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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 37 · 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 all the whole numbers from 15 to 51? (a) 18 (b) 34 (c) 33 (d) 36
  2. 2.What is the average of all the whole numbers from 35 to 69? (a) 17 (b) 34 (c) 52 (d) 53
  3. 3.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 30? (a) 58 (b) 32 (c) 34 (d) 30
  4. 4.What is the average of 39, 18, 32, 13, 20 and 28? (a) 30 (b) 26 (c) 25 (d) 24
  5. 5.What is the average of all the whole numbers from 51 to 77? (a) 13 (b) 26 (c) 64 (d) 65
  6. 6.What is the average of 57, 62, 76, 68, 57 and 76? (a) 65 (b) 67 (c) 68 (d) 66
  7. 7.The average of 7 numbers is 30. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 28 (b) 56 (c) 54 (d) 30
  8. 8.What is the average of all the whole numbers from 55 to 95? (a) 40 (b) 76 (c) 75 (d) 20
  9. 9.The average of 8 numbers is 31. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 31 (b) 24 (c) 63 (d) 25
  10. 10.The average of 6 numbers is 22. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 22 (b) 43 (c) 6 (d) 27
  11. 11.The average of 7 numbers is 38. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 73 (b) 56 (c) 38 (d) 21
  12. 12.What is the average of all the whole numbers from 31 to 41? (a) 37 (b) 5 (c) 36 (d) 10
  13. 13.What is the average of all the whole numbers from 20 to 52? (a) 36 (b) 37 (c) 32 (d) 16
  14. 14.What is the average of all the whole numbers from 27 to 59? (a) 44 (b) 43 (c) 32 (d) 16
  15. 15.The average of 6 numbers is 30. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 45 (b) 18 (c) 57 (d) 30
  16. 16.A batter has an average of 21 runs in 7 matches. How many runs are needed in the next match to raise the average to 27? (a) 69 (b) 48 (c) 27 (d) 33
  17. 17.A batter has an average of 27 runs in 5 matches. How many runs are needed in the next match to raise the average to 30? (a) 30 (b) 18 (c) 45 (d) 33
  18. 18.A batter has an average of 43 runs in 5 matches. How many runs are needed in the next match to raise the average to 48? (a) 53 (b) 73 (c) 30 (d) 48
  19. 19.What is the average of 36, 40, 42, 51 and 46? (a) 42 (b) 44 (c) 45 (d) 43
  20. 20.What is the average of 76, 92, 86 and 66? (a) 79 (b) 81 (c) 80 (d) 82
  21. 21.A batter has an average of 49 runs in 5 matches. How many runs are needed in the next match to raise the average to 55? (a) 61 (b) 55 (c) 36 (d) 85
  22. 22.What is the average of all the whole numbers from 18 to 50? (a) 32 (b) 34 (c) 16 (d) 35
  23. 23.What is the average of all the whole numbers from 18 to 34? (a) 16 (b) 8 (c) 27 (d) 26
  24. 24.The average of 7 numbers is 33. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 39 (b) 65 (c) 7 (d) 33
  25. 25.What is the average of all the whole numbers from 24 to 46? (a) 36 (b) 11 (c) 35 (d) 22
  26. 26.What is the average of 76, 79, 73, 77, 56 and 29? (a) 78 (b) 66 (c) 64 (d) 65
  27. 27.A batter has an average of 21 runs in 8 matches. How many runs are needed in the next match to raise the average to 27? (a) 54 (b) 75 (c) 27 (d) 33
  28. 28.What is the average of 46, 59, 45, 61 and 49? (a) 65 (b) 53 (c) 52 (d) 51
  29. 29.What is the average of all the whole numbers from 19 to 39? (a) 29 (b) 20 (c) 30 (d) 10
  30. 30.What is the average of 22, 40, 20, 40 and 48? (a) 33 (b) 36 (c) 35 (d) 34
  31. 31.A batter has an average of 22 runs in 5 matches. How many runs are needed in the next match to raise the average to 30? (a) 70 (b) 48 (c) 30 (d) 38
  32. 32.A batter has an average of 44 runs in 5 matches. How many runs are needed in the next match to raise the average to 52? (a) 60 (b) 92 (c) 48 (d) 52
  33. 33.A batter has an average of 49 runs in 7 matches. How many runs are needed in the next match to raise the average to 51? (a) 51 (b) 65 (c) 53 (d) 16
  34. 34.The average of 6 numbers is 32. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 37 (b) 63 (c) 32 (d) 6
  35. 35.A batter has an average of 46 runs in 9 matches. How many runs are needed in the next match to raise the average to 52? (a) 60 (b) 106 (c) 58 (d) 52
  36. 36.The average of 6 numbers is 21. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 40 (b) 12 (c) 31 (d) 21
  37. 37.What is the average of 61, 50, 56, 50, 75 and 74? (a) 63 (b) 61 (c) 60 (d) 62
  38. 38.A batter has an average of 52 runs in 5 matches. How many runs are needed in the next match to raise the average to 59? (a) 59 (b) 42 (c) 94 (d) 66
  39. 39.The average of 5 numbers is 30. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 50 (b) 30 (c) 55 (d) 25
  40. 40.The average of 4 numbers is 22. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 43 (b) 25 (c) 22 (d) 4

Answer key

  1. 33
  2. 52
  3. 58
  4. 25
  5. 64
  6. 66
  7. 54
  8. 75
  9. 24
  10. 27
  11. 56
  12. 36
  13. 36
  14. 43
  15. 45
  16. 69
  17. 45
  18. 73
  19. 43
  20. 80
  21. 85
  22. 34
  23. 26
  24. 39
  25. 35
  26. 65
  27. 75
  28. 52
  29. 29
  30. 34
  31. 70
  32. 92
  33. 65
  34. 37
  35. 106
  36. 31
  37. 61
  38. 94
  39. 50
  40. 25

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