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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 957 · 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.What is the average of all the whole numbers from 41 to 77? (a) 18 (b) 59 (c) 36 (d) 60
  2. 2.What is the average of all the whole numbers from 24 to 38? (a) 32 (b) 14 (c) 31 (d) 7
  3. 3.What is the average of all the whole numbers from 39 to 61? (a) 22 (b) 51 (c) 11 (d) 50
  4. 4.The average of 4 numbers is 27. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 27 (b) 33 (c) 52 (d) 8
  5. 5.What is the average of all the whole numbers from 54 to 62? (a) 8 (b) 58 (c) 59 (d) 4
  6. 6.The average of 5 numbers is 18. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 18 (b) 20 (c) 34 (d) 32
  7. 7.What is the average of 60, 62, 74 and 104? (a) 100 (b) 74 (c) 76 (d) 75
  8. 8.The average of 6 numbers is 45. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 45 (b) 89 (c) 50 (d) 6
  9. 9.The average of 6 numbers is 14. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 27 (b) 6 (c) 14 (d) 19
  10. 10.The average of 4 numbers is 21. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 21 (b) 7 (c) 47 (d) 6
  11. 11.The average of 4 numbers is 25. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 25 (b) 37 (c) 46 (d) 16
  12. 12.What is the average of all the whole numbers from 5 to 13? (a) 8 (b) 4 (c) 10 (d) 9
  13. 13.What is the average of 65, 67, 88 and 96? (a) 81 (b) 79 (c) 80 (d) 78
  14. 14.A batter has an average of 23 runs in 8 matches. How many runs are needed in the next match to raise the average to 28? (a) 68 (b) 33 (c) 45 (d) 28
  15. 15.A batter has an average of 58 runs in 4 matches. How many runs are needed in the next match to raise the average to 64? (a) 64 (b) 30 (c) 88 (d) 70
  16. 16.What is the average of 65, 68, 86 and 77? (a) 74 (b) 73 (c) 76 (d) 75
  17. 17.The average of 7 numbers is 10. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 10 (b) 5 (c) 4 (d) 21
  18. 18.A batter has an average of 26 runs in 3 matches. How many runs are needed in the next match to raise the average to 32? (a) 50 (b) 38 (c) 32 (d) 24
  19. 19.The average of 6 numbers is 16. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 6 (b) 16 (c) 34 (d) 7
  20. 20.The average of 5 numbers is 30. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 10 (b) 30 (c) 65 (d) 11
  21. 21.What is the average of all the whole numbers from 23 to 43? (a) 20 (b) 34 (c) 10 (d) 33
  22. 22.What is the average of 56, 70, 73 and 69? (a) 66 (b) 68 (c) 69 (d) 67
  23. 23.What is the average of 69, 77, 91, 65 and 83? (a) 77 (b) 79 (c) 78 (d) 76
  24. 24.The average of 6 numbers is 37. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 37 (b) 76 (c) 28 (d) 27
  25. 25.What is the average of 49, 48, 42 and 49? (a) 49 (b) 48 (c) 46 (d) 47
  26. 26.What is the average of 15, 34, 39, 42, 15 and 17? (a) 29 (b) 28 (c) 27 (d) 26
  27. 27.The average of 8 numbers is 15. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 22 (b) 15 (c) 29 (d) 8
  28. 28.A batter has an average of 58 runs in 5 matches. How many runs are needed in the next match to raise the average to 65? (a) 65 (b) 42 (c) 100 (d) 72
  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.What is the average of 24, 21, 11, 11, 33 and 56? (a) 26 (b) 27 (c) 28 (d) 25
  31. 31.What is the average of all the whole numbers from 46 to 78? (a) 32 (b) 63 (c) 62 (d) 16
  32. 32.A batter has an average of 43 runs in 7 matches. How many runs are needed in the next match to raise the average to 49? (a) 91 (b) 49 (c) 48 (d) 55
  33. 33.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 34? (a) 37 (b) 34 (c) 46 (d) 15
  34. 34.What is the average of 28, 28, 43 and 21? (a) 30 (b) 31 (c) 29 (d) 40
  35. 35.What is the average of 52, 62, 46, 75 and 65? (a) 59 (b) 60 (c) 75 (d) 61
  36. 36.What is the average of all the whole numbers from 13 to 23? (a) 5 (b) 10 (c) 18 (d) 19
  37. 37.What is the average of all the whole numbers from 51 to 69? (a) 9 (b) 61 (c) 60 (d) 18
  38. 38.What is the average of 13, 13, 12 and 66? (a) 27 (b) 28 (c) 26 (d) 25
  39. 39.The average of 7 numbers is 31. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 1 (b) 31 (c) 67 (d) 2
  40. 40.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 29? (a) 31 (b) 29 (c) 10 (d) 37

Answer key

  1. 59
  2. 31
  3. 50
  4. 33
  5. 58
  6. 34
  7. 75
  8. 50
  9. 19
  10. 6
  11. 37
  12. 9
  13. 79
  14. 68
  15. 88
  16. 74
  17. 4
  18. 50
  19. 6
  20. 10
  21. 33
  22. 67
  23. 77
  24. 27
  25. 47
  26. 27
  27. 22
  28. 100
  29. 49
  30. 26
  31. 62
  32. 91
  33. 46
  34. 30
  35. 60
  36. 18
  37. 60
  38. 26
  39. 1
  40. 37

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