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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 430 · 40 questions
TalentJR

How to think it through (Middle first): Put “both” in the overlap. Only A = A − both; only B = B − both; at least one = A + B − both. Neither = total − at least one; exactly one = only A + only B.

NameDateTime takenScore ___ / 40
  1. 1.In a group of 31 children, 18 play cricket, 20 play football and 11 play both. How many play only football?
  2. 2.In a group of 49 children, 25 play cricket, 18 play football and 9 play both. How many play neither of the two?
  3. 3.In a group of 25 children, 17 sing Hindi songs, 12 sing English songs and 5 sing both. How many sing only Hindi songs?
  4. 4.In a group of 36 children, 16 like mangoes, 29 like bananas and 11 like both. How many like exactly one of the two?
  5. 5.In a group of 37 children, 15 sing Hindi songs, 14 sing English songs and 4 sing both. How many sing only Hindi songs?
  6. 6.In a group of 39 children, 21 play chess, 15 play carrom and 7 play both. How many play at least one of the two?
  7. 7.In a group of 51 children, 32 sing Hindi songs, 30 sing English songs and 12 sing both. How many sing at least one of the two?
  8. 8.In a group of 30 children, 16 enjoy drawing, 14 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  9. 9.In a group of 56 children, 24 sing Hindi songs, 28 sing English songs and 11 sing both. How many sing only Hindi songs?
  10. 10.In a group of 40 children, 15 play cricket, 24 play football and 4 play both. How many play neither of the two?
  11. 11.In a group of 37 children, 21 like mangoes, 17 like bananas and 2 like both. How many like neither of the two?
  12. 12.In a group of 34 children, 16 like mangoes, 24 like bananas and 12 like both. How many like only bananas?
  13. 13.In a group of 36 children, 22 sing Hindi songs, 16 sing English songs and 3 sing both. How many sing only Hindi songs?
  14. 14.In a group of 39 children, 15 enjoy drawing, 30 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  15. 15.In a group of 45 children, 21 like mangoes, 28 like bananas and 8 like both. How many like at least one of the two?
  16. 16.In a group of 48 children, 22 enjoy drawing, 21 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  17. 17.In a group of 61 children, 31 like mangoes, 32 like bananas and 12 like both. How many like at least one of the two?
  18. 18.In a group of 26 children, 6 like mangoes, 15 like bananas and 3 like both. How many like only bananas?
  19. 19.In a group of 43 children, 16 play cricket, 21 play football and 7 play both. How many play neither of the two?
  20. 20.In a group of 55 children, 27 enjoy drawing, 27 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  21. 21.In a group of 34 children, 9 enjoy drawing, 17 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  22. 22.In a group of 41 children, 14 like mangoes, 16 like bananas and 3 like both. How many like at least one of the two?
  23. 23.In a group of 20 children, 15 play cricket, 14 play football and 11 play both. How many play only football?
  24. 24.In a group of 32 children, 18 play chess, 24 play carrom and 11 play both. How many play only chess?
  25. 25.In a group of 55 children, 24 sing Hindi songs, 25 sing English songs and 6 sing both. How many sing exactly one of the two?
  26. 26.In a group of 30 children, 11 play cricket, 15 play football and 3 play both. How many play at least one of the two?
  27. 27.In a group of 31 children, 14 play chess, 22 play carrom and 8 play both. How many play only carrom?
  28. 28.In a group of 40 children, 13 enjoy drawing, 20 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  29. 29.In a group of 36 children, 12 enjoy drawing, 20 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  30. 30.In a group of 41 children, 16 play cricket, 26 play football and 7 play both. How many play at least one of the two?
  31. 31.In a group of 45 children, 23 enjoy drawing, 23 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  32. 32.In a group of 23 children, 16 like mangoes, 7 like bananas and 2 like both. How many like only bananas?
  33. 33.In a group of 31 children, 9 enjoy drawing, 9 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  34. 34.In a group of 41 children, 23 enjoy drawing, 13 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  35. 35.In a group of 49 children, 21 sing Hindi songs, 29 sing English songs and 12 sing both. How many sing at least one of the two?
  36. 36.In a group of 44 children, 25 play chess, 20 play carrom and 12 play both. How many play only carrom?
  37. 37.In a group of 33 children, 19 play cricket, 9 play football and 5 play both. How many play only cricket?
  38. 38.In a group of 34 children, 16 enjoy drawing, 24 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  39. 39.In a group of 25 children, 8 play cricket, 8 play football and 4 play both. How many play at least one of the two?
  40. 40.In a group of 44 children, 11 sing Hindi songs, 24 sing English songs and 4 sing both. How many sing at least one of the two?

Answer key

  1. 9
  2. 15
  3. 12
  4. 23
  5. 11
  6. 29
  7. 50
  8. 19
  9. 13
  10. 5
  11. 1
  12. 12
  13. 19
  14. 21
  15. 41
  16. 39
  17. 51
  18. 12
  19. 13
  20. 17
  21. 18
  22. 27
  23. 3
  24. 7
  25. 37
  26. 23
  27. 14
  28. 25
  29. 4
  30. 35
  31. 2
  32. 5
  33. 16
  34. 32
  35. 38
  36. 8
  37. 14
  38. 15
  39. 12
  40. 31

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