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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 323 · 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 74, 67, 83 and 92? (a) 78 (b) 81 (c) 79 (d) 80
  2. 2.What is the average of 32, 38, 37, 18, 23 and 14? (a) 27 (b) 26 (c) 29 (d) 28
  3. 3.The average of 5 numbers is 18. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 10 (b) 11 (c) 18 (d) 38
  4. 4.What is the average of all the whole numbers from 10 to 32? (a) 22 (b) 20 (c) 11 (d) 21
  5. 5.What is the average of 38, 37, 38 and 55? (a) 43 (b) 56 (c) 42 (d) 41
  6. 6.What is the average of 68, 46, 41, 52, 45 and 72? (a) 55 (b) 53 (c) 54 (d) 56
  7. 7.What is the average of 67, 92, 92, 90 and 49? (a) 78 (b) 80 (c) 77 (d) 79
  8. 8.A batter has an average of 51 runs in 9 matches. How many runs are needed in the next match to raise the average to 55? (a) 91 (b) 55 (c) 59 (d) 40
  9. 9.What is the average of all the whole numbers from 27 to 59? (a) 44 (b) 32 (c) 16 (d) 43
  10. 10.What is the average of all the whole numbers from 14 to 30? (a) 8 (b) 23 (c) 16 (d) 22
  11. 11.A batter has an average of 44 runs in 6 matches. How many runs are needed in the next match to raise the average to 47? (a) 47 (b) 21 (c) 65 (d) 50
  12. 12.What is the average of all the whole numbers from 53 to 85? (a) 16 (b) 70 (c) 32 (d) 69
  13. 13.What is the average of 55, 32, 30 and 43? (a) 39 (b) 40 (c) 42 (d) 41
  14. 14.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) 51 (b) 25 (c) 56 (d) 71
  15. 15.What is the average of 85, 85, 93, 90, 63 and 52? (a) 77 (b) 80 (c) 79 (d) 78
  16. 16.What is the average of all the whole numbers from 10 to 18? (a) 4 (b) 8 (c) 14 (d) 15
  17. 17.The average of 4 numbers is 33. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 33 (b) 64 (c) 39 (d) 8
  18. 18.The average of 5 numbers is 26. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 23 (b) 26 (c) 53 (d) 22
  19. 19.The average of 4 numbers is 13. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 13 (b) 28 (c) 8 (d) 7
  20. 20.What is the average of all the whole numbers from 10 to 20? (a) 10 (b) 5 (c) 15 (d) 16
  21. 21.The average of 7 numbers is 31. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 31 (b) 61 (c) 57 (d) 35
  22. 22.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 31? (a) 31 (b) 20 (c) 46 (d) 36
  23. 23.A batter has an average of 46 runs in 8 matches. How many runs are needed in the next match to raise the average to 48? (a) 48 (b) 50 (c) 18 (d) 64
  24. 24.What is the average of 81, 95, 65 and 79? (a) 79 (b) 81 (c) 80 (d) 82
  25. 25.The average of 6 numbers is 13. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 24 (b) 12 (c) 13 (d) 23
  26. 26.What is the average of all the whole numbers from 15 to 33? (a) 18 (b) 9 (c) 24 (d) 25
  27. 27.A batter has an average of 24 runs in 6 matches. How many runs are needed in the next match to raise the average to 28? (a) 28 (b) 32 (c) 53 (d) 52
  28. 28.The average of 7 numbers is 27. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 21 (b) 55 (c) 22 (d) 27
  29. 29.What is the average of all the whole numbers from 36 to 60? (a) 12 (b) 24 (c) 48 (d) 49
  30. 30.A batter has an average of 59 runs in 7 matches. How many runs are needed in the next match to raise the average to 65? (a) 71 (b) 48 (c) 107 (d) 65
  31. 31.What is the average of all the whole numbers from 20 to 54? (a) 37 (b) 34 (c) 17 (d) 38
  32. 32.What is the average of 71, 58, 52 and 79? (a) 66 (b) 67 (c) 65 (d) 64
  33. 33.A batter has an average of 28 runs in 8 matches. How many runs are needed in the next match to raise the average to 31? (a) 34 (b) 31 (c) 55 (d) 27
  34. 34.What is the average of all the whole numbers from 17 to 47? (a) 32 (b) 33 (c) 30 (d) 15
  35. 35.What is the average of all the whole numbers from 24 to 58? (a) 17 (b) 41 (c) 42 (d) 34
  36. 36.What is the average of 34, 28, 9 and 13? (a) 21 (b) 20 (c) 22 (d) 28
  37. 37.The average of 4 numbers is 26. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 26 (b) 57 (c) 12 (d) 11
  38. 38.What is the average of all the whole numbers from 21 to 47? (a) 26 (b) 35 (c) 34 (d) 13
  39. 39.The average of 6 numbers is 15. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 11 (b) 15 (c) 10 (d) 31
  40. 40.What is the average of all the whole numbers from 26 to 40? (a) 14 (b) 33 (c) 7 (d) 34

Answer key

  1. 79
  2. 27
  3. 10
  4. 21
  5. 42
  6. 54
  7. 78
  8. 91
  9. 43
  10. 22
  11. 65
  12. 69
  13. 40
  14. 71
  15. 78
  16. 14
  17. 39
  18. 22
  19. 7
  20. 15
  21. 61
  22. 46
  23. 64
  24. 80
  25. 23
  26. 24
  27. 52
  28. 21
  29. 48
  30. 107
  31. 37
  32. 65
  33. 55
  34. 32
  35. 41
  36. 21
  37. 11
  38. 34
  39. 10
  40. 33

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