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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 71 · 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 51, 55, 41, 43 and 80? (a) 55 (b) 54 (c) 53 (d) 56
  2. 2.The average of 7 numbers is 36. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 31 (b) 36 (c) 73 (d) 30
  3. 3.What is the average of 25, 29, 18 and 28? (a) 25 (b) 24 (c) 26 (d) 27
  4. 4.The average of 4 numbers is 16. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 4 (b) 16 (c) 31 (d) 19
  5. 5.The average of 8 numbers is 12. When one number is taken away, the average of the rest is 9. Which number was taken away? (a) 12 (b) 33 (c) 24 (d) 21
  6. 6.What is the average of 58, 64, 64 and 98? (a) 72 (b) 70 (c) 73 (d) 71
  7. 7.The average of 8 numbers is 37. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 9 (b) 78 (c) 37 (d) 10
  8. 8.What is the average of all the whole numbers from 39 to 77? (a) 58 (b) 19 (c) 59 (d) 38
  9. 9.A batter has an average of 41 runs in 3 matches. How many runs are needed in the next match to raise the average to 45? (a) 16 (b) 57 (c) 49 (d) 45
  10. 10.The average of 4 numbers is 24. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 18 (b) 50 (c) 19 (d) 24
  11. 11.What is the average of all the whole numbers from 26 to 64? (a) 19 (b) 38 (c) 45 (d) 46
  12. 12.The average of 8 numbers is 38. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 80 (b) 38 (c) 10 (d) 11
  13. 13.What is the average of all the whole numbers from 6 to 18? (a) 13 (b) 11 (c) 6 (d) 12
  14. 14.What is the average of all the whole numbers from 52 to 88? (a) 18 (b) 36 (c) 70 (d) 71
  15. 15.What is the average of 34, 38, 48, 37, 42 and 23? (a) 38 (b) 36 (c) 37 (d) 39
  16. 16.The average of 4 numbers is 50. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 50 (b) 12 (c) 59 (d) 97
  17. 17.What is the average of all the whole numbers from 50 to 64? (a) 14 (b) 58 (c) 7 (d) 57
  18. 18.What is the average of 48, 26, 38 and 36? (a) 38 (b) 37 (c) 39 (d) 36
  19. 19.A batter has an average of 37 runs in 8 matches. How many runs are needed in the next match to raise the average to 40? (a) 40 (b) 64 (c) 43 (d) 27
  20. 20.A batter has an average of 58 runs in 3 matches. How many runs are needed in the next match to raise the average to 65? (a) 72 (b) 65 (c) 28 (d) 86
  21. 21.What is the average of 84, 86, 65, 92 and 68? (a) 78 (b) 81 (c) 79 (d) 80
  22. 22.What is the average of 78, 68, 48, 64 and 57? (a) 62 (b) 63 (c) 65 (d) 64
  23. 23.What is the average of all the whole numbers from 49 to 57? (a) 53 (b) 54 (c) 8 (d) 4
  24. 24.The average of 5 numbers is 49. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 97 (b) 5 (c) 49 (d) 53
  25. 25.What is the average of 15, 27, 34, 9, 22 and 25? (a) 22 (b) 23 (c) 24 (d) 21
  26. 26.The average of 5 numbers is 17. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 17 (b) 2 (c) 38 (d) 1
  27. 27.A batter has an average of 54 runs in 9 matches. How many runs are needed in the next match to raise the average to 61? (a) 68 (b) 124 (c) 70 (d) 61
  28. 28.A batter has an average of 53 runs in 6 matches. How many runs are needed in the next match to raise the average to 56? (a) 21 (b) 56 (c) 59 (d) 74
  29. 29.What is the average of 84, 79, 71, 72 and 64? (a) 76 (b) 73 (c) 74 (d) 75
  30. 30.A batter has an average of 51 runs in 4 matches. How many runs are needed in the next match to raise the average to 56? (a) 56 (b) 76 (c) 61 (d) 25
  31. 31.What is the average of 37, 20, 47 and 28? (a) 44 (b) 34 (c) 32 (d) 33
  32. 32.The average of 8 numbers is 10. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 24 (b) 10 (c) 31 (d) 17
  33. 33.The average of 8 numbers is 33. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 27 (b) 33 (c) 26 (d) 67
  34. 34.What is the average of 22, 46, 34, 19, 18 and 59? (a) 33 (b) 32 (c) 35 (d) 34
  35. 35.What is the average of 13, 17, 29 and 25? (a) 28 (b) 20 (c) 21 (d) 22
  36. 36.The average of 5 numbers is 21. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 21 (b) 10 (c) 29 (d) 40
  37. 37.The average of 5 numbers is 38. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 78 (b) 31 (c) 30 (d) 38
  38. 38.The average of 4 numbers is 20. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 11 (b) 12 (c) 20 (d) 43
  39. 39.What is the average of 18, 21, 15 and 62? (a) 28 (b) 31 (c) 29 (d) 30
  40. 40.The average of 6 numbers is 36. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 75 (b) 21 (c) 36 (d) 22

Answer key

  1. 54
  2. 30
  3. 25
  4. 19
  5. 33
  6. 71
  7. 9
  8. 58
  9. 57
  10. 18
  11. 45
  12. 10
  13. 12
  14. 70
  15. 37
  16. 59
  17. 57
  18. 37
  19. 64
  20. 86
  21. 79
  22. 63
  23. 53
  24. 53
  25. 22
  26. 1
  27. 124
  28. 74
  29. 74
  30. 76
  31. 33
  32. 31
  33. 26
  34. 33
  35. 21
  36. 29
  37. 30
  38. 11
  39. 29
  40. 21

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