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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 448 · 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 4 numbers is 20. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 20 (b) 23 (c) 4 (d) 39
  2. 2.The average of 7 numbers is 27. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 52 (b) 27 (c) 39 (d) 14
  3. 3.The average of 5 numbers is 24. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 47 (b) 5 (c) 24 (d) 28
  4. 4.What is the average of 81, 85, 78 and 60? (a) 75 (b) 78 (c) 77 (d) 76
  5. 5.What is the average of 61, 56, 48, 59, 69 and 37? (a) 56 (b) 55 (c) 66 (d) 54
  6. 6.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) 28 (b) 13 (c) 8 (d) 7
  7. 7.What is the average of 51, 51, 45, 62, 52 and 99? (a) 72 (b) 60 (c) 61 (d) 59
  8. 8.The average of 6 numbers is 45. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 45 (b) 88 (c) 55 (d) 12
  9. 9.What is the average of all the whole numbers from 10 to 24? (a) 17 (b) 18 (c) 7 (d) 14
  10. 10.The average of 5 numbers is 18. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 26 (b) 18 (c) 10 (d) 34
  11. 11.A batter has an average of 35 runs in 7 matches. How many runs are needed in the next match to raise the average to 43? (a) 99 (b) 43 (c) 51 (d) 64
  12. 12.A batter has an average of 24 runs in 8 matches. How many runs are needed in the next match to raise the average to 32? (a) 32 (b) 72 (c) 40 (d) 96
  13. 13.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) 47 (b) 27 (c) 50 (d) 24
  14. 14.What is the average of 69, 76, 79, 64 and 62? (a) 72 (b) 69 (c) 71 (d) 70
  15. 15.What is the average of 61, 61, 72, 68 and 118? (a) 77 (b) 95 (c) 75 (d) 76
  16. 16.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) 12 (b) 32 (c) 13 (d) 69
  17. 17.What is the average of 36, 27, 22 and 3? (a) 21 (b) 24 (c) 23 (d) 22
  18. 18.What is the average of 41, 43, 51 and 69? (a) 52 (b) 50 (c) 51 (d) 68
  19. 19.What is the average of all the whole numbers from 60 to 78? (a) 18 (b) 9 (c) 69 (d) 70
  20. 20.What is the average of all the whole numbers from 25 to 63? (a) 44 (b) 45 (c) 19 (d) 38
  21. 21.A batter has an average of 54 runs in 8 matches. How many runs are needed in the next match to raise the average to 60? (a) 54 (b) 108 (c) 66 (d) 60
  22. 22.A batter has an average of 55 runs in 8 matches. How many runs are needed in the next match to raise the average to 60? (a) 100 (b) 45 (c) 65 (d) 60
  23. 23.What is the average of all the whole numbers from 17 to 57? (a) 20 (b) 38 (c) 40 (d) 37
  24. 24.What is the average of all the whole numbers from 24 to 48? (a) 37 (b) 12 (c) 24 (d) 36
  25. 25.A batter has an average of 24 runs in 4 matches. How many runs are needed in the next match to raise the average to 31? (a) 35 (b) 59 (c) 38 (d) 31
  26. 26.What is the average of all the whole numbers from 56 to 64? (a) 61 (b) 8 (c) 60 (d) 4
  27. 27.A batter has an average of 54 runs in 8 matches. How many runs are needed in the next match to raise the average to 62? (a) 72 (b) 126 (c) 70 (d) 62
  28. 28.A batter has an average of 47 runs in 6 matches. How many runs are needed in the next match to raise the average to 49? (a) 14 (b) 61 (c) 49 (d) 51
  29. 29.The average of 6 numbers is 11. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 26 (b) 19 (c) 18 (d) 11
  30. 30.What is the average of all the whole numbers from 36 to 72? (a) 54 (b) 18 (c) 36 (d) 55
  31. 31.What is the average of 25, 38, 28, 18, 21 and 50? (a) 29 (b) 31 (c) 30 (d) 36
  32. 32.What is the average of 13, 19, 16, 23 and 54? (a) 24 (b) 25 (c) 26 (d) 27
  33. 33.What is the average of 93, 82, 90 and 55? (a) 82 (b) 80 (c) 81 (d) 79
  34. 34.The average of 4 numbers is 26. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 51 (b) 4 (c) 29 (d) 26
  35. 35.What is the average of 75, 76, 75, 82 and 52? (a) 73 (b) 72 (c) 71 (d) 90
  36. 36.What is the average of 42, 54, 53 and 75? (a) 56 (b) 55 (c) 58 (d) 57
  37. 37.The average of 7 numbers is 16. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 10 (b) 33 (c) 16 (d) 11
  38. 38.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 42? (a) 67 (b) 30 (c) 47 (d) 42
  39. 39.What is the average of all the whole numbers from 48 to 54? (a) 3 (b) 52 (c) 6 (d) 51
  40. 40.The average of 8 numbers is 13. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 16 (b) 24 (c) 13 (d) 27

Answer key

  1. 23
  2. 39
  3. 28
  4. 76
  5. 55
  6. 7
  7. 60
  8. 55
  9. 17
  10. 26
  11. 99
  12. 96
  13. 47
  14. 70
  15. 76
  16. 12
  17. 22
  18. 51
  19. 69
  20. 44
  21. 108
  22. 100
  23. 37
  24. 36
  25. 59
  26. 60
  27. 126
  28. 61
  29. 26
  30. 54
  31. 30
  32. 25
  33. 80
  34. 29
  35. 72
  36. 56
  37. 10
  38. 67
  39. 51
  40. 27

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