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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 279 · 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 10. When one number is taken away, the average of the rest is 5. Which number was taken away? (a) 10 (b) 15 (c) 30 (d) 35
  2. 2.The average of 4 numbers is 41. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 53 (b) 41 (c) 16 (d) 78
  3. 3.A batter has an average of 35 runs in 4 matches. How many runs are needed in the next match to raise the average to 37? (a) 45 (b) 39 (c) 37 (d) 10
  4. 4.The average of 6 numbers is 10. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 10 (b) 21 (c) 6 (d) 5
  5. 5.What is the average of 63, 77, 69, 58, 65 and 70? (a) 68 (b) 67 (c) 69 (d) 66
  6. 6.What is the average of 42, 25, 33 and 40? (a) 36 (b) 37 (c) 34 (d) 35
  7. 7.What is the average of 15, 18, 18 and 33? (a) 28 (b) 22 (c) 20 (d) 21
  8. 8.The average of 7 numbers is 12. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 42 (b) 35 (c) 19 (d) 12
  9. 9.The average of 8 numbers is 15. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 43 (b) 15 (c) 26 (d) 32
  10. 10.A batter has an average of 22 runs in 8 matches. How many runs are needed in the next match to raise the average to 26? (a) 58 (b) 30 (c) 26 (d) 36
  11. 11.What is the average of all the whole numbers from 35 to 65? (a) 50 (b) 15 (c) 51 (d) 30
  12. 12.What is the average of 57, 36, 31, 28, 35 and 65? (a) 44 (b) 41 (c) 42 (d) 43
  13. 13.What is the average of 9, 24, 8, 11, 33 and 35? (a) 21 (b) 20 (c) 19 (d) 24
  14. 14.A batter has an average of 49 runs in 5 matches. How many runs are needed in the next match to raise the average to 55? (a) 85 (b) 36 (c) 61 (d) 55
  15. 15.A batter has an average of 42 runs in 4 matches. How many runs are needed in the next match to raise the average to 50? (a) 58 (b) 40 (c) 82 (d) 50
  16. 16.What is the average of 25, 40, 38 and 1? (a) 27 (b) 25 (c) 26 (d) 28
  17. 17.A batter has an average of 25 runs in 4 matches. How many runs are needed in the next match to raise the average to 30? (a) 50 (b) 35 (c) 25 (d) 30
  18. 18.What is the average of all the whole numbers from 11 to 51? (a) 40 (b) 20 (c) 32 (d) 31
  19. 19.The average of 4 numbers is 33. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 20 (b) 61 (c) 33 (d) 48
  20. 20.What is the average of 24, 28, 39 and 17? (a) 26 (b) 27 (c) 36 (d) 28
  21. 21.The average of 7 numbers is 44. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 44 (b) 74 (c) 35 (d) 83
  22. 22.The average of 8 numbers is 32. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 66 (b) 19 (c) 18 (d) 32
  23. 23.What is the average of 70, 76, 54, 72, 79 and 57? (a) 69 (b) 70 (c) 68 (d) 67
  24. 24.The average of 7 numbers is 32. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 62 (b) 59 (c) 32 (d) 35
  25. 25.What is the average of 68, 64, 47, 64 and 57? (a) 59 (b) 61 (c) 75 (d) 60
  26. 26.What is the average of all the whole numbers from 10 to 38? (a) 28 (b) 14 (c) 25 (d) 24
  27. 27.A batter has an average of 23 runs in 7 matches. How many runs are needed in the next match to raise the average to 25? (a) 25 (b) 27 (c) 16 (d) 39
  28. 28.What is the average of 83, 78, 69 and 74? (a) 78 (b) 77 (c) 76 (d) 75
  29. 29.What is the average of all the whole numbers from 60 to 78? (a) 9 (b) 69 (c) 18 (d) 70
  30. 30.The average of 4 numbers is 40. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 40 (b) 79 (c) 43 (d) 4
  31. 31.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 36? (a) 76 (b) 45 (c) 41 (d) 36
  32. 32.What is the average of 55, 39, 59 and 55? (a) 52 (b) 51 (c) 54 (d) 53
  33. 33.The average of 7 numbers is 45. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 92 (b) 45 (c) 34 (d) 33
  34. 34.What is the average of 46, 39, 32, 39, 39 and 3? (a) 32 (b) 34 (c) 33 (d) 35
  35. 35.What is the average of 18, 40, 24, 40, 36 and 34? (a) 31 (b) 32 (c) 33 (d) 34
  36. 36.What is the average of all the whole numbers from 42 to 62? (a) 10 (b) 52 (c) 53 (d) 20
  37. 37.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 49? (a) 49 (b) 52 (c) 70 (d) 24
  38. 38.What is the average of all the whole numbers from 12 to 26? (a) 7 (b) 14 (c) 20 (d) 19
  39. 39.What is the average of 54, 67, 49, 44 and 76? (a) 58 (b) 57 (c) 59 (d) 60
  40. 40.The average of 5 numbers is 16. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 5 (b) 31 (c) 16 (d) 20

Answer key

  1. 35
  2. 53
  3. 45
  4. 5
  5. 67
  6. 35
  7. 21
  8. 42
  9. 43
  10. 58
  11. 50
  12. 42
  13. 20
  14. 85
  15. 82
  16. 26
  17. 50
  18. 31
  19. 48
  20. 27
  21. 74
  22. 18
  23. 68
  24. 62
  25. 60
  26. 24
  27. 39
  28. 76
  29. 69
  30. 43
  31. 76
  32. 52
  33. 33
  34. 33
  35. 32
  36. 52
  37. 70
  38. 19
  39. 58
  40. 20

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