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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 939 · 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 41. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 41 (b) 78 (c) 28 (d) 65
  2. 2.The average of 6 numbers is 16. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 33 (b) 11 (c) 12 (d) 16
  3. 3.What is the average of 59, 77, 55, 77 and 77? (a) 71 (b) 68 (c) 70 (d) 69
  4. 4.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 44? (a) 12 (b) 44 (c) 53 (d) 47
  5. 5.The average of 8 numbers is 13. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 16 (b) 27 (c) 24 (d) 13
  6. 6.The average of 4 numbers is 29. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 24 (b) 29 (c) 60 (d) 23
  7. 7.What is the average of all the whole numbers from 49 to 85? (a) 36 (b) 67 (c) 18 (d) 68
  8. 8.A batter has an average of 58 runs in 9 matches. How many runs are needed in the next match to raise the average to 61? (a) 64 (b) 30 (c) 88 (d) 61
  9. 9.The average of 8 numbers is 32. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 61 (b) 59 (c) 32 (d) 60
  10. 10.The average of 4 numbers is 44. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 16 (b) 44 (c) 56 (d) 84
  11. 11.What is the average of 38, 34, 39, 52, 42 and 47? (a) 44 (b) 41 (c) 42 (d) 43
  12. 12.A batter has an average of 55 runs in 9 matches. How many runs are needed in the next match to raise the average to 57? (a) 57 (b) 20 (c) 59 (d) 75
  13. 13.The average of 5 numbers is 20. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 20 (b) 40 (c) 25 (d) 35
  14. 14.What is the average of all the whole numbers from 20 to 54? (a) 34 (b) 17 (c) 37 (d) 38
  15. 15.The average of 6 numbers is 41. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 30 (b) 66 (c) 41 (d) 77
  16. 16.A batter has an average of 40 runs in 7 matches. How many runs are needed in the next match to raise the average to 48? (a) 104 (b) 56 (c) 48 (d) 64
  17. 17.The average of 8 numbers is 18. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 47 (b) 32 (c) 46 (d) 18
  18. 18.What is the average of 58, 63, 73, 70, 81 and 63? (a) 70 (b) 67 (c) 68 (d) 69
  19. 19.The average of 7 numbers is 26. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 14 (b) 15 (c) 54 (d) 26
  20. 20.What is the average of 31, 54, 31, 28, 33 and 75? (a) 44 (b) 42 (c) 43 (d) 41
  21. 21.What is the average of 52, 50, 51 and 19? (a) 42 (b) 44 (c) 43 (d) 45
  22. 22.The average of 4 numbers is 35. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 35 (b) 32 (c) 71 (d) 33
  23. 23.What is the average of all the whole numbers from 11 to 29? (a) 20 (b) 21 (c) 9 (d) 18
  24. 24.What is the average of 46, 41, 49, 50 and 19? (a) 43 (b) 41 (c) 42 (d) 40
  25. 25.What is the average of 39, 43, 59 and 67? (a) 53 (b) 52 (c) 54 (d) 51
  26. 26.What is the average of 29, 45, 24 and 46? (a) 36 (b) 35 (c) 37 (d) 48
  27. 27.The average of 6 numbers is 29. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 39 (b) 56 (c) 12 (d) 29
  28. 28.A batter has an average of 46 runs in 3 matches. How many runs are needed in the next match to raise the average to 51? (a) 51 (b) 20 (c) 66 (d) 56
  29. 29.The average of 4 numbers is 38. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 38 (b) 80 (c) 26 (d) 27
  30. 30.What is the average of 61, 62, 62, 71 and 119? (a) 75 (b) 76 (c) 74 (d) 77
  31. 31.What is the average of 61, 57, 61, 71, 49 and 79? (a) 63 (b) 65 (c) 62 (d) 64
  32. 32.The average of 4 numbers is 33. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 48 (b) 61 (c) 20 (d) 33
  33. 33.What is the average of 56, 57, 62 and 53? (a) 58 (b) 57 (c) 56 (d) 76
  34. 34.What is the average of 71, 86, 85, 68, 71 and 93? (a) 81 (b) 79 (c) 80 (d) 78
  35. 35.What is the average of all the whole numbers from 18 to 54? (a) 35 (b) 37 (c) 36 (d) 18
  36. 36.A batter has an average of 30 runs in 3 matches. How many runs are needed in the next match to raise the average to 32? (a) 38 (b) 8 (c) 32 (d) 34
  37. 37.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 49? (a) 51 (b) 49 (c) 12 (d) 59
  38. 38.What is the average of 45, 60, 52 and 39? (a) 51 (b) 49 (c) 48 (d) 50
  39. 39.What is the average of 39, 27, 48, 43 and 13? (a) 34 (b) 33 (c) 36 (d) 35
  40. 40.The average of 6 numbers is 36. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 11 (b) 36 (c) 12 (d) 77

Answer key

  1. 65
  2. 11
  3. 69
  4. 53
  5. 27
  6. 23
  7. 67
  8. 88
  9. 60
  10. 56
  11. 42
  12. 75
  13. 40
  14. 37
  15. 66
  16. 104
  17. 46
  18. 68
  19. 14
  20. 42
  21. 43
  22. 32
  23. 20
  24. 41
  25. 52
  26. 36
  27. 39
  28. 66
  29. 26
  30. 75
  31. 63
  32. 48
  33. 57
  34. 79
  35. 36
  36. 38
  37. 59
  38. 49
  39. 34
  40. 11

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