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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 631 · 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 5 numbers is 15. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 15 (b) 5 (c) 19 (d) 29
  2. 2.The average of 7 numbers is 20. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 39 (b) 20 (c) 26 (d) 7
  3. 3.What is the average of all the whole numbers from 47 to 73? (a) 60 (b) 61 (c) 26 (d) 13
  4. 4.A batter has an average of 45 runs in 4 matches. How many runs are needed in the next match to raise the average to 51? (a) 30 (b) 51 (c) 75 (d) 57
  5. 5.The average of 5 numbers is 28. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 40 (b) 28 (c) 15 (d) 53
  6. 6.What is the average of 17, 12, 14, 22, 19 and 66? (a) 30 (b) 26 (c) 25 (d) 24
  7. 7.What is the average of all the whole numbers from 59 to 97? (a) 19 (b) 79 (c) 38 (d) 78
  8. 8.What is the average of 32, 33, 31 and 72? (a) 42 (b) 41 (c) 43 (d) 56
  9. 9.A batter has an average of 54 runs in 9 matches. How many runs are needed in the next match to raise the average to 62? (a) 70 (b) 80 (c) 134 (d) 62
  10. 10.What is the average of all the whole numbers from 51 to 59? (a) 8 (b) 4 (c) 56 (d) 55
  11. 11.What is the average of 11, 17, 11, 10 and 51? (a) 19 (b) 20 (c) 25 (d) 21
  12. 12.A batter has an average of 33 runs in 5 matches. How many runs are needed in the next match to raise the average to 36? (a) 39 (b) 51 (c) 18 (d) 36
  13. 13.A batter has an average of 59 runs in 9 matches. How many runs are needed in the next match to raise the average to 61? (a) 20 (b) 61 (c) 63 (d) 79
  14. 14.What is the average of 29, 34, 46 and 67? (a) 45 (b) 46 (c) 44 (d) 43
  15. 15.The average of 4 numbers is 50. When one number is taken away, the average of the rest is 54. Which number was taken away? (a) 104 (b) 38 (c) 50 (d) 39
  16. 16.A batter has an average of 44 runs in 3 matches. How many runs are needed in the next match to raise the average to 52? (a) 32 (b) 60 (c) 52 (d) 76
  17. 17.The average of 4 numbers is 19. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 8 (b) 25 (c) 36 (d) 19
  18. 18.What is the average of 41, 47, 29, 47 and 56? (a) 44 (b) 45 (c) 43 (d) 55
  19. 19.What is the average of all the whole numbers from 14 to 46? (a) 32 (b) 30 (c) 31 (d) 16
  20. 20.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 26? (a) 36 (b) 26 (c) 30 (d) 58
  21. 21.What is the average of all the whole numbers from 42 to 50? (a) 47 (b) 46 (c) 8 (d) 4
  22. 22.What is the average of all the whole numbers from 27 to 47? (a) 37 (b) 10 (c) 38 (d) 20
  23. 23.A batter has an average of 55 runs in 6 matches. How many runs are needed in the next match to raise the average to 58? (a) 76 (b) 61 (c) 58 (d) 21
  24. 24.What is the average of 65, 81, 66, 81 and 102? (a) 80 (b) 79 (c) 81 (d) 78
  25. 25.The average of 7 numbers is 38. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 9 (b) 81 (c) 8 (d) 38
  26. 26.What is the average of all the whole numbers from 35 to 43? (a) 4 (b) 8 (c) 40 (d) 39
  27. 27.A batter has an average of 39 runs in 3 matches. How many runs are needed in the next match to raise the average to 46? (a) 28 (b) 53 (c) 67 (d) 46
  28. 28.What is the average of 69, 61, 85 and 65? (a) 72 (b) 71 (c) 70 (d) 69
  29. 29.A batter has an average of 26 runs in 6 matches. How many runs are needed in the next match to raise the average to 30? (a) 30 (b) 34 (c) 54 (d) 28
  30. 30.A batter has an average of 38 runs in 7 matches. How many runs are needed in the next match to raise the average to 45? (a) 56 (b) 52 (c) 94 (d) 45
  31. 31.A batter has an average of 54 runs in 4 matches. How many runs are needed in the next match to raise the average to 61? (a) 68 (b) 89 (c) 35 (d) 61
  32. 32.The average of 6 numbers is 43. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 43 (b) 18 (c) 83 (d) 58
  33. 33.What is the average of 31, 8, 14, 25, 21 and 27? (a) 21 (b) 23 (c) 22 (d) 20
  34. 34.The average of 8 numbers is 46. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 74 (b) 88 (c) 32 (d) 46
  35. 35.What is the average of all the whole numbers from 8 to 40? (a) 16 (b) 25 (c) 32 (d) 24
  36. 36.What is the average of all the whole numbers from 42 to 62? (a) 10 (b) 53 (c) 20 (d) 52
  37. 37.The average of 4 numbers is 14. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 12 (b) 23 (c) 14 (d) 25
  38. 38.What is the average of all the whole numbers from 32 to 56? (a) 24 (b) 44 (c) 12 (d) 45
  39. 39.The average of 4 numbers is 47. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 47 (b) 42 (c) 41 (d) 96
  40. 40.The average of 7 numbers is 37. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 37 (b) 7 (c) 79 (d) 8

Answer key

  1. 19
  2. 26
  3. 60
  4. 75
  5. 40
  6. 25
  7. 78
  8. 42
  9. 134
  10. 55
  11. 20
  12. 51
  13. 79
  14. 44
  15. 38
  16. 76
  17. 25
  18. 44
  19. 30
  20. 58
  21. 46
  22. 37
  23. 76
  24. 79
  25. 8
  26. 39
  27. 67
  28. 70
  29. 54
  30. 94
  31. 89
  32. 58
  33. 21
  34. 74
  35. 24
  36. 52
  37. 23
  38. 44
  39. 41
  40. 7

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