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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 616 · 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 15. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 29 (b) 20 (c) 6 (d) 15
  2. 2.What is the average of all the whole numbers from 15 to 51? (a) 34 (b) 33 (c) 36 (d) 18
  3. 3.What is the average of 38, 36, 35, 46, 33 and 40? (a) 39 (b) 37 (c) 40 (d) 38
  4. 4.A batter has an average of 55 runs in 6 matches. How many runs are needed in the next match to raise the average to 58? (a) 61 (b) 21 (c) 76 (d) 58
  5. 5.What is the average of all the whole numbers from 41 to 49? (a) 45 (b) 46 (c) 4 (d) 8
  6. 6.The average of 8 numbers is 10. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 21 (b) 3 (c) 10 (d) 4
  7. 7.The average of 4 numbers is 29. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 38 (b) 12 (c) 29 (d) 55
  8. 8.A batter has an average of 36 runs in 5 matches. How many runs are needed in the next match to raise the average to 38? (a) 38 (b) 40 (c) 12 (d) 48
  9. 9.The average of 5 numbers is 17. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 17 (b) 2 (c) 1 (d) 38
  10. 10.A batter has an average of 20 runs in 6 matches. How many runs are needed in the next match to raise the average to 22? (a) 34 (b) 14 (c) 24 (d) 22
  11. 11.The average of 7 numbers is 23. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 53 (b) 41 (c) 35 (d) 23
  12. 12.What is the average of 59, 58, 60, 64 and 44? (a) 57 (b) 59 (c) 56 (d) 58
  13. 13.The average of 4 numbers is 47. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 93 (b) 50 (c) 47 (d) 4
  14. 14.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 30? (a) 30 (b) 32 (c) 48 (d) 20
  15. 15.A batter has an average of 48 runs in 4 matches. How many runs are needed in the next match to raise the average to 56? (a) 88 (b) 64 (c) 56 (d) 40
  16. 16.What is the average of 43, 51, 55, 60 and 66? (a) 56 (b) 57 (c) 55 (d) 54
  17. 17.A batter has an average of 36 runs in 7 matches. How many runs are needed in the next match to raise the average to 44? (a) 64 (b) 52 (c) 44 (d) 100
  18. 18.What is the average of 20, 31, 23, 23 and 78? (a) 37 (b) 36 (c) 35 (d) 34
  19. 19.The average of 6 numbers is 26. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 26 (b) 51 (c) 6 (d) 31
  20. 20.A batter has an average of 21 runs in 5 matches. How many runs are needed in the next match to raise the average to 23? (a) 25 (b) 23 (c) 12 (d) 33
  21. 21.A batter has an average of 24 runs in 4 matches. How many runs are needed in the next match to raise the average to 26? (a) 26 (b) 28 (c) 10 (d) 34
  22. 22.What is the average of 41, 36, 32, 40, 51 and 76? (a) 45 (b) 48 (c) 47 (d) 46
  23. 23.What is the average of 22, 18, 32, 36, 17 and 67? (a) 31 (b) 34 (c) 32 (d) 33
  24. 24.The average of 8 numbers is 25. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 25 (b) 47 (c) 46 (d) 24
  25. 25.The average of 4 numbers is 21. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 18 (b) 19 (c) 43 (d) 21
  26. 26.What is the average of all the whole numbers from 46 to 72? (a) 26 (b) 60 (c) 59 (d) 13
  27. 27.What is the average of 21, 33, 20 and 14? (a) 23 (b) 21 (c) 24 (d) 22
  28. 28.A batter has an average of 50 runs in 4 matches. How many runs are needed in the next match to raise the average to 55? (a) 25 (b) 60 (c) 75 (d) 55
  29. 29.A batter has an average of 20 runs in 5 matches. How many runs are needed in the next match to raise the average to 27? (a) 62 (b) 34 (c) 42 (d) 27
  30. 30.What is the average of 53, 57, 59 and 75? (a) 62 (b) 60 (c) 61 (d) 63
  31. 31.What is the average of all the whole numbers from 17 to 25? (a) 21 (b) 8 (c) 22 (d) 4
  32. 32.What is the average of all the whole numbers from 22 to 38? (a) 31 (b) 16 (c) 8 (d) 30
  33. 33.What is the average of all the whole numbers from 9 to 37? (a) 24 (b) 23 (c) 28 (d) 14
  34. 34.What is the average of 48, 41, 37 and 66? (a) 48 (b) 49 (c) 64 (d) 47
  35. 35.The average of 5 numbers is 31. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 24 (b) 23 (c) 64 (d) 31
  36. 36.What is the average of all the whole numbers from 22 to 36? (a) 7 (b) 29 (c) 30 (d) 14
  37. 37.What is the average of all the whole numbers from 29 to 47? (a) 18 (b) 38 (c) 39 (d) 9
  38. 38.A batter has an average of 27 runs in 3 matches. How many runs are needed in the next match to raise the average to 34? (a) 55 (b) 34 (c) 41 (d) 28
  39. 39.A batter has an average of 31 runs in 4 matches. How many runs are needed in the next match to raise the average to 34? (a) 37 (b) 15 (c) 34 (d) 46
  40. 40.The average of 6 numbers is 27. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 57 (b) 13 (c) 27 (d) 12

Answer key

  1. 20
  2. 33
  3. 38
  4. 76
  5. 45
  6. 3
  7. 38
  8. 48
  9. 1
  10. 34
  11. 53
  12. 57
  13. 50
  14. 48
  15. 88
  16. 55
  17. 100
  18. 35
  19. 31
  20. 33
  21. 34
  22. 46
  23. 32
  24. 46
  25. 18
  26. 59
  27. 22
  28. 75
  29. 62
  30. 61
  31. 21
  32. 30
  33. 23
  34. 48
  35. 23
  36. 29
  37. 38
  38. 55
  39. 46
  40. 12

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