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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 488 · 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 5 numbers is 50. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 101 (b) 47 (c) 46 (d) 50
  2. 2.What is the average of all the whole numbers from 50 to 56? (a) 3 (b) 6 (c) 54 (d) 53
  3. 3.The average of 5 numbers is 30. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 56 (b) 20 (c) 46 (d) 30
  4. 4.What is the average of all the whole numbers from 36 to 56? (a) 46 (b) 20 (c) 47 (d) 10
  5. 5.A batter has an average of 38 runs in 9 matches. How many runs are needed in the next match to raise the average to 41? (a) 30 (b) 68 (c) 41 (d) 44
  6. 6.What is the average of 77, 55, 61 and 67? (a) 67 (b) 65 (c) 66 (d) 64
  7. 7.What is the average of 66, 75, 79, 75 and 65? (a) 90 (b) 71 (c) 73 (d) 72
  8. 8.The average of 6 numbers is 13. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 23 (b) 28 (c) 13 (d) 18
  9. 9.The average of 7 numbers is 41. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 85 (b) 41 (c) 23 (d) 24
  10. 10.A batter has an average of 46 runs in 4 matches. How many runs are needed in the next match to raise the average to 51? (a) 25 (b) 71 (c) 56 (d) 51
  11. 11.What is the average of all the whole numbers from 31 to 67? (a) 18 (b) 36 (c) 49 (d) 50
  12. 12.What is the average of 59, 74, 70, 63 and 54? (a) 63 (b) 64 (c) 65 (d) 80
  13. 13.The average of 8 numbers is 16. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 51 (b) 27 (c) 16 (d) 40
  14. 14.What is the average of 49, 24, 50, 35 and 37? (a) 38 (b) 39 (c) 41 (d) 40
  15. 15.What is the average of all the whole numbers from 59 to 73? (a) 7 (b) 14 (c) 66 (d) 67
  16. 16.What is the average of all the whole numbers from 34 to 40? (a) 3 (b) 37 (c) 6 (d) 38
  17. 17.A batter has an average of 25 runs in 9 matches. How many runs are needed in the next match to raise the average to 30? (a) 35 (b) 50 (c) 30 (d) 75
  18. 18.What is the average of all the whole numbers from 35 to 51? (a) 16 (b) 44 (c) 8 (d) 43
  19. 19.The average of 6 numbers is 49. When one number is taken away, the average of the rest is 50. Which number was taken away? (a) 45 (b) 99 (c) 49 (d) 44
  20. 20.The average of 4 numbers is 29. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 29 (b) 14 (c) 63 (d) 15
  21. 21.A batter has an average of 23 runs in 4 matches. How many runs are needed in the next match to raise the average to 31? (a) 40 (b) 31 (c) 39 (d) 63
  22. 22.What is the average of 64, 66, 51 and 59? (a) 80 (b) 59 (c) 61 (d) 60
  23. 23.What is the average of 67, 61, 65 and 19? (a) 53 (b) 52 (c) 54 (d) 55
  24. 24.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 47? (a) 47 (b) 65 (c) 24 (d) 53
  25. 25.What is the average of all the whole numbers from 6 to 12? (a) 6 (b) 9 (c) 3 (d) 10
  26. 26.What is the average of 56, 37, 30, 41, 40 and 60? (a) 43 (b) 45 (c) 46 (d) 44
  27. 27.The average of 4 numbers is 37. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 70 (b) 49 (c) 37 (d) 16
  28. 28.What is the average of 35, 30, 51, 56 and 53? (a) 44 (b) 45 (c) 46 (d) 47
  29. 29.The average of 6 numbers is 17. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 2 (b) 3 (c) 17 (d) 37
  30. 30.What is the average of 50, 42, 46 and 74? (a) 53 (b) 54 (c) 55 (d) 52
  31. 31.What is the average of all the whole numbers from 29 to 41? (a) 6 (b) 12 (c) 35 (d) 36
  32. 32.The average of 7 numbers is 36. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 30 (b) 36 (c) 31 (d) 73
  33. 33.A batter has an average of 27 runs in 6 matches. How many runs are needed in the next match to raise the average to 30? (a) 33 (b) 21 (c) 30 (d) 48
  34. 34.A batter has an average of 37 runs in 3 matches. How many runs are needed in the next match to raise the average to 42? (a) 57 (b) 47 (c) 20 (d) 42
  35. 35.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) 41 (b) 25 (c) 5 (d) 21
  36. 36.A batter has an average of 48 runs in 7 matches. How many runs are needed in the next match to raise the average to 52? (a) 32 (b) 80 (c) 56 (d) 52
  37. 37.The average of 7 numbers is 32. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 56 (b) 32 (c) 60 (d) 28
  38. 38.What is the average of all the whole numbers from 59 to 67? (a) 8 (b) 64 (c) 4 (d) 63
  39. 39.What is the average of 52, 65, 69 and 62? (a) 61 (b) 62 (c) 63 (d) 64
  40. 40.What is the average of 61, 66, 67 and 106? (a) 76 (b) 100 (c) 74 (d) 75

Answer key

  1. 46
  2. 53
  3. 46
  4. 46
  5. 68
  6. 65
  7. 72
  8. 28
  9. 23
  10. 71
  11. 49
  12. 64
  13. 51
  14. 39
  15. 66
  16. 37
  17. 75
  18. 43
  19. 44
  20. 14
  21. 63
  22. 60
  23. 53
  24. 65
  25. 9
  26. 44
  27. 49
  28. 45
  29. 2
  30. 53
  31. 35
  32. 30
  33. 48
  34. 57
  35. 25
  36. 80
  37. 56
  38. 63
  39. 62
  40. 75

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