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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 917 · 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 all the whole numbers from 14 to 36? (a) 26 (b) 22 (c) 11 (d) 25
  2. 2.The average of 4 numbers is 30. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 24 (b) 25 (c) 62 (d) 30
  3. 3.The average of 7 numbers is 43. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 32 (b) 31 (c) 88 (d) 43
  4. 4.What is the average of all the whole numbers from 57 to 97? (a) 20 (b) 78 (c) 40 (d) 77
  5. 5.A batter has an average of 53 runs in 6 matches. How many runs are needed in the next match to raise the average to 59? (a) 65 (b) 42 (c) 95 (d) 59
  6. 6.What is the average of 58, 78, 72 and 80? (a) 71 (b) 73 (c) 96 (d) 72
  7. 7.What is the average of all the whole numbers from 15 to 45? (a) 29 (b) 31 (c) 30 (d) 15
  8. 8.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 37? (a) 37 (b) 61 (c) 45 (d) 32
  9. 9.The average of 6 numbers is 15. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 10 (b) 31 (c) 15 (d) 11
  10. 10.What is the average of 77, 57, 70 and 72? (a) 68 (b) 92 (c) 70 (d) 69
  11. 11.The average of 6 numbers is 50. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 12 (b) 60 (c) 98 (d) 50
  12. 12.What is the average of all the whole numbers from 35 to 73? (a) 38 (b) 54 (c) 55 (d) 19
  13. 13.The average of 7 numbers is 11. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 19 (b) 11 (c) 21 (d) 29
  14. 14.The average of 4 numbers is 37. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 70 (b) 16 (c) 37 (d) 49
  15. 15.A batter has an average of 28 runs in 7 matches. How many runs are needed in the next match to raise the average to 30? (a) 32 (b) 16 (c) 44 (d) 30
  16. 16.The average of 6 numbers is 33. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 67 (b) 29 (c) 33 (d) 28
  17. 17.A batter has an average of 20 runs in 8 matches. How many runs are needed in the next match to raise the average to 27? (a) 27 (b) 34 (c) 83 (d) 63
  18. 18.The average of 8 numbers is 26. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 51 (b) 26 (c) 33 (d) 8
  19. 19.The average of 6 numbers is 31. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 41 (b) 31 (c) 12 (d) 60
  20. 20.What is the average of 39, 34, 43, 42, 26 and 62? (a) 42 (b) 40 (c) 41 (d) 43
  21. 21.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 47? (a) 47 (b) 55 (c) 49 (d) 10
  22. 22.What is the average of all the whole numbers from 23 to 51? (a) 38 (b) 37 (c) 28 (d) 14
  23. 23.What is the average of 6, 30, 18 and 30? (a) 20 (b) 28 (c) 22 (d) 21
  24. 24.A batter has an average of 57 runs in 3 matches. How many runs are needed in the next match to raise the average to 61? (a) 61 (b) 16 (c) 73 (d) 65
  25. 25.What is the average of all the whole numbers from 19 to 41? (a) 31 (b) 11 (c) 22 (d) 30
  26. 26.A batter has an average of 46 runs in 7 matches. How many runs are needed in the next match to raise the average to 50? (a) 78 (b) 50 (c) 32 (d) 54
  27. 27.What is the average of all the whole numbers from 60 to 66? (a) 6 (b) 3 (c) 63 (d) 64
  28. 28.What is the average of all the whole numbers from 21 to 27? (a) 6 (b) 25 (c) 24 (d) 3
  29. 29.The average of 5 numbers is 43. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 10 (b) 84 (c) 51 (d) 43
  30. 30.A batter has an average of 34 runs in 9 matches. How many runs are needed in the next match to raise the average to 37? (a) 37 (b) 30 (c) 64 (d) 40
  31. 31.The average of 6 numbers is 50. When one number is taken away, the average of the rest is 53. Which number was taken away? (a) 103 (b) 36 (c) 50 (d) 35
  32. 32.A batter has an average of 34 runs in 9 matches. How many runs are needed in the next match to raise the average to 40? (a) 60 (b) 94 (c) 46 (d) 40
  33. 33.What is the average of all the whole numbers from 48 to 64? (a) 8 (b) 16 (c) 56 (d) 57
  34. 34.The average of 8 numbers is 24. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 24 (b) 31 (c) 8 (d) 47
  35. 35.What is the average of 64, 62, 55, 45 and 19? (a) 48 (b) 50 (c) 49 (d) 51
  36. 36.A batter has an average of 53 runs in 8 matches. How many runs are needed in the next match to raise the average to 58? (a) 98 (b) 58 (c) 45 (d) 63
  37. 37.The average of 6 numbers is 44. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 40 (b) 89 (c) 44 (d) 39
  38. 38.What is the average of all the whole numbers from 53 to 87? (a) 34 (b) 71 (c) 70 (d) 17
  39. 39.A batter has an average of 26 runs in 9 matches. How many runs are needed in the next match to raise the average to 30? (a) 34 (b) 30 (c) 66 (d) 40
  40. 40.The average of 4 numbers is 17. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 5 (b) 38 (c) 17 (d) 6

Answer key

  1. 25
  2. 24
  3. 31
  4. 77
  5. 95
  6. 72
  7. 30
  8. 61
  9. 10
  10. 69
  11. 60
  12. 54
  13. 29
  14. 49
  15. 44
  16. 28
  17. 83
  18. 33
  19. 41
  20. 41
  21. 55
  22. 37
  23. 21
  24. 73
  25. 30
  26. 78
  27. 63
  28. 24
  29. 51
  30. 64
  31. 35
  32. 94
  33. 56
  34. 31
  35. 49
  36. 98
  37. 39
  38. 70
  39. 66
  40. 5

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