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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 860 · 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 8 numbers is 46. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 88 (b) 46 (c) 32 (d) 74
  2. 2.What is the average of all the whole numbers from 39 to 79? (a) 60 (b) 20 (c) 40 (d) 59
  3. 3.The average of 7 numbers is 47. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 96 (b) 36 (c) 35 (d) 47
  4. 4.What is the average of 47, 32, 54 and 39? (a) 42 (b) 44 (c) 43 (d) 45
  5. 5.A batter has an average of 32 runs in 9 matches. How many runs are needed in the next match to raise the average to 38? (a) 38 (b) 60 (c) 44 (d) 92
  6. 6.The average of 7 numbers is 37. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 71 (b) 37 (c) 55 (d) 21
  7. 7.A batter has an average of 31 runs in 8 matches. How many runs are needed in the next match to raise the average to 35? (a) 67 (b) 39 (c) 36 (d) 35
  8. 8.A batter has an average of 29 runs in 8 matches. How many runs are needed in the next match to raise the average to 34? (a) 45 (b) 74 (c) 34 (d) 39
  9. 9.What is the average of all the whole numbers from 8 to 16? (a) 4 (b) 8 (c) 13 (d) 12
  10. 10.What is the average of all the whole numbers from 40 to 68? (a) 54 (b) 28 (c) 14 (d) 55
  11. 11.What is the average of 10, 19, 27 and 40? (a) 23 (b) 32 (c) 25 (d) 24
  12. 12.What is the average of all the whole numbers from 16 to 50? (a) 33 (b) 32 (c) 34 (d) 17
  13. 13.The average of 7 numbers is 23. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 29 (b) 7 (c) 45 (d) 23
  14. 14.A batter has an average of 47 runs in 7 matches. How many runs are needed in the next match to raise the average to 50? (a) 50 (b) 24 (c) 53 (d) 71
  15. 15.The average of 8 numbers is 22. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 8 (b) 46 (c) 9 (d) 22
  16. 16.What is the average of 49, 32, 46 and 45? (a) 43 (b) 45 (c) 42 (d) 44
  17. 17.What is the average of 48, 71, 72, 55, 52 and 68? (a) 63 (b) 62 (c) 60 (d) 61
  18. 18.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) 26 (b) 24 (c) 14 (d) 12
  19. 19.A batter has an average of 40 runs in 6 matches. How many runs are needed in the next match to raise the average to 48? (a) 48 (b) 97 (c) 96 (d) 56
  20. 20.The average of 7 numbers is 42. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 60 (b) 81 (c) 21 (d) 42
  21. 21.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
  22. 22.A batter has an average of 59 runs in 4 matches. How many runs are needed in the next match to raise the average to 63? (a) 20 (b) 67 (c) 79 (d) 63
  23. 23.A batter has an average of 44 runs in 9 matches. How many runs are needed in the next match to raise the average to 48? (a) 48 (b) 52 (c) 40 (d) 84
  24. 24.What is the average of all the whole numbers from 52 to 78? (a) 65 (b) 13 (c) 26 (d) 66
  25. 25.What is the average of 50, 56, 54 and 48? (a) 53 (b) 52 (c) 51 (d) 54
  26. 26.What is the average of all the whole numbers from 21 to 53? (a) 16 (b) 32 (c) 37 (d) 38
  27. 27.What is the average of 44, 49, 38, 48 and 46? (a) 47 (b) 46 (c) 44 (d) 45
  28. 28.What is the average of all the whole numbers from 26 to 48? (a) 37 (b) 11 (c) 38 (d) 22
  29. 29.What is the average of 80, 52, 80 and 56? (a) 69 (b) 67 (c) 66 (d) 68
  30. 30.What is the average of all the whole numbers from 52 to 90? (a) 72 (b) 19 (c) 38 (d) 71
  31. 31.A batter has an average of 20 runs in 7 matches. How many runs are needed in the next match to raise the average to 26? (a) 26 (b) 32 (c) 68 (d) 48
  32. 32.What is the average of all the whole numbers from 28 to 60? (a) 44 (b) 16 (c) 45 (d) 32
  33. 33.What is the average of 52, 60, 50, 37, 61 and 16? (a) 45 (b) 47 (c) 48 (d) 46
  34. 34.What is the average of 80, 64, 83, 68, 65 and 108? (a) 78 (b) 80 (c) 79 (d) 77
  35. 35.The average of 4 numbers is 33. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 61 (b) 48 (c) 33 (d) 20
  36. 36.What is the average of 66, 74, 78, 77, 50 and 45? (a) 78 (b) 64 (c) 66 (d) 65
  37. 37.The average of 8 numbers is 18. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 39 (b) 18 (c) 24 (d) 33
  38. 38.The average of 4 numbers is 39. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 8 (b) 39 (c) 45 (d) 76
  39. 39.The average of 6 numbers is 39. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 81 (b) 25 (c) 24 (d) 39
  40. 40.What is the average of all the whole numbers from 10 to 50? (a) 40 (b) 20 (c) 30 (d) 31

Answer key

  1. 74
  2. 59
  3. 35
  4. 43
  5. 92
  6. 55
  7. 67
  8. 74
  9. 12
  10. 54
  11. 24
  12. 33
  13. 29
  14. 71
  15. 8
  16. 43
  17. 61
  18. 24
  19. 96
  20. 60
  21. 55
  22. 79
  23. 84
  24. 65
  25. 52
  26. 37
  27. 45
  28. 37
  29. 67
  30. 71
  31. 68
  32. 44
  33. 46
  34. 78
  35. 48
  36. 65
  37. 39
  38. 45
  39. 24
  40. 30

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