d) 53
  16. 16.The average of 5 numbers is 39. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 39 (b) 20 (c) 74 (d) 55
  17. 17.A batter has an average of 22 runs in 7 matches. How many runs are needed in the next match to raise the average to 27? (a) 27 (b) 32 (c) 40 (d) 62
  18. 18.What is the average of all the whole numbers from 56 to 68? (a) 63 (b) 6 (c) 12 (d) 62
  19. 19.What is the average of all the whole numbers from 54 to 94? (a) 75 (b) 40 (c) 20 (d) 74
  20. 20.What is the average of all the whole numbers from 14 to 26? (a) 21 (b) 6 (c) 12 (d) 20
  21. 21.A batter has an average of 34 runs in 5 matches. How many runs are needed in the next match to raise the average to 37? (a) 18 (b) 52 (c) 37 (d) 40
  22. 22.The average of 8 numbers is 38. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 17 (b) 79 (c) 18 (d) 38
  23. 23.What is the average of all the whole numbers from 43 to 59? (a) 52 (b) 51 (c) 16 (d) 8
  24. 24.What is the average of all the whole numbers from 28 to 46? (a) 18 (b) 38 (c) 9 (d) 37
  25. 25.What is the average of 82, 94, 80, 68 and 71? (a) 78 (b) 80 (c) 79 (d) 81
  26. 26.What is the average of 47, 38, 59 and 36? (a) 46 (b) 60 (c) 45 (d) 44
  27. 27.The average of 4 numbers is 21. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 21 (b) 8 (c) 27 (d) 40
  28. 28.The average of 4 numbers is 34. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 70 (b) 34 (c) 29 (d) 28
  29. 29.The average of 4 numbers is 10. When one number is taken away, the average of the rest is 9. Which number was taken away? (a) 10 (b) 19 (c) 13 (d) 4
  30. 30.The average of 4 numbers is 31. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 63 (b) 31 (c) 29 (d) 28
  31. 31.What is the average of all the whole numbers from 58 to 90? (a) 75 (b) 16 (c) 32 (d) 74
  32. 32.A batter has an average of 27 runs in 5 matches. How many runs are needed in the next match to raise the average to 30? (a) 30 (b) 18 (c) 45 (d) 33
  33. 33.What is the average of 28, 43, 37, 37, 44 and 57? (a) 42 (b) 41 (c) 40 (d) 43
  34. 34.What is the average of 55, 65, 67, 59, 48 and 30? (a) 56 (b) 55 (c) 54 (d) 53
  35. 35.What is the average of all the whole numbers from 31 to 39? (a) 4 (b) 35 (c) 36 (d) 8
  36. 36.What is the average of 86, 76, 77, 59, 87 and 53? (a) 73 (b) 75 (c) 74 (d) 72
  37. 37.What is the average of all the whole numbers from 26 to 62? (a) 36 (b) 18 (c) 44 (d) 45
  38. 38.What is the average of 79, 85, 67, 62, 84 and 73? (a) 76 (b) 74 (c) 90 (d) 75
  39. 39.The average of 7 numbers is 24. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 24 (b) 49 (c) 18 (d) 19
  40. 40.The average of 6 numbers is 47. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 42 (b) 47 (c) 43 (d) 95

Answer key

  1. 23
  2. 17
  3. 66
  4. 21
  5. 34
  6. 70
  7. 49
  8. 68
  9. 62
  10. 39
  11. 10
  12. 43
  13. 79
  14. 69
  15. 51
  16. 55
  17. 62
  18. 62
  19. 74
  20. 20
  21. 52
  22. 17
  23. 51
  24. 37
  25. 79
  26. 45
  27. 27
  28. 28
  29. 13
  30. 28
  31. 74
  32. 45
  33. 41
  34. 54
  35. 35
  36. 73
  37. 44
  38. 75
  39. 18
  40. 42

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