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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 105 · 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 31, 22, 22, 14, 21 and 40? (a) 26 (b) 25 (c) 24 (d) 30
  2. 2.The average of 4 numbers is 12. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 4 (b) 23 (c) 15 (d) 12
  3. 3.The average of 6 numbers is 16. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 41 (b) 30 (c) 27 (d) 16
  4. 4.What is the average of 46, 55, 42, 50 and 82? (a) 55 (b) 57 (c) 54 (d) 56
  5. 5.A batter has an average of 42 runs in 5 matches. How many runs are needed in the next match to raise the average to 50? (a) 90 (b) 48 (c) 50 (d) 58
  6. 6.What is the average of all the whole numbers from 13 to 45? (a) 30 (b) 32 (c) 16 (d) 29
  7. 7.The average of 5 numbers is 33. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 15 (b) 45 (c) 33 (d) 63
  8. 8.The average of 4 numbers is 24. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 44 (b) 36 (c) 24 (d) 16
  9. 9.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 49? (a) 49 (b) 57 (c) 32 (d) 73
  10. 10.What is the average of 45, 53, 44 and 54? (a) 48 (b) 49 (c) 51 (d) 50
  11. 11.The average of 8 numbers is 21. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 21 (b) 8 (c) 44 (d) 7
  12. 12.A batter has an average of 21 runs in 3 matches. How many runs are needed in the next match to raise the average to 24? (a) 24 (b) 33 (c) 12 (d) 27
  13. 13.What is the average of 17, 40, 36, 28, 20 and 51? (a) 32 (b) 34 (c) 31 (d) 33
  14. 14.What is the average of all the whole numbers from 32 to 38? (a) 6 (b) 3 (c) 36 (d) 35
  15. 15.What is the average of 45, 49, 43 and 55? (a) 47 (b) 49 (c) 48 (d) 64
  16. 16.What is the average of all the whole numbers from 10 to 26? (a) 8 (b) 16 (c) 19 (d) 18
  17. 17.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) 52 (b) 28 (c) 53 (d) 32
  18. 18.What is the average of 62, 65, 79 and 102? (a) 76 (b) 79 (c) 78 (d) 77
  19. 19.A batter has an average of 37 runs in 5 matches. How many runs are needed in the next match to raise the average to 43? (a) 43 (b) 49 (c) 36 (d) 73
  20. 20.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 55? (a) 58 (b) 55 (c) 70 (d) 18
  21. 21.The average of 7 numbers is 39. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 39 (b) 14 (c) 51 (d) 76
  22. 22.The average of 7 numbers is 29. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 57 (b) 35 (c) 7 (d) 29
  23. 23.What is the average of all the whole numbers from 35 to 47? (a) 42 (b) 41 (c) 12 (d) 6
  24. 24.What is the average of 57, 62, 79, 60 and 77? (a) 66 (b) 68 (c) 67 (d) 69
  25. 25.What is the average of all the whole numbers from 46 to 52? (a) 49 (b) 50 (c) 6 (d) 3
  26. 26.The average of 6 numbers is 30. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 55 (b) 56 (c) 30 (d) 54
  27. 27.The average of 6 numbers is 47. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 52 (b) 93 (c) 6 (d) 47
  28. 28.What is the average of 86, 64, 89, 63, 69 and 97? (a) 77 (b) 79 (c) 80 (d) 78
  29. 29.A batter has an average of 43 runs in 7 matches. How many runs are needed in the next match to raise the average to 49? (a) 49 (b) 48 (c) 55 (d) 91
  30. 30.A batter has an average of 42 runs in 5 matches. How many runs are needed in the next match to raise the average to 44? (a) 12 (b) 44 (c) 54 (d) 46
  31. 31.What is the average of all the whole numbers from 22 to 32? (a) 10 (b) 28 (c) 5 (d) 27
  32. 32.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 45? (a) 52 (b) 70 (c) 108 (d) 45
  33. 33.A batter has an average of 36 runs in 5 matches. How many runs are needed in the next match to raise the average to 40? (a) 60 (b) 40 (c) 24 (d) 44
  34. 34.A batter has an average of 20 runs in 5 matches. How many runs are needed in the next match to raise the average to 28? (a) 68 (b) 36 (c) 28 (d) 48
  35. 35.The average of 8 numbers is 34. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 34 (b) 69 (c) 63 (d) 40
  36. 36.What is the average of 49, 51, 62 and 58? (a) 55 (b) 57 (c) 54 (d) 56
  37. 37.A batter has an average of 31 runs in 3 matches. How many runs are needed in the next match to raise the average to 36? (a) 51 (b) 20 (c) 36 (d) 41
  38. 38.What is the average of 74, 57, 61 and 76? (a) 67 (b) 66 (c) 69 (d) 68
  39. 39.The average of 7 numbers is 15. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 15 (b) 25 (c) 45 (d) 35
  40. 40.What is the average of 38, 29, 42 and 19? (a) 34 (b) 33 (c) 31 (d) 32

Answer key

  1. 25
  2. 15
  3. 41
  4. 55
  5. 90
  6. 29
  7. 45
  8. 36
  9. 73
  10. 49
  11. 7
  12. 33
  13. 32
  14. 35
  15. 48
  16. 18
  17. 52
  18. 77
  19. 73
  20. 70
  21. 51
  22. 35
  23. 41
  24. 67
  25. 49
  26. 55
  27. 52
  28. 78
  29. 91
  30. 54
  31. 27
  32. 108
  33. 60
  34. 68
  35. 69
  36. 55
  37. 51
  38. 67
  39. 45
  40. 32

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