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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 459 · 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 11. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 6 (b) 23 (c) 7 (d) 11
  2. 2.What is the average of 26, 37, 39, 44 and 14? (a) 40 (b) 32 (c) 33 (d) 31
  3. 3.A batter has an average of 31 runs in 8 matches. How many runs are needed in the next match to raise the average to 33? (a) 35 (b) 18 (c) 33 (d) 49
  4. 4.What is the average of all the whole numbers from 20 to 56? (a) 36 (b) 38 (c) 39 (d) 18
  5. 5.The average of 4 numbers is 12. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 26 (b) 12 (c) 7 (d) 6
  6. 6.What is the average of 61, 78, 84, 77, 63 and 57? (a) 69 (b) 84 (c) 70 (d) 71
  7. 7.The average of 5 numbers is 48. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 25 (b) 48 (c) 68 (d) 91
  8. 8.What is the average of 82, 62, 89 and 67? (a) 76 (b) 100 (c) 75 (d) 74
  9. 9.The average of 4 numbers is 29. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 60 (b) 24 (c) 23 (d) 29
  10. 10.What is the average of all the whole numbers from 54 to 64? (a) 10 (b) 5 (c) 59 (d) 60
  11. 11.What is the average of all the whole numbers from 36 to 74? (a) 38 (b) 56 (c) 55 (d) 19
  12. 12.The average of 6 numbers is 46. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 90 (b) 12 (c) 56 (d) 46
  13. 13.What is the average of 31, 29, 43, 27 and 50? (a) 36 (b) 37 (c) 45 (d) 35
  14. 14.The average of 6 numbers is 32. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 18 (b) 17 (c) 32 (d) 67
  15. 15.The average of 6 numbers is 41. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 36 (b) 37 (c) 41 (d) 83
  16. 16.A batter has an average of 47 runs in 7 matches. How many runs are needed in the next match to raise the average to 52? (a) 40 (b) 57 (c) 87 (d) 52
  17. 17.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 36? (a) 44 (b) 36 (c) 84 (d) 56
  18. 18.The average of 7 numbers is 31. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 49 (b) 21 (c) 59 (d) 31
  19. 19.A batter has an average of 33 runs in 9 matches. How many runs are needed in the next match to raise the average to 36? (a) 30 (b) 39 (c) 63 (d) 36
  20. 20.What is the average of all the whole numbers from 12 to 48? (a) 31 (b) 18 (c) 30 (d) 36
  21. 21.The average of 4 numbers is 17. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 17 (b) 33 (c) 4 (d) 20
  22. 22.The average of 6 numbers is 13. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 23 (b) 24 (c) 12 (d) 13
  23. 23.The average of 5 numbers is 17. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 17 (b) 29 (c) 25 (d) 37
  24. 24.The average of 8 numbers is 39. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 32 (b) 39 (c) 33 (d) 79
  25. 25.What is the average of 34, 55, 33, 31 and 67? (a) 44 (b) 45 (c) 55 (d) 43
  26. 26.What is the average of all the whole numbers from 48 to 68? (a) 20 (b) 10 (c) 58 (d) 59
  27. 27.The average of 4 numbers is 30. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 30 (b) 19 (c) 18 (d) 64
  28. 28.A batter has an average of 53 runs in 7 matches. How many runs are needed in the next match to raise the average to 61? (a) 69 (b) 61 (c) 117 (d) 64
  29. 29.What is the average of all the whole numbers from 55 to 93? (a) 38 (b) 75 (c) 19 (d) 74
  30. 30.What is the average of 30, 44, 19, 30, 21 and 36? (a) 36 (b) 30 (c) 31 (d) 29
  31. 31.What is the average of 32, 56, 44, 36 and 67? (a) 46 (b) 48 (c) 47 (d) 49
  32. 32.What is the average of all the whole numbers from 55 to 95? (a) 40 (b) 20 (c) 75 (d) 76
  33. 33.What is the average of all the whole numbers from 7 to 31? (a) 12 (b) 19 (c) 20 (d) 24
  34. 34.What is the average of all the whole numbers from 35 to 43? (a) 8 (b) 4 (c) 40 (d) 39
  35. 35.A batter has an average of 50 runs in 9 matches. How many runs are needed in the next match to raise the average to 52? (a) 54 (b) 20 (c) 70 (d) 52
  36. 36.The average of 6 numbers is 17. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 31 (b) 18 (c) 32 (d) 17
  37. 37.The average of 5 numbers is 11. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 5 (b) 11 (c) 21 (d) 15
  38. 38.What is the average of 86, 61, 91, 77, 89 and 52? (a) 76 (b) 75 (c) 77 (d) 78
  39. 39.The average of 5 numbers is 39. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 76 (b) 47 (c) 10 (d) 39
  40. 40.What is the average of all the whole numbers from 12 to 50? (a) 31 (b) 19 (c) 32 (d) 38

Answer key

  1. 6
  2. 32
  3. 49
  4. 38
  5. 6
  6. 70
  7. 68
  8. 75
  9. 23
  10. 59
  11. 55
  12. 56
  13. 36
  14. 17
  15. 36
  16. 87
  17. 84
  18. 49
  19. 63
  20. 30
  21. 20
  22. 23
  23. 37
  24. 32
  25. 44
  26. 58
  27. 18
  28. 117
  29. 74
  30. 30
  31. 47
  32. 75
  33. 19
  34. 39
  35. 70
  36. 32
  37. 15
  38. 76
  39. 47
  40. 31

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