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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 996 · 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 53, 70, 55 and 66? (a) 63 (b) 60 (c) 62 (d) 61
  2. 2.What is the average of all the whole numbers from 57 to 89? (a) 32 (b) 74 (c) 73 (d) 16
  3. 3.What is the average of all the whole numbers from 8 to 18? (a) 5 (b) 13 (c) 10 (d) 14
  4. 4.The average of 4 numbers is 36. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 21 (b) 36 (c) 77 (d) 22
  5. 5.What is the average of 82, 75, 66, 72 and 100? (a) 81 (b) 80 (c) 78 (d) 79
  6. 6.What is the average of all the whole numbers from 35 to 75? (a) 40 (b) 20 (c) 56 (d) 55
  7. 7.A batter has an average of 38 runs in 8 matches. How many runs are needed in the next match to raise the average to 46? (a) 72 (b) 46 (c) 54 (d) 110
  8. 8.The average of 5 numbers is 30. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 27 (b) 26 (c) 30 (d) 61
  9. 9.What is the average of 39, 9, 31 and 17? (a) 32 (b) 25 (c) 24 (d) 23
  10. 10.The average of 4 numbers is 48. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 8 (b) 54 (c) 94 (d) 48
  11. 11.The average of 5 numbers is 46. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 46 (b) 87 (c) 25 (d) 66
  12. 12.What is the average of all the whole numbers from 7 to 25? (a) 16 (b) 17 (c) 9 (d) 18
  13. 13.The average of 5 numbers is 30. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 62 (b) 23 (c) 30 (d) 22
  14. 14.What is the average of all the whole numbers from 13 to 27? (a) 14 (b) 21 (c) 7 (d) 20
  15. 15.A batter has an average of 33 runs in 6 matches. How many runs are needed in the next match to raise the average to 35? (a) 37 (b) 14 (c) 35 (d) 47
  16. 16.What is the average of 35, 25, 24, 31 and 60? (a) 36 (b) 37 (c) 35 (d) 34
  17. 17.The average of 4 numbers is 25. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 20 (b) 40 (c) 45 (d) 25
  18. 18.The average of 7 numbers is 32. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 50 (b) 61 (c) 21 (d) 32
  19. 19.A batter has an average of 57 runs in 5 matches. How many runs are needed in the next match to raise the average to 63? (a) 36 (b) 69 (c) 63 (d) 93
  20. 20.The average of 6 numbers is 50. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 50 (b) 6 (c) 55 (d) 99
  21. 21.The average of 7 numbers is 40. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 40 (b) 16 (c) 17 (d) 84
  22. 22.The average of 4 numbers is 14. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 14 (b) 25 (c) 23 (d) 12
  23. 23.The average of 5 numbers is 28. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 32 (b) 5 (c) 28 (d) 55
  24. 24.A batter has an average of 28 runs in 9 matches. How many runs are needed in the next match to raise the average to 33? (a) 78 (b) 33 (c) 50 (d) 38
  25. 25.What is the average of all the whole numbers from 11 to 21? (a) 16 (b) 10 (c) 5 (d) 17
  26. 26.A batter has an average of 33 runs in 5 matches. How many runs are needed in the next match to raise the average to 38? (a) 30 (b) 63 (c) 38 (d) 43
  27. 27.The average of 6 numbers is 47. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 47 (b) 91 (c) 62 (d) 18
  28. 28.A batter has an average of 53 runs in 7 matches. How many runs are needed in the next match to raise the average to 56? (a) 56 (b) 77 (c) 59 (d) 24
  29. 29.What is the average of 42, 60, 55, 57 and 66? (a) 57 (b) 70 (c) 55 (d) 56
  30. 30.A batter has an average of 53 runs in 7 matches. How many runs are needed in the next match to raise the average to 57? (a) 32 (b) 57 (c) 61 (d) 85
  31. 31.The average of 4 numbers is 23. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 45 (b) 4 (c) 26 (d) 23
  32. 32.The average of 6 numbers is 25. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 30 (b) 25 (c) 6 (d) 49
  33. 33.What is the average of 37, 26, 47 and 26? (a) 33 (b) 35 (c) 34 (d) 36
  34. 34.The average of 7 numbers is 18. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 38 (b) 6 (c) 7 (d) 18
  35. 35.The average of 6 numbers is 10. When one number is taken away, the average of the rest is 6. Which number was taken away? (a) 16 (b) 10 (c) 30 (d) 24
  36. 36.What is the average of 51, 71, 65, 51, 70 and 70? (a) 62 (b) 64 (c) 65 (d) 63
  37. 37.What is the average of all the whole numbers from 49 to 57? (a) 8 (b) 54 (c) 4 (d) 53
  38. 38.The average of 8 numbers is 12. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 20 (b) 12 (c) 32 (d) 40
  39. 39.The average of 5 numbers is 25. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 48 (b) 25 (c) 10 (d) 33
  40. 40.The average of 4 numbers is 15. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 27 (b) 16 (c) 26 (d) 15

Answer key

  1. 61
  2. 73
  3. 13
  4. 21
  5. 79
  6. 55
  7. 110
  8. 26
  9. 24
  10. 54
  11. 66
  12. 16
  13. 22
  14. 20
  15. 47
  16. 35
  17. 40
  18. 50
  19. 93
  20. 55
  21. 16
  22. 23
  23. 32
  24. 78
  25. 16
  26. 63
  27. 62
  28. 77
  29. 56
  30. 85
  31. 26
  32. 30
  33. 34
  34. 6
  35. 30
  36. 63
  37. 53
  38. 40
  39. 33
  40. 27

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