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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 145 · 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 24. Which number was taken away? (a) 10 (b) 34 (c) 50 (d) 26
  2. 2.What is the average of all the whole numbers from 14 to 38? (a) 12 (b) 27 (c) 24 (d) 26
  3. 3.A batter has an average of 38 runs in 3 matches. How many runs are needed in the next match to raise the average to 42? (a) 54 (b) 46 (c) 16 (d) 42
  4. 4.What is the average of 63, 57, 49, 46 and 55? (a) 55 (b) 53 (c) 56 (d) 54
  5. 5.What is the average of 39, 20, 41, 15 and 15? (a) 26 (b) 28 (c) 25 (d) 27
  6. 6.What is the average of 30, 28, 53, 28 and 51? (a) 39 (b) 40 (c) 38 (d) 37
  7. 7.The average of 4 numbers is 27. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 27 (b) 33 (c) 52 (d) 8
  8. 8.The average of 4 numbers is 23. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 23 (b) 42 (c) 35 (d) 16
  9. 9.A batter has an average of 24 runs in 9 matches. How many runs are needed in the next match to raise the average to 26? (a) 26 (b) 20 (c) 28 (d) 44
  10. 10.What is the average of all the whole numbers from 13 to 25? (a) 20 (b) 6 (c) 19 (d) 12
  11. 11.What is the average of 36, 50, 53, 30, 40 and 37? (a) 40 (b) 41 (c) 42 (d) 43
  12. 12.What is the average of 44, 42, 35, 45 and 69? (a) 46 (b) 49 (c) 47 (d) 48
  13. 13.A batter has an average of 39 runs in 3 matches. How many runs are needed in the next match to raise the average to 43? (a) 16 (b) 55 (c) 43 (d) 47
  14. 14.The average of 6 numbers is 48. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 48 (b) 63 (c) 93 (d) 18
  15. 15.The average of 4 numbers is 20. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 14 (b) 20 (c) 42 (d) 15
  16. 16.A batter has an average of 31 runs in 5 matches. How many runs are needed in the next match to raise the average to 33? (a) 35 (b) 43 (c) 33 (d) 12
  17. 17.What is the average of 23, 35, 18, 7 and 22? (a) 23 (b) 21 (c) 20 (d) 22
  18. 18.What is the average of 67, 61, 59, 55, 64 and 114? (a) 71 (b) 84 (c) 70 (d) 69
  19. 19.The average of 8 numbers is 21. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 40 (b) 56 (c) 21 (d) 37
  20. 20.The average of 4 numbers is 12. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 4 (b) 23 (c) 15 (d) 12
  21. 21.What is the average of 49, 50, 50, 61, 57 and 45? (a) 51 (b) 52 (c) 54 (d) 53
  22. 22.The average of 5 numbers is 12. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 12 (b) 26 (c) 5 (d) 4
  23. 23.What is the average of 15, 16, 8 and 53? (a) 22 (b) 24 (c) 25 (d) 23
  24. 24.What is the average of 61, 72, 66, 57 and 89? (a) 70 (b) 69 (c) 71 (d) 68
  25. 25.What is the average of 78, 76, 58, 73, 68 and 55? (a) 67 (b) 69 (c) 68 (d) 70
  26. 26.What is the average of 42, 59, 48, 46 and 90? (a) 56 (b) 59 (c) 58 (d) 57
  27. 27.What is the average of 37, 18, 36, 11 and 18? (a) 30 (b) 25 (c) 23 (d) 24
  28. 28.What is the average of 30, 36, 25, 32, 12 and 3? (a) 24 (b) 25 (c) 23 (d) 22
  29. 29.A batter has an average of 37 runs in 5 matches. How many runs are needed in the next match to raise the average to 43? (a) 43 (b) 49 (c) 73 (d) 36
  30. 30.The average of 5 numbers is 46. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 46 (b) 10 (c) 90 (d) 54
  31. 31.What is the average of 52, 64, 54, 51 and 69? (a) 57 (b) 59 (c) 58 (d) 60
  32. 32.What is the average of 16, 23, 17, 30, 33 and 55? (a) 30 (b) 28 (c) 29 (d) 31
  33. 33.The average of 7 numbers is 43. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 28 (b) 67 (c) 82 (d) 43
  34. 34.What is the average of 74, 68, 84, 69 and 70? (a) 73 (b) 74 (c) 75 (d) 72
  35. 35.The average of 6 numbers is 30. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 30 (b) 6 (c) 59 (d) 35
  36. 36.What is the average of 30, 36, 20 and 42? (a) 33 (b) 34 (c) 31 (d) 32
  37. 37.What is the average of all the whole numbers from 32 to 68? (a) 51 (b) 18 (c) 50 (d) 36
  38. 38.What is the average of 34, 14, 20 and 40? (a) 27 (b) 36 (c) 28 (d) 26
  39. 39.The average of 5 numbers is 34. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 34 (b) 73 (c) 14 (d) 15
  40. 40.A batter has an average of 32 runs in 9 matches. How many runs are needed in the next match to raise the average to 34? (a) 34 (b) 52 (c) 20 (d) 36

Answer key

  1. 34
  2. 26
  3. 54
  4. 54
  5. 26
  6. 38
  7. 33
  8. 35
  9. 44
  10. 19
  11. 41
  12. 47
  13. 55
  14. 63
  15. 14
  16. 43
  17. 21
  18. 70
  19. 56
  20. 15
  21. 52
  22. 4
  23. 23
  24. 69
  25. 68
  26. 57
  27. 24
  28. 23
  29. 73
  30. 54
  31. 58
  32. 29
  33. 67
  34. 73
  35. 35
  36. 32
  37. 50
  38. 27
  39. 14
  40. 52

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