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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 176 · 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 12. When one number is taken away, the average of the rest is 9. Which number was taken away? (a) 15 (b) 12 (c) 21 (d) 24
  2. 2.What is the average of 65, 88, 92 and 67? (a) 77 (b) 79 (c) 78 (d) 104
  3. 3.The average of 5 numbers is 10. When one number is taken away, the average of the rest is 5. Which number was taken away? (a) 25 (b) 15 (c) 10 (d) 30
  4. 4.What is the average of 57, 65, 73, 67, 53 and 51? (a) 60 (b) 62 (c) 63 (d) 61
  5. 5.What is the average of all the whole numbers from 10 to 20? (a) 5 (b) 16 (c) 15 (d) 10
  6. 6.A batter has an average of 48 runs in 3 matches. How many runs are needed in the next match to raise the average to 50? (a) 56 (b) 50 (c) 52 (d) 8
  7. 7.What is the average of 51, 50, 52 and 71? (a) 55 (b) 57 (c) 56 (d) 58
  8. 8.What is the average of all the whole numbers from 39 to 47? (a) 43 (b) 8 (c) 4 (d) 44
  9. 9.The average of 7 numbers is 22. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 22 (b) 21 (c) 41 (d) 40
  10. 10.What is the average of 70, 43, 71, 61 and 45? (a) 57 (b) 60 (c) 58 (d) 59
  11. 11.What is the average of 34, 44, 16 and 30? (a) 31 (b) 33 (c) 30 (d) 32
  12. 12.What is the average of all the whole numbers from 59 to 65? (a) 6 (b) 62 (c) 3 (d) 63
  13. 13.What is the average of 65, 63, 59 and 57? (a) 61 (b) 63 (c) 60 (d) 62
  14. 14.What is the average of all the whole numbers from 22 to 34? (a) 12 (b) 29 (c) 6 (d) 28
  15. 15.What is the average of all the whole numbers from 5 to 31? (a) 26 (b) 18 (c) 19 (d) 13
  16. 16.The average of 8 numbers is 37. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 44 (b) 73 (c) 8 (d) 37
  17. 17.The average of 4 numbers is 37. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 46 (b) 12 (c) 37 (d) 71
  18. 18.A batter has an average of 41 runs in 3 matches. How many runs are needed in the next match to raise the average to 43? (a) 45 (b) 49 (c) 43 (d) 8
  19. 19.The average of 8 numbers is 29. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 22 (b) 23 (c) 59 (d) 29
  20. 20.A batter has an average of 48 runs in 8 matches. How many runs are needed in the next match to raise the average to 51? (a) 51 (b) 54 (c) 27 (d) 75
  21. 21.A batter has an average of 47 runs in 4 matches. How many runs are needed in the next match to raise the average to 50? (a) 53 (b) 50 (c) 62 (d) 15
  22. 22.What is the average of all the whole numbers from 30 to 70? (a) 40 (b) 50 (c) 20 (d) 51
  23. 23.The average of 6 numbers is 42. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 57 (b) 42 (c) 81 (d) 18
  24. 24.A batter has an average of 56 runs in 4 matches. How many runs are needed in the next match to raise the average to 63? (a) 35 (b) 70 (c) 63 (d) 91
  25. 25.The average of 6 numbers is 31. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 63 (b) 31 (c) 26 (d) 27
  26. 26.What is the average of all the whole numbers from 8 to 42? (a) 25 (b) 26 (c) 34 (d) 17
  27. 27.What is the average of all the whole numbers from 33 to 51? (a) 18 (b) 9 (c) 43 (d) 42
  28. 28.What is the average of 80, 94, 69, 93 and 59? (a) 80 (b) 81 (c) 79 (d) 78
  29. 29.A batter has an average of 33 runs in 4 matches. How many runs are needed in the next match to raise the average to 35? (a) 37 (b) 10 (c) 35 (d) 43
  30. 30.What is the average of 64, 85, 82 and 73? (a) 77 (b) 78 (c) 76 (d) 75
  31. 31.What is the average of all the whole numbers from 29 to 43? (a) 37 (b) 7 (c) 14 (d) 36
  32. 32.The average of 5 numbers is 21. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 17 (b) 43 (c) 21 (d) 18
  33. 33.What is the average of 53, 26, 31, 52 and 43? (a) 42 (b) 43 (c) 40 (d) 41
  34. 34.The average of 8 numbers is 16. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 16 (b) 8 (c) 31 (d) 23
  35. 35.What is the average of 62, 87, 88 and 71? (a) 79 (b) 78 (c) 76 (d) 77
  36. 36.What is the average of 40, 62, 36 and 62? (a) 52 (b) 51 (c) 50 (d) 49
  37. 37.A batter has an average of 47 runs in 4 matches. How many runs are needed in the next match to raise the average to 52? (a) 52 (b) 25 (c) 72 (d) 57
  38. 38.The average of 6 numbers is 24. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 14 (b) 15 (c) 50 (d) 24
  39. 39.What is the average of 50, 72, 53, 67, 73 and 57? (a) 63 (b) 64 (c) 62 (d) 61
  40. 40.What is the average of all the whole numbers from 37 to 67? (a) 53 (b) 15 (c) 30 (d) 52

Answer key

  1. 24
  2. 78
  3. 30
  4. 61
  5. 15
  6. 56
  7. 56
  8. 43
  9. 40
  10. 58
  11. 31
  12. 62
  13. 61
  14. 28
  15. 18
  16. 44
  17. 46
  18. 49
  19. 22
  20. 75
  21. 62
  22. 50
  23. 57
  24. 91
  25. 26
  26. 25
  27. 42
  28. 79
  29. 43
  30. 76
  31. 36
  32. 17
  33. 41
  34. 23
  35. 77
  36. 50
  37. 72
  38. 14
  39. 62
  40. 52

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