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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 457 · 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 46. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 87 (b) 20 (c) 46 (d) 61
  2. 2.The average of 4 numbers is 42. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 79 (b) 42 (c) 57 (d) 20
  3. 3.What is the average of 48, 39, 20 and 33? (a) 34 (b) 37 (c) 35 (d) 36
  4. 4.A batter has an average of 53 runs in 9 matches. How many runs are needed in the next match to raise the average to 60? (a) 67 (b) 123 (c) 70 (d) 60
  5. 5.What is the average of all the whole numbers from 40 to 64? (a) 53 (b) 12 (c) 24 (d) 52
  6. 6.What is the average of all the whole numbers from 39 to 49? (a) 10 (b) 45 (c) 44 (d) 5
  7. 7.What is the average of 19, 30, 13, 14, 24 and 68? (a) 27 (b) 29 (c) 28 (d) 30
  8. 8.The average of 8 numbers is 27. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 34 (b) 53 (c) 8 (d) 27
  9. 9.What is the average of 69, 60, 78 and 81? (a) 73 (b) 96 (c) 71 (d) 72
  10. 10.What is the average of all the whole numbers from 39 to 57? (a) 18 (b) 49 (c) 48 (d) 9
  11. 11.What is the average of all the whole numbers from 33 to 39? (a) 6 (b) 37 (c) 36 (d) 3
  12. 12.What is the average of all the whole numbers from 60 to 86? (a) 73 (b) 74 (c) 26 (d) 13
  13. 13.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 58? (a) 86 (b) 32 (c) 62 (d) 58
  14. 14.The average of 8 numbers is 14. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 14 (b) 42 (c) 32 (d) 24
  15. 15.What is the average of all the whole numbers from 44 to 56? (a) 50 (b) 12 (c) 51 (d) 6
  16. 16.The average of 5 numbers is 49. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 97 (b) 49 (c) 53 (d) 5
  17. 17.A batter has an average of 26 runs in 7 matches. How many runs are needed in the next match to raise the average to 29? (a) 50 (b) 24 (c) 32 (d) 29
  18. 18.What is the average of all the whole numbers from 8 to 48? (a) 29 (b) 28 (c) 40 (d) 20
  19. 19.A batter has an average of 48 runs in 3 matches. How many runs are needed in the next match to raise the average to 50? (a) 8 (b) 52 (c) 56 (d) 50
  20. 20.The average of 5 numbers is 31. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 31 (b) 24 (c) 64 (d) 23
  21. 21.What is the average of all the whole numbers from 19 to 51? (a) 36 (b) 16 (c) 35 (d) 32
  22. 22.A batter has an average of 32 runs in 4 matches. How many runs are needed in the next match to raise the average to 40? (a) 48 (b) 72 (c) 40 (d) 73
  23. 23.What is the average of all the whole numbers from 39 to 75? (a) 58 (b) 18 (c) 36 (d) 57
  24. 24.A batter has an average of 28 runs in 4 matches. How many runs are needed in the next match to raise the average to 30? (a) 30 (b) 10 (c) 38 (d) 32
  25. 25.The average of 8 numbers is 24. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 18 (b) 49 (c) 24 (d) 17
  26. 26.What is the average of 84, 83, 93, 67 and 68? (a) 79 (b) 81 (c) 78 (d) 80
  27. 27.The average of 4 numbers is 41. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 30 (b) 86 (c) 41 (d) 29
  28. 28.A batter has an average of 32 runs in 3 matches. How many runs are needed in the next match to raise the average to 37? (a) 20 (b) 52 (c) 37 (d) 42
  29. 29.What is the average of 90, 68, 68, 74 and 75? (a) 75 (b) 74 (c) 77 (d) 76
  30. 30.What is the average of all the whole numbers from 60 to 84? (a) 24 (b) 73 (c) 12 (d) 72
  31. 31.The average of 5 numbers is 35. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 10 (b) 68 (c) 43 (d) 35
  32. 32.A batter has an average of 30 runs in 4 matches. How many runs are needed in the next match to raise the average to 36? (a) 42 (b) 30 (c) 36 (d) 60
  33. 33.The average of 6 numbers is 12. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 37 (b) 19 (c) 30 (d) 12
  34. 34.What is the average of 40, 14, 31, 35 and 25? (a) 30 (b) 29 (c) 28 (d) 31
  35. 35.The average of 6 numbers is 10. When one number is taken away, the average of the rest is 9. Which number was taken away? (a) 15 (b) 10 (c) 19 (d) 6
  36. 36.A batter has an average of 42 runs in 8 matches. How many runs are needed in the next match to raise the average to 48? (a) 48 (b) 54 (c) 97 (d) 96
  37. 37.What is the average of 35, 18, 46 and 25? (a) 30 (b) 33 (c) 32 (d) 31
  38. 38.A batter has an average of 42 runs in 3 matches. How many runs are needed in the next match to raise the average to 48? (a) 24 (b) 66 (c) 54 (d) 48
  39. 39.What is the average of 45, 65, 58, 67, 62 and 39? (a) 55 (b) 57 (c) 58 (d) 56
  40. 40.The average of 4 numbers is 29. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 44 (b) 20 (c) 53 (d) 29

Answer key

  1. 61
  2. 57
  3. 35
  4. 123
  5. 52
  6. 44
  7. 28
  8. 34
  9. 72
  10. 48
  11. 36
  12. 73
  13. 86
  14. 42
  15. 50
  16. 53
  17. 50
  18. 28
  19. 56
  20. 23
  21. 35
  22. 72
  23. 57
  24. 38
  25. 17
  26. 79
  27. 29
  28. 52
  29. 75
  30. 72
  31. 43
  32. 60
  33. 37
  34. 29
  35. 15
  36. 96
  37. 31
  38. 66
  39. 56
  40. 44

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