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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 617 · 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 7 numbers is 44. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 44 (b) 14 (c) 56 (d) 86
  2. 2.The average of 4 numbers is 13. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 22 (b) 13 (c) 12 (d) 23
  3. 3.The average of 4 numbers is 43. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 43 (b) 82 (c) 16 (d) 55
  4. 4.What is the average of 66, 53, 56, 56, 74 and 97? (a) 69 (b) 67 (c) 68 (d) 66
  5. 5.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 51? (a) 60 (b) 54 (c) 12 (d) 51
  6. 6.What is the average of 51, 44, 50 and 7? (a) 39 (b) 37 (c) 40 (d) 38
  7. 7.A batter has an average of 58 runs in 8 matches. How many runs are needed in the next match to raise the average to 63? (a) 103 (b) 68 (c) 45 (d) 63
  8. 8.A batter has an average of 58 runs in 7 matches. How many runs are needed in the next match to raise the average to 61? (a) 24 (b) 61 (c) 82 (d) 64
  9. 9.What is the average of 55, 60, 62 and 67? (a) 60 (b) 62 (c) 61 (d) 63
  10. 10.The average of 4 numbers is 12. When one number is taken away, the average of the rest is 9. Which number was taken away? (a) 12 (b) 22 (c) 21 (d) 20
  11. 11.What is the average of all the whole numbers from 42 to 62? (a) 10 (b) 53 (c) 52 (d) 20
  12. 12.The average of 7 numbers is 25. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 54 (b) 1 (c) 2 (d) 25
  13. 13.What is the average of 59, 42, 45, 37 and 72? (a) 53 (b) 50 (c) 51 (d) 52
  14. 14.What is the average of 28, 15, 21 and 56? (a) 40 (b) 30 (c) 31 (d) 29
  15. 15.What is the average of 37, 31, 33, 41 and 13? (a) 31 (b) 33 (c) 32 (d) 30
  16. 16.What is the average of all the whole numbers from 41 to 53? (a) 12 (b) 48 (c) 47 (d) 6
  17. 17.What is the average of 34, 8, 14, 22, 21 and 27? (a) 21 (b) 23 (c) 20 (d) 22
  18. 18.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 39? (a) 39 (b) 67 (c) 43 (d) 32
  19. 19.What is the average of all the whole numbers from 22 to 30? (a) 27 (b) 4 (c) 26 (d) 8
  20. 20.What is the average of 57, 69, 78, 70 and 81? (a) 70 (b) 72 (c) 73 (d) 71
  21. 21.What is the average of 20, 28, 20 and 32? (a) 27 (b) 24 (c) 25 (d) 26
  22. 22.A batter has an average of 51 runs in 9 matches. How many runs are needed in the next match to raise the average to 54? (a) 30 (b) 54 (c) 57 (d) 81
  23. 23.What is the average of 54, 66, 47, 67, 76 and 56? (a) 62 (b) 60 (c) 61 (d) 63
  24. 24.What is the average of 48, 58, 55, 53, 49 and 79? (a) 57 (b) 59 (c) 56 (d) 58
  25. 25.A batter has an average of 30 runs in 4 matches. How many runs are needed in the next match to raise the average to 38? (a) 40 (b) 46 (c) 70 (d) 38
  26. 26.The average of 4 numbers is 48. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 48 (b) 99 (c) 39 (d) 40
  27. 27.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 62? (a) 62 (b) 94 (c) 40 (d) 70
  28. 28.The average of 4 numbers is 50. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 95 (b) 50 (c) 20 (d) 65
  29. 29.The average of 5 numbers is 13. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 9 (b) 10 (c) 27 (d) 13
  30. 30.The average of 7 numbers is 35. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 65 (b) 35 (c) 64 (d) 66
  31. 31.A batter has an average of 28 runs in 9 matches. How many runs are needed in the next match to raise the average to 33? (a) 33 (b) 78 (c) 38 (d) 50
  32. 32.What is the average of all the whole numbers from 13 to 31? (a) 23 (b) 9 (c) 22 (d) 18
  33. 33.What is the average of all the whole numbers from 29 to 37? (a) 8 (b) 34 (c) 4 (d) 33
  34. 34.The average of 4 numbers is 15. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 27 (b) 12 (c) 15 (d) 24
  35. 35.What is the average of 46, 34, 38, 49 and 38? (a) 42 (b) 43 (c) 40 (d) 41
  36. 36.What is the average of 76, 56, 51 and 69? (a) 84 (b) 63 (c) 62 (d) 64
  37. 37.What is the average of 53, 41, 46 and 68? (a) 52 (b) 53 (c) 51 (d) 54
  38. 38.What is the average of 88, 76, 71 and 81? (a) 81 (b) 80 (c) 79 (d) 78
  39. 39.What is the average of 13, 15, 5 and 47? (a) 22 (b) 20 (c) 21 (d) 19
  40. 40.What is the average of all the whole numbers from 18 to 28? (a) 10 (b) 5 (c) 24 (d) 23

Answer key

  1. 56
  2. 22
  3. 55
  4. 67
  5. 60
  6. 38
  7. 103
  8. 82
  9. 61
  10. 21
  11. 52
  12. 1
  13. 51
  14. 30
  15. 31
  16. 47
  17. 21
  18. 67
  19. 26
  20. 71
  21. 25
  22. 81
  23. 61
  24. 57
  25. 70
  26. 39
  27. 94
  28. 65
  29. 9
  30. 65
  31. 78
  32. 22
  33. 33
  34. 24
  35. 41
  36. 63
  37. 52
  38. 79
  39. 20
  40. 23

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