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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 123 · 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 36. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 21 (b) 36 (c) 69 (d) 54
  2. 2.What is the average of all the whole numbers from 39 to 45? (a) 3 (b) 6 (c) 43 (d) 42
  3. 3.The average of 8 numbers is 30. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 37 (b) 30 (c) 8 (d) 59
  4. 4.What is the average of 56, 70, 72, 50 and 67? (a) 64 (b) 62 (c) 65 (d) 63
  5. 5.The average of 7 numbers is 47. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 59 (b) 47 (c) 92 (d) 14
  6. 6.What is the average of all the whole numbers from 17 to 23? (a) 21 (b) 20 (c) 3 (d) 6
  7. 7.What is the average of 85, 66, 72, 69, 71 and 105? (a) 79 (b) 77 (c) 80 (d) 78
  8. 8.What is the average of 30, 35, 22, 39 and 54? (a) 45 (b) 35 (c) 37 (d) 36
  9. 9.What is the average of 38, 60, 64, 41, 52 and 45? (a) 49 (b) 60 (c) 50 (d) 51
  10. 10.The average of 5 numbers is 36. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 36 (b) 56 (c) 25 (d) 67
  11. 11.A batter has an average of 38 runs in 9 matches. How many runs are needed in the next match to raise the average to 43? (a) 48 (b) 50 (c) 43 (d) 88
  12. 12.The average of 4 numbers is 18. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 18 (b) 37 (c) 16 (d) 15
  13. 13.The average of 4 numbers is 44. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 42 (b) 44 (c) 41 (d) 89
  14. 14.What is the average of 47, 22, 25, 31, 24 and 73? (a) 38 (b) 36 (c) 39 (d) 37
  15. 15.What is the average of 83, 80, 63 and 74? (a) 75 (b) 100 (c) 74 (d) 76
  16. 16.The average of 5 numbers is 28. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 16 (b) 59 (c) 17 (d) 28
  17. 17.What is the average of 41, 31, 30 and 62? (a) 40 (b) 41 (c) 43 (d) 42
  18. 18.A batter has an average of 36 runs in 4 matches. How many runs are needed in the next match to raise the average to 42? (a) 30 (b) 42 (c) 48 (d) 66
  19. 19.What is the average of all the whole numbers from 32 to 64? (a) 49 (b) 48 (c) 16 (d) 32
  20. 20.What is the average of 25, 7, 27 and 21? (a) 22 (b) 20 (c) 21 (d) 19
  21. 21.What is the average of 79, 80, 68 and 49? (a) 92 (b) 70 (c) 69 (d) 68
  22. 22.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 29? (a) 35 (b) 77 (c) 54 (d) 29
  23. 23.What is the average of all the whole numbers from 55 to 63? (a) 60 (b) 4 (c) 59 (d) 8
  24. 24.What is the average of 44, 46, 26, 47 and 27? (a) 37 (b) 39 (c) 38 (d) 40
  25. 25.The average of 6 numbers is 34. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 49 (b) 34 (c) 65 (d) 18
  26. 26.The average of 4 numbers is 18. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 20 (b) 18 (c) 31 (d) 33
  27. 27.What is the average of 47, 63, 42, 58 and 50? (a) 65 (b) 53 (c) 51 (d) 52
  28. 28.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) 43 (b) 64 (c) 40 (d) 27
  29. 29.The average of 4 numbers is 44. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 83 (b) 59 (c) 44 (d) 20
  30. 30.What is the average of all the whole numbers from 7 to 13? (a) 10 (b) 6 (c) 3 (d) 11
  31. 31.What is the average of all the whole numbers from 41 to 73? (a) 32 (b) 58 (c) 57 (d) 16
  32. 32.What is the average of all the whole numbers from 35 to 55? (a) 45 (b) 10 (c) 20 (d) 46
  33. 33.The average of 5 numbers is 27. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 5 (b) 53 (c) 31 (d) 27
  34. 34.A batter has an average of 45 runs in 8 matches. How many runs are needed in the next match to raise the average to 50? (a) 50 (b) 45 (c) 90 (d) 55
  35. 35.What is the average of all the whole numbers from 30 to 68? (a) 49 (b) 38 (c) 50 (d) 19
  36. 36.What is the average of 35, 32, 30 and 79? (a) 44 (b) 43 (c) 45 (d) 46
  37. 37.A batter has an average of 27 runs in 6 matches. How many runs are needed in the next match to raise the average to 33? (a) 33 (b) 69 (c) 42 (d) 39
  38. 38.What is the average of all the whole numbers from 17 to 47? (a) 33 (b) 32 (c) 15 (d) 30
  39. 39.The average of 8 numbers is 13. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 40 (b) 21 (c) 13 (d) 48
  40. 40.What is the average of all the whole numbers from 11 to 21? (a) 5 (b) 10 (c) 16 (d) 17

Answer key

  1. 54
  2. 42
  3. 37
  4. 63
  5. 59
  6. 20
  7. 78
  8. 36
  9. 50
  10. 56
  11. 88
  12. 15
  13. 41
  14. 37
  15. 75
  16. 16
  17. 41
  18. 66
  19. 48
  20. 20
  21. 69
  22. 77
  23. 59
  24. 38
  25. 49
  26. 33
  27. 52
  28. 64
  29. 59
  30. 10
  31. 57
  32. 45
  33. 31
  34. 90
  35. 49
  36. 44
  37. 69
  38. 32
  39. 48
  40. 16

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