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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 648 · 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 6 numbers is 38. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 33 (b) 77 (c) 34 (d) 38
  2. 2.The average of 5 numbers is 25. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 9 (b) 54 (c) 10 (d) 25
  3. 3.What is the average of 45, 26, 20, 37 and 32? (a) 33 (b) 40 (c) 32 (d) 31
  4. 4.A batter has an average of 45 runs in 3 matches. How many runs are needed in the next match to raise the average to 49? (a) 16 (b) 53 (c) 61 (d) 49
  5. 5.A batter has an average of 31 runs in 3 matches. How many runs are needed in the next match to raise the average to 35? (a) 35 (b) 39 (c) 47 (d) 16
  6. 6.What is the average of 78, 57, 71, 74 and 65? (a) 70 (b) 71 (c) 69 (d) 68
  7. 7.A batter has an average of 21 runs in 3 matches. How many runs are needed in the next match to raise the average to 24? (a) 27 (b) 33 (c) 12 (d) 24
  8. 8.The average of 4 numbers is 41. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 12 (b) 41 (c) 79 (d) 50
  9. 9.A batter has an average of 32 runs in 8 matches. How many runs are needed in the next match to raise the average to 40? (a) 40 (b) 104 (c) 72 (d) 48
  10. 10.What is the average of 24, 29, 25, 46, 46 and 46? (a) 37 (b) 38 (c) 36 (d) 35
  11. 11.A batter has an average of 54 runs in 7 matches. How many runs are needed in the next match to raise the average to 57? (a) 60 (b) 57 (c) 78 (d) 24
  12. 12.What is the average of all the whole numbers from 49 to 77? (a) 14 (b) 64 (c) 63 (d) 28
  13. 13.The average of 7 numbers is 30. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 30 (b) 61 (c) 24 (d) 25
  14. 14.What is the average of all the whole numbers from 33 to 67? (a) 34 (b) 17 (c) 51 (d) 50
  15. 15.What is the average of 39, 20, 17, 17 and 52? (a) 29 (b) 31 (c) 28 (d) 30
  16. 16.A batter has an average of 29 runs in 7 matches. How many runs are needed in the next match to raise the average to 35? (a) 77 (b) 48 (c) 35 (d) 41
  17. 17.The average of 5 numbers is 41. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 25 (b) 77 (c) 41 (d) 61
  18. 18.What is the average of all the whole numbers from 22 to 54? (a) 38 (b) 32 (c) 39 (d) 16
  19. 19.The average of 6 numbers is 45. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 87 (b) 60 (c) 45 (d) 18
  20. 20.The average of 6 numbers is 47. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 6 (b) 93 (c) 52 (d) 47
  21. 21.What is the average of 60, 53, 71, 79, 82 and 63? (a) 68 (b) 70 (c) 67 (d) 69
  22. 22.A batter has an average of 22 runs in 5 matches. How many runs are needed in the next match to raise the average to 25? (a) 25 (b) 18 (c) 28 (d) 40
  23. 23.A batter has an average of 55 runs in 5 matches. How many runs are needed in the next match to raise the average to 63? (a) 48 (b) 63 (c) 103 (d) 71
  24. 24.What is the average of all the whole numbers from 19 to 45? (a) 33 (b) 13 (c) 26 (d) 32
  25. 25.A batter has an average of 55 runs in 3 matches. How many runs are needed in the next match to raise the average to 60? (a) 60 (b) 75 (c) 20 (d) 65
  26. 26.A batter has an average of 26 runs in 4 matches. How many runs are needed in the next match to raise the average to 31? (a) 25 (b) 36 (c) 51 (d) 31
  27. 27.The average of 5 numbers is 21. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 21 (b) 5 (c) 25 (d) 41
  28. 28.The average of 6 numbers is 16. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 24 (b) 36 (c) 28 (d) 16
  29. 29.What is the average of 8, 29, 30 and 21? (a) 23 (b) 22 (c) 24 (d) 21
  30. 30.What is the average of all the whole numbers from 23 to 37? (a) 14 (b) 30 (c) 7 (d) 31
  31. 31.The average of 6 numbers is 24. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 52 (b) 24 (c) 5 (d) 4
  32. 32.What is the average of 19, 25, 12, 12 and 62? (a) 26 (b) 28 (c) 25 (d) 27
  33. 33.A batter has an average of 34 runs in 7 matches. How many runs are needed in the next match to raise the average to 39? (a) 40 (b) 39 (c) 44 (d) 74
  34. 34.What is the average of 19, 14, 10 and 49? (a) 23 (b) 24 (c) 25 (d) 22
  35. 35.The average of 5 numbers is 22. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 43 (b) 5 (c) 22 (d) 26
  36. 36.The average of 5 numbers is 42. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 10 (b) 82 (c) 42 (d) 50
  37. 37.The average of 8 numbers is 23. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 32 (b) 51 (c) 42 (d) 23
  38. 38.What is the average of 62, 42, 58, 56, 66 and 22? (a) 50 (b) 53 (c) 52 (d) 51
  39. 39.The average of 5 numbers is 13. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 13 (b) 2 (c) 29 (d) 1
  40. 40.A batter has an average of 45 runs in 4 matches. How many runs are needed in the next match to raise the average to 51? (a) 75 (b) 30 (c) 57 (d) 51

Answer key

  1. 33
  2. 9
  3. 32
  4. 61
  5. 47
  6. 69
  7. 33
  8. 50
  9. 104
  10. 36
  11. 78
  12. 63
  13. 24
  14. 50
  15. 29
  16. 77
  17. 61
  18. 38
  19. 60
  20. 52
  21. 68
  22. 40
  23. 103
  24. 32
  25. 75
  26. 51
  27. 25
  28. 36
  29. 22
  30. 30
  31. 4
  32. 26
  33. 74
  34. 23
  35. 26
  36. 50
  37. 51
  38. 51
  39. 1
  40. 75

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