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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 757 · 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 4 numbers is 10. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 21 (b) 8 (c) 7 (d) 10
  2. 2.The average of 7 numbers is 50. When one number is taken away, the average of the rest is 53. Which number was taken away? (a) 33 (b) 50 (c) 103 (d) 32
  3. 3.The average of 7 numbers is 33. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 39 (b) 33 (c) 7 (d) 65
  4. 4.A batter has an average of 55 runs in 6 matches. How many runs are needed in the next match to raise the average to 63? (a) 71 (b) 111 (c) 56 (d) 63
  5. 5.What is the average of all the whole numbers from 41 to 79? (a) 60 (b) 38 (c) 61 (d) 19
  6. 6.The average of 7 numbers is 26. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 26 (b) 38 (c) 14 (d) 50
  7. 7.What is the average of 89, 91, 62 and 62? (a) 78 (b) 76 (c) 75 (d) 77
  8. 8.What is the average of all the whole numbers from 30 to 40? (a) 35 (b) 10 (c) 5 (d) 36
  9. 9.What is the average of all the whole numbers from 7 to 21? (a) 15 (b) 13 (c) 7 (d) 14
  10. 10.What is the average of all the whole numbers from 21 to 45? (a) 34 (b) 33 (c) 24 (d) 12
  11. 11.A batter has an average of 26 runs in 3 matches. How many runs are needed in the next match to raise the average to 29? (a) 32 (b) 29 (c) 12 (d) 38
  12. 12.The average of 7 numbers is 20. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 41 (b) 20 (c) 15 (d) 14
  13. 13.What is the average of all the whole numbers from 17 to 35? (a) 9 (b) 26 (c) 27 (d) 18
  14. 14.The average of 7 numbers is 42. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 88 (b) 19 (c) 42 (d) 18
  15. 15.The average of 5 numbers is 35. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 16 (b) 75 (c) 15 (d) 35
  16. 16.A batter has an average of 41 runs in 5 matches. How many runs are needed in the next match to raise the average to 47? (a) 53 (b) 77 (c) 47 (d) 36
  17. 17.The average of 7 numbers is 41. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 41 (b) 18 (c) 17 (d) 86
  18. 18.What is the average of 61, 46, 45, 42 and 76? (a) 53 (b) 54 (c) 56 (d) 55
  19. 19.What is the average of all the whole numbers from 31 to 43? (a) 38 (b) 37 (c) 6 (d) 12
  20. 20.A batter has an average of 55 runs in 8 matches. How many runs are needed in the next match to raise the average to 61? (a) 61 (b) 109 (c) 54 (d) 67
  21. 21.What is the average of all the whole numbers from 20 to 42? (a) 32 (b) 31 (c) 11 (d) 22
  22. 22.The average of 4 numbers is 18. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 18 (b) 8 (c) 34 (d) 24
  23. 23.What is the average of all the whole numbers from 42 to 48? (a) 6 (b) 45 (c) 3 (d) 46
  24. 24.The average of 8 numbers is 26. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 26 (b) 8 (c) 33 (d) 51
  25. 25.The average of 4 numbers is 23. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 20 (b) 38 (c) 23 (d) 41
  26. 26.A batter has an average of 28 runs in 7 matches. How many runs are needed in the next match to raise the average to 32? (a) 36 (b) 61 (c) 60 (d) 32
  27. 27.What is the average of 37, 32, 43, 18 and 10? (a) 28 (b) 35 (c) 27 (d) 29
  28. 28.The average of 5 numbers is 14. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 14 (b) 30 (c) 6 (d) 7
  29. 29.What is the average of 52, 54, 52 and 94? (a) 64 (b) 84 (c) 63 (d) 62
  30. 30.The average of 6 numbers is 14. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 30 (b) 5 (c) 4 (d) 14
  31. 31.The average of 5 numbers is 22. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 19 (b) 22 (c) 18 (d) 45
  32. 32.What is the average of 79, 56, 55, 63, 77 and 90? (a) 84 (b) 70 (c) 69 (d) 71
  33. 33.The average of 5 numbers is 46. When one number is taken away, the average of the rest is 50. Which number was taken away? (a) 96 (b) 46 (c) 30 (d) 31
  34. 34.What is the average of 43, 56, 61 and 56? (a) 54 (b) 72 (c) 53 (d) 55
  35. 35.What is the average of 48, 47, 30 and 15? (a) 36 (b) 37 (c) 35 (d) 34
  36. 36.What is the average of 32, 36, 27, 36 and 54? (a) 38 (b) 36 (c) 37 (d) 39
  37. 37.The average of 5 numbers is 34. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 34 (b) 72 (c) 18 (d) 19
  38. 38.The average of 7 numbers is 22. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 39 (b) 52 (c) 22 (d) 35
  39. 39.A batter has an average of 56 runs in 7 matches. How many runs are needed in the next match to raise the average to 61? (a) 96 (b) 61 (c) 40 (d) 66
  40. 40.The average of 4 numbers is 46. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 46 (b) 43 (c) 44 (d) 93

Answer key

  1. 7
  2. 32
  3. 39
  4. 111
  5. 60
  6. 38
  7. 76
  8. 35
  9. 14
  10. 33
  11. 38
  12. 14
  13. 26
  14. 18
  15. 15
  16. 77
  17. 17
  18. 54
  19. 37
  20. 109
  21. 31
  22. 24
  23. 45
  24. 33
  25. 38
  26. 60
  27. 28
  28. 6
  29. 63
  30. 4
  31. 18
  32. 70
  33. 30
  34. 54
  35. 35
  36. 37
  37. 18
  38. 52
  39. 96
  40. 43

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