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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 954 · 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 10. When one number is taken away, the average of the rest is 6. Which number was taken away? (a) 16 (b) 28 (c) 10 (d) 34
  2. 2.The average of 6 numbers is 42. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 17 (b) 42 (c) 18 (d) 89
  3. 3.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 25? (a) 53 (b) 32 (c) 29 (d) 25
  4. 4.What is the average of all the whole numbers from 55 to 83? (a) 28 (b) 70 (c) 14 (d) 69
  5. 5.The average of 4 numbers is 13. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 4 (b) 25 (c) 13 (d) 16
  6. 6.What is the average of 58, 57, 76 and 89? (a) 69 (b) 71 (c) 70 (d) 72
  7. 7.The average of 8 numbers is 32. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 8 (b) 32 (c) 63 (d) 39
  8. 8.What is the average of 29, 26, 26, 37 and 22? (a) 29 (b) 28 (c) 27 (d) 35
  9. 9.The average of 6 numbers is 47. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 28 (b) 98 (c) 27 (d) 47
  10. 10.A batter has an average of 22 runs in 8 matches. How many runs are needed in the next match to raise the average to 27? (a) 27 (b) 45 (c) 67 (d) 32
  11. 11.What is the average of all the whole numbers from 21 to 51? (a) 37 (b) 36 (c) 15 (d) 30
  12. 12.A batter has an average of 29 runs in 3 matches. How many runs are needed in the next match to raise the average to 31? (a) 31 (b) 37 (c) 33 (d) 8
  13. 13.A batter has an average of 31 runs in 4 matches. How many runs are needed in the next match to raise the average to 37? (a) 37 (b) 30 (c) 61 (d) 43
  14. 14.What is the average of 85, 59, 74 and 78? (a) 73 (b) 75 (c) 74 (d) 76
  15. 15.A batter has an average of 31 runs in 9 matches. How many runs are needed in the next match to raise the average to 38? (a) 38 (b) 70 (c) 45 (d) 101
  16. 16.The average of 6 numbers is 17. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 36 (b) 17 (c) 8 (d) 7
  17. 17.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 55? (a) 61 (b) 55 (c) 48 (d) 97
  18. 18.A batter has an average of 42 runs in 4 matches. How many runs are needed in the next match to raise the average to 44? (a) 46 (b) 10 (c) 44 (d) 52
  19. 19.The average of 8 numbers is 43. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 8 (b) 85 (c) 43 (d) 50
  20. 20.The average of 4 numbers is 25. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 25 (b) 16 (c) 37 (d) 46
  21. 21.What is the average of 31, 12, 29, 33 and 30? (a) 28 (b) 26 (c) 29 (d) 27
  22. 22.The average of 6 numbers is 47. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 47 (b) 62 (c) 18 (d) 91
  23. 23.The average of 5 numbers is 15. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 27 (b) 26 (c) 15 (d) 28
  24. 24.The average of 6 numbers is 47. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 24 (b) 90 (c) 47 (d) 67
  25. 25.What is the average of 21, 24, 40, 28, 33 and 16? (a) 28 (b) 29 (c) 27 (d) 26
  26. 26.What is the average of all the whole numbers from 45 to 79? (a) 63 (b) 17 (c) 34 (d) 62
  27. 27.A batter has an average of 57 runs in 7 matches. How many runs are needed in the next match to raise the average to 65? (a) 64 (b) 65 (c) 121 (d) 73
  28. 28.What is the average of 41, 24, 22 and 49? (a) 36 (b) 35 (c) 33 (d) 34
  29. 29.What is the average of all the whole numbers from 57 to 73? (a) 16 (b) 8 (c) 65 (d) 66
  30. 30.What is the average of all the whole numbers from 46 to 52? (a) 6 (b) 3 (c) 49 (d) 50
  31. 31.What is the average of all the whole numbers from 43 to 75? (a) 32 (b) 59 (c) 60 (d) 16
  32. 32.What is the average of all the whole numbers from 27 to 63? (a) 36 (b) 18 (c) 46 (d) 45
  33. 33.What is the average of all the whole numbers from 28 to 40? (a) 6 (b) 12 (c) 35 (d) 34
  34. 34.What is the average of 73, 90, 87, 70 and 80? (a) 80 (b) 100 (c) 79 (d) 81
  35. 35.What is the average of all the whole numbers from 40 to 66? (a) 53 (b) 26 (c) 13 (d) 54
  36. 36.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 33? (a) 33 (b) 82 (c) 40 (d) 56
  37. 37.What is the average of 68, 83, 81, 74 and 39? (a) 68 (b) 69 (c) 71 (d) 70
  38. 38.A batter has an average of 27 runs in 6 matches. How many runs are needed in the next match to raise the average to 29? (a) 29 (b) 31 (c) 14 (d) 41
  39. 39.The average of 6 numbers is 34. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 34 (b) 71 (c) 19 (d) 20
  40. 40.What is the average of 81, 71, 56, 57, 59 and 96? (a) 84 (b) 70 (c) 71 (d) 69

Answer key

  1. 34
  2. 17
  3. 53
  4. 69
  5. 16
  6. 70
  7. 39
  8. 28
  9. 27
  10. 67
  11. 36
  12. 37
  13. 61
  14. 74
  15. 101
  16. 7
  17. 97
  18. 52
  19. 50
  20. 37
  21. 27
  22. 62
  23. 27
  24. 67
  25. 27
  26. 62
  27. 121
  28. 34
  29. 65
  30. 49
  31. 59
  32. 45
  33. 34
  34. 80
  35. 53
  36. 82
  37. 69
  38. 41
  39. 19
  40. 70

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