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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 204 · 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 7 numbers is 26. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 49 (b) 26 (c) 21 (d) 44
  2. 2.A batter has an average of 53 runs in 4 matches. How many runs are needed in the next match to raise the average to 55? (a) 10 (b) 57 (c) 63 (d) 55
  3. 3.What is the average of all the whole numbers from 14 to 46? (a) 32 (b) 16 (c) 31 (d) 30
  4. 4.What is the average of 31, 20, 22, 38, 30 and 45? (a) 32 (b) 33 (c) 31 (d) 30
  5. 5.What is the average of all the whole numbers from 51 to 69? (a) 18 (b) 61 (c) 60 (d) 9
  6. 6.A batter has an average of 28 runs in 9 matches. How many runs are needed in the next match to raise the average to 32? (a) 68 (b) 32 (c) 40 (d) 36
  7. 7.What is the average of all the whole numbers from 29 to 45? (a) 37 (b) 38 (c) 8 (d) 16
  8. 8.What is the average of 74, 67, 66 and 89? (a) 75 (b) 76 (c) 74 (d) 73
  9. 9.A batter has an average of 40 runs in 5 matches. How many runs are needed in the next match to raise the average to 45? (a) 70 (b) 50 (c) 30 (d) 45
  10. 10.What is the average of 41, 18, 38, 34, 32 and 11? (a) 30 (b) 28 (c) 29 (d) 31
  11. 11.A batter has an average of 32 runs in 7 matches. How many runs are needed in the next match to raise the average to 38? (a) 48 (b) 38 (c) 80 (d) 44
  12. 12.A batter has an average of 23 runs in 8 matches. How many runs are needed in the next match to raise the average to 25? (a) 41 (b) 25 (c) 18 (d) 27
  13. 13.A batter has an average of 23 runs in 6 matches. How many runs are needed in the next match to raise the average to 28? (a) 33 (b) 58 (c) 35 (d) 28
  14. 14.The average of 5 numbers is 17. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 10 (b) 17 (c) 9 (d) 36
  15. 15.The average of 6 numbers is 27. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 50 (b) 27 (c) 47 (d) 24
  16. 16.What is the average of all the whole numbers from 18 to 56? (a) 36 (b) 37 (c) 19 (d) 38
  17. 17.What is the average of all the whole numbers from 27 to 37? (a) 33 (b) 10 (c) 32 (d) 5
  18. 18.What is the average of 47, 49, 37, 58 and 54? (a) 49 (b) 51 (c) 48 (d) 50
  19. 19.The average of 6 numbers is 15. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 32 (b) 5 (c) 6 (d) 15
  20. 20.A batter has an average of 36 runs in 8 matches. How many runs are needed in the next match to raise the average to 41? (a) 41 (b) 45 (c) 46 (d) 81
  21. 21.The average of 5 numbers is 17. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 2 (b) 38 (c) 17 (d) 1
  22. 22.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) 57 (b) 31 (c) 35 (d) 61
  23. 23.The average of 5 numbers is 28. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 60 (b) 28 (c) 13 (d) 12
  24. 24.What is the average of all the whole numbers from 20 to 32? (a) 12 (b) 26 (c) 27 (d) 6
  25. 25.What is the average of 57, 62, 56, 40 and 55? (a) 54 (b) 53 (c) 56 (d) 55
  26. 26.A batter has an average of 56 runs in 9 matches. How many runs are needed in the next match to raise the average to 59? (a) 59 (b) 30 (c) 62 (d) 86
  27. 27.What is the average of 26, 37, 42 and 43? (a) 37 (b) 39 (c) 36 (d) 38
  28. 28.A batter has an average of 39 runs in 7 matches. How many runs are needed in the next match to raise the average to 41? (a) 16 (b) 41 (c) 55 (d) 43
  29. 29.A batter has an average of 58 runs in 7 matches. How many runs are needed in the next match to raise the average to 61? (a) 24 (b) 82 (c) 64 (d) 61
  30. 30.What is the average of all the whole numbers from 56 to 78? (a) 67 (b) 68 (c) 11 (d) 22
  31. 31.A batter has an average of 36 runs in 3 matches. How many runs are needed in the next match to raise the average to 42? (a) 60 (b) 42 (c) 48 (d) 24
  32. 32.What is the average of 30, 42, 35, 23 and 25? (a) 30 (b) 32 (c) 33 (d) 31
  33. 33.A batter has an average of 29 runs in 5 matches. How many runs are needed in the next match to raise the average to 31? (a) 41 (b) 31 (c) 33 (d) 12
  34. 34.A batter has an average of 59 runs in 3 matches. How many runs are needed in the next match to raise the average to 61? (a) 61 (b) 63 (c) 8 (d) 67
  35. 35.A batter has an average of 24 runs in 5 matches. How many runs are needed in the next match to raise the average to 31? (a) 66 (b) 38 (c) 42 (d) 31
  36. 36.What is the average of 62, 81, 66 and 71? (a) 71 (b) 69 (c) 70 (d) 72
  37. 37.What is the average of 33, 26, 49 and 52? (a) 40 (b) 39 (c) 42 (d) 41
  38. 38.What is the average of all the whole numbers from 16 to 24? (a) 8 (b) 4 (c) 20 (d) 21
  39. 39.The average of 6 numbers is 18. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 12 (b) 34 (c) 18 (d) 28
  40. 40.The average of 5 numbers is 32. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 13 (b) 32 (c) 12 (d) 69

Answer key

  1. 44
  2. 63
  3. 30
  4. 31
  5. 60
  6. 68
  7. 37
  8. 74
  9. 70
  10. 29
  11. 80
  12. 41
  13. 58
  14. 9
  15. 47
  16. 37
  17. 32
  18. 49
  19. 5
  20. 81
  21. 1
  22. 61
  23. 12
  24. 26
  25. 54
  26. 86
  27. 37
  28. 55
  29. 82
  30. 67
  31. 60
  32. 31
  33. 41
  34. 67
  35. 66
  36. 70
  37. 40
  38. 20
  39. 28
  40. 12

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