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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 948 · 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 6 numbers is 23. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 33 (b) 44 (c) 23 (d) 12
  2. 2.What is the average of 65, 63, 67, 69 and 116? (a) 75 (b) 77 (c) 95 (d) 76
  3. 3.The average of 5 numbers is 31. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 10 (b) 60 (c) 31 (d) 39
  4. 4.A batter has an average of 40 runs in 9 matches. How many runs are needed in the next match to raise the average to 48? (a) 48 (b) 120 (c) 80 (d) 56
  5. 5.A batter has an average of 22 runs in 6 matches. How many runs are needed in the next match to raise the average to 24? (a) 14 (b) 36 (c) 26 (d) 24
  6. 6.The average of 4 numbers is 27. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 27 (b) 58 (c) 16 (d) 15
  7. 7.The average of 5 numbers is 13. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 9 (b) 13 (c) 10 (d) 27
  8. 8.What is the average of all the whole numbers from 54 to 66? (a) 61 (b) 6 (c) 60 (d) 12
  9. 9.What is the average of all the whole numbers from 13 to 21? (a) 8 (b) 17 (c) 18 (d) 4
  10. 10.What is the average of all the whole numbers from 39 to 79? (a) 59 (b) 60 (c) 20 (d) 40
  11. 11.The average of 6 numbers is 10. When one number is taken away, the average of the rest is 6. Which number was taken away? (a) 10 (b) 16 (c) 24 (d) 30
  12. 12.The average of 5 numbers is 47. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 96 (b) 47 (c) 39 (d) 40
  13. 13.The average of 8 numbers is 13. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 7 (b) 27 (c) 6 (d) 13
  14. 14.What is the average of all the whole numbers from 28 to 42? (a) 36 (b) 35 (c) 14 (d) 7
  15. 15.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) 33 (b) 10 (c) 16 (d) 11
  16. 16.A batter has an average of 43 runs in 8 matches. How many runs are needed in the next match to raise the average to 51? (a) 51 (b) 115 (c) 59 (d) 72
  17. 17.The average of 8 numbers is 38. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 45 (b) 75 (c) 8 (d) 38
  18. 18.A batter has an average of 39 runs in 5 matches. How many runs are needed in the next match to raise the average to 47? (a) 87 (b) 47 (c) 55 (d) 48
  19. 19.What is the average of all the whole numbers from 48 to 70? (a) 22 (b) 59 (c) 11 (d) 60
  20. 20.What is the average of all the whole numbers from 30 to 60? (a) 30 (b) 45 (c) 46 (d) 15
  21. 21.What is the average of all the whole numbers from 52 to 88? (a) 70 (b) 71 (c) 36 (d) 18
  22. 22.The average of 4 numbers is 26. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 26 (b) 24 (c) 53 (d) 23
  23. 23.A batter has an average of 55 runs in 9 matches. How many runs are needed in the next match to raise the average to 62? (a) 62 (b) 70 (c) 125 (d) 69
  24. 24.A batter has an average of 28 runs in 6 matches. How many runs are needed in the next match to raise the average to 34? (a) 70 (b) 34 (c) 42 (d) 40
  25. 25.The average of 7 numbers is 26. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 35 (b) 47 (c) 26 (d) 56
  26. 26.The average of 8 numbers is 33. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 47 (b) 16 (c) 64 (d) 33
  27. 27.What is the average of all the whole numbers from 9 to 25? (a) 8 (b) 16 (c) 18 (d) 17
  28. 28.What is the average of all the whole numbers from 9 to 31? (a) 21 (b) 11 (c) 20 (d) 22
  29. 29.The average of 7 numbers is 36. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 24 (b) 36 (c) 25 (d) 74
  30. 30.A batter has an average of 55 runs in 3 matches. How many runs are needed in the next match to raise the average to 57? (a) 8 (b) 63 (c) 59 (d) 57
  31. 31.What is the average of 45, 45, 55, 55 and 100? (a) 60 (b) 59 (c) 75 (d) 61
  32. 32.The average of 8 numbers is 42. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 81 (b) 42 (c) 63 (d) 24
  33. 33.What is the average of 59, 47, 55, 43, 49 and 41? (a) 51 (b) 49 (c) 48 (d) 50
  34. 34.A batter has an average of 35 runs in 5 matches. How many runs are needed in the next match to raise the average to 40? (a) 30 (b) 45 (c) 65 (d) 40
  35. 35.What is the average of 63, 50, 52 and 83? (a) 61 (b) 64 (c) 63 (d) 62
  36. 36.What is the average of all the whole numbers from 58 to 68? (a) 10 (b) 5 (c) 63 (d) 64
  37. 37.The average of 8 numbers is 13. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 25 (b) 8 (c) 13 (d) 20
  38. 38.What is the average of all the whole numbers from 15 to 25? (a) 5 (b) 20 (c) 10 (d) 21
  39. 39.What is the average of 95, 91, 79 and 55? (a) 82 (b) 81 (c) 79 (d) 80
  40. 40.What is the average of 10, 24, 32 and 14? (a) 19 (b) 20 (c) 22 (d) 21

Answer key

  1. 33
  2. 76
  3. 39
  4. 120
  5. 36
  6. 15
  7. 9
  8. 60
  9. 17
  10. 59
  11. 30
  12. 39
  13. 6
  14. 35
  15. 10
  16. 115
  17. 45
  18. 87
  19. 59
  20. 45
  21. 70
  22. 23
  23. 125
  24. 70
  25. 56
  26. 47
  27. 17
  28. 20
  29. 24
  30. 63
  31. 60
  32. 63
  33. 49
  34. 65
  35. 62
  36. 63
  37. 20
  38. 20
  39. 80
  40. 20

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