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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 613 · 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 26. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 26 (b) 57 (c) 6 (d) 7
  2. 2.A batter has an average of 25 runs in 8 matches. How many runs are needed in the next match to raise the average to 32? (a) 63 (b) 39 (c) 88 (d) 32
  3. 3.A batter has an average of 24 runs in 3 matches. How many runs are needed in the next match to raise the average to 26? (a) 26 (b) 8 (c) 28 (d) 32
  4. 4.The average of 6 numbers is 23. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 24 (b) 42 (c) 23 (d) 43
  5. 5.The average of 7 numbers is 15. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 27 (b) 15 (c) 33 (d) 21
  6. 6.The average of 8 numbers is 30. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 9 (b) 10 (c) 63 (d) 30
  7. 7.What is the average of 22, 24, 49 and 53? (a) 38 (b) 36 (c) 39 (d) 37
  8. 8.What is the average of all the whole numbers from 43 to 55? (a) 12 (b) 50 (c) 6 (d) 49
  9. 9.What is the average of all the whole numbers from 16 to 28? (a) 12 (b) 23 (c) 6 (d) 22
  10. 10.What is the average of all the whole numbers from 56 to 62? (a) 60 (b) 3 (c) 59 (d) 6
  11. 11.What is the average of 30, 30, 44, 32 and 24? (a) 33 (b) 32 (c) 40 (d) 31
  12. 12.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) 10 (b) 39 (c) 47 (d) 76
  13. 13.What is the average of all the whole numbers from 19 to 57? (a) 37 (b) 38 (c) 19 (d) 39
  14. 14.What is the average of 39, 33, 32, 36 and 5? (a) 30 (b) 29 (c) 31 (d) 28
  15. 15.A batter has an average of 35 runs in 7 matches. How many runs are needed in the next match to raise the average to 38? (a) 41 (b) 24 (c) 59 (d) 38
  16. 16.What is the average of all the whole numbers from 9 to 47? (a) 38 (b) 19 (c) 29 (d) 28
  17. 17.A batter has an average of 59 runs in 4 matches. How many runs are needed in the next match to raise the average to 61? (a) 61 (b) 63 (c) 10 (d) 69
  18. 18.What is the average of 20, 36, 45 and 27? (a) 31 (b) 32 (c) 34 (d) 33
  19. 19.What is the average of 51, 48, 39, 25, 43 and 22? (a) 37 (b) 38 (c) 40 (d) 39
  20. 20.What is the average of 18, 23, 31, 24, 19 and 23? (a) 22 (b) 24 (c) 25 (d) 23
  21. 21.The average of 4 numbers is 10. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 10 (b) 16 (c) 8 (d) 18
  22. 22.The average of 5 numbers is 21. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 2 (b) 47 (c) 21 (d) 1
  23. 23.The average of 5 numbers is 46. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 46 (b) 62 (c) 20 (d) 88
  24. 24.What is the average of all the whole numbers from 38 to 62? (a) 24 (b) 51 (c) 12 (d) 50
  25. 25.A batter has an average of 25 runs in 7 matches. How many runs are needed in the next match to raise the average to 32? (a) 56 (b) 32 (c) 39 (d) 81
  26. 26.A batter has an average of 60 runs in 6 matches. How many runs are needed in the next match to raise the average to 63? (a) 21 (b) 81 (c) 63 (d) 66
  27. 27.A batter has an average of 38 runs in 8 matches. How many runs are needed in the next match to raise the average to 45? (a) 52 (b) 63 (c) 101 (d) 45
  28. 28.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) 29 (b) 15 (c) 19 (d) 5
  29. 29.A batter has an average of 55 runs in 8 matches. How many runs are needed in the next match to raise the average to 63? (a) 63 (b) 71 (c) 127 (d) 72
  30. 30.A batter has an average of 32 runs in 8 matches. How many runs are needed in the next match to raise the average to 39? (a) 95 (b) 39 (c) 63 (d) 46
  31. 31.What is the average of 56, 79, 73 and 68? (a) 70 (b) 69 (c) 92 (d) 68
  32. 32.What is the average of all the whole numbers from 11 to 39? (a) 28 (b) 14 (c) 25 (d) 26
  33. 33.The average of 8 numbers is 37. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 70 (b) 32 (c) 37 (d) 65
  34. 34.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 64? (a) 64 (b) 28 (c) 71 (d) 85
  35. 35.What is the average of 62, 55, 71 and 52? (a) 80 (b) 60 (c) 61 (d) 59
  36. 36.What is the average of 71, 84, 66 and 99? (a) 82 (b) 79 (c) 80 (d) 81
  37. 37.The average of 4 numbers is 47. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 8 (b) 53 (c) 92 (d) 47
  38. 38.The average of 7 numbers is 28. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 11 (b) 28 (c) 59 (d) 10
  39. 39.What is the average of 28, 23, 18, 27, 17 and 43? (a) 27 (b) 28 (c) 26 (d) 25
  40. 40.A batter has an average of 21 runs in 9 matches. How many runs are needed in the next match to raise the average to 23? (a) 23 (b) 25 (c) 20 (d) 41

Answer key

  1. 6
  2. 88
  3. 32
  4. 43
  5. 33
  6. 9
  7. 37
  8. 49
  9. 22
  10. 59
  11. 32
  12. 47
  13. 38
  14. 29
  15. 59
  16. 28
  17. 69
  18. 32
  19. 38
  20. 23
  21. 16
  22. 1
  23. 62
  24. 50
  25. 81
  26. 81
  27. 101
  28. 19
  29. 127
  30. 95
  31. 69
  32. 25
  33. 65
  34. 85
  35. 60
  36. 80
  37. 53
  38. 10
  39. 26
  40. 41

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