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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 705 · 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 60, 61, 55, 52, 62 and 40? (a) 54 (b) 66 (c) 56 (d) 55
  2. 2.The average of 8 numbers is 45. When one number is taken away, the average of the rest is 50. Which number was taken away? (a) 45 (b) 10 (c) 95 (d) 11
  3. 3.The average of 6 numbers is 14. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 12 (b) 14 (c) 26 (d) 24
  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 43? (a) 8 (b) 49 (c) 45 (d) 43
  5. 5.A batter has an average of 53 runs in 3 matches. How many runs are needed in the next match to raise the average to 60? (a) 28 (b) 67 (c) 60 (d) 81
  6. 6.The average of 5 numbers is 46. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 54 (b) 10 (c) 46 (d) 90
  7. 7.What is the average of 74, 62, 81, 58 and 75? (a) 69 (b) 71 (c) 70 (d) 72
  8. 8.What is the average of 34, 55, 58 and 45? (a) 64 (b) 49 (c) 47 (d) 48
  9. 9.What is the average of all the whole numbers from 44 to 60? (a) 16 (b) 52 (c) 53 (d) 8
  10. 10.What is the average of all the whole numbers from 44 to 78? (a) 17 (b) 62 (c) 61 (d) 34
  11. 11.What is the average of all the whole numbers from 15 to 39? (a) 24 (b) 28 (c) 12 (d) 27
  12. 12.What is the average of 44, 61, 56, 60 and 44? (a) 54 (b) 52 (c) 53 (d) 55
  13. 13.What is the average of all the whole numbers from 6 to 34? (a) 14 (b) 20 (c) 21 (d) 28
  14. 14.What is the average of all the whole numbers from 15 to 29? (a) 14 (b) 7 (c) 23 (d) 22
  15. 15.The average of 5 numbers is 38. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 18 (b) 38 (c) 19 (d) 81
  16. 16.What is the average of 46, 18, 18 and 42? (a) 33 (b) 31 (c) 30 (d) 32
  17. 17.What is the average of all the whole numbers from 12 to 40? (a) 27 (b) 14 (c) 26 (d) 28
  18. 18.The average of 4 numbers is 14. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 11 (b) 29 (c) 12 (d) 14
  19. 19.The average of 8 numbers is 17. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 45 (b) 32 (c) 30 (d) 17
  20. 20.A batter has an average of 40 runs in 9 matches. How many runs are needed in the next match to raise the average to 42? (a) 44 (b) 42 (c) 20 (d) 60
  21. 21.What is the average of all the whole numbers from 19 to 33? (a) 14 (b) 27 (c) 7 (d) 26
  22. 22.The average of 7 numbers is 35. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 65 (b) 66 (c) 35 (d) 64
  23. 23.A batter has an average of 47 runs in 4 matches. How many runs are needed in the next match to raise the average to 50? (a) 53 (b) 15 (c) 50 (d) 62
  24. 24.What is the average of 87, 76, 84 and 65? (a) 79 (b) 78 (c) 104 (d) 77
  25. 25.A batter has an average of 30 runs in 5 matches. How many runs are needed in the next match to raise the average to 38? (a) 78 (b) 38 (c) 48 (d) 46
  26. 26.What is the average of all the whole numbers from 20 to 58? (a) 19 (b) 39 (c) 40 (d) 38
  27. 27.What is the average of all the whole numbers from 13 to 29? (a) 16 (b) 22 (c) 8 (d) 21
  28. 28.A batter has an average of 32 runs in 6 matches. How many runs are needed in the next match to raise the average to 40? (a) 88 (b) 56 (c) 48 (d) 40
  29. 29.What is the average of 75, 58, 46, 55, 63 and 63? (a) 59 (b) 72 (c) 61 (d) 60
  30. 30.The average of 8 numbers is 46. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 32 (b) 74 (c) 46 (d) 88
  31. 31.What is the average of 47, 48, 40, 30, 40 and 17? (a) 38 (b) 36 (c) 39 (d) 37
  32. 32.A batter has an average of 36 runs in 9 matches. How many runs are needed in the next match to raise the average to 42? (a) 60 (b) 48 (c) 42 (d) 96
  33. 33.A batter has an average of 45 runs in 6 matches. How many runs are needed in the next match to raise the average to 50? (a) 35 (b) 55 (c) 50 (d) 80
  34. 34.What is the average of all the whole numbers from 28 to 68? (a) 40 (b) 48 (c) 20 (d) 49
  35. 35.The average of 6 numbers is 32. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 32 (b) 12 (c) 13 (d) 68
  36. 36.What is the average of 66, 68, 41 and 49? (a) 55 (b) 56 (c) 57 (d) 58
  37. 37.The average of 7 numbers is 25. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 14 (b) 48 (c) 25 (d) 37
  38. 38.What is the average of 20, 25, 44, 30 and 56? (a) 35 (b) 34 (c) 37 (d) 36
  39. 39.The average of 4 numbers is 21. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 21 (b) 44 (c) 15 (d) 16
  40. 40.The average of 6 numbers is 10. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 10 (b) 21 (c) 6 (d) 5

Answer key

  1. 55
  2. 10
  3. 24
  4. 49
  5. 81
  6. 54
  7. 70
  8. 48
  9. 52
  10. 61
  11. 27
  12. 53
  13. 20
  14. 22
  15. 18
  16. 31
  17. 26
  18. 11
  19. 45
  20. 60
  21. 26
  22. 65
  23. 62
  24. 78
  25. 78
  26. 39
  27. 21
  28. 88
  29. 60
  30. 74
  31. 37
  32. 96
  33. 80
  34. 48
  35. 12
  36. 56
  37. 37
  38. 35
  39. 15
  40. 5

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