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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 223 · 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 34 children, 18 enjoy drawing, 27 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  2. 2.In a group of 34 children, 25 play cricket, 19 play football and 12 play both. How many play only cricket?
  3. 3.In a group of 49 children, 22 sing Hindi songs, 27 sing English songs and 8 sing both. How many sing only Hindi songs?
  4. 4.In a group of 33 children, 23 play cricket, 19 play football and 12 play both. How many play exactly one of the two?
  5. 5.In a group of 30 children, 14 play chess, 9 play carrom and 4 play both. How many play only carrom?
  6. 6.In a group of 45 children, 23 play chess, 22 play carrom and 8 play both. How many play at least one of the two?
  7. 7.In a group of 31 children, 15 play cricket, 10 play football and 3 play both. How many play only football?
  8. 8.In a group of 20 children, 10 sing Hindi songs, 14 sing English songs and 5 sing both. How many sing only Hindi songs?
  9. 9.In a group of 55 children, 25 play chess, 26 play carrom and 9 play both. How many play only chess?
  10. 10.In a group of 52 children, 27 like mangoes, 22 like bananas and 7 like both. How many like at least one of the two?
  11. 11.In a group of 33 children, 18 enjoy drawing, 13 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  12. 12.In a group of 30 children, 8 play cricket, 11 play football and 4 play both. How many play only football?
  13. 13.In a group of 34 children, 8 play chess, 18 play carrom and 3 play both. How many play at least one of the two?
  14. 14.In a group of 49 children, 31 sing Hindi songs, 24 sing English songs and 11 sing both. How many sing at least one of the two?
  15. 15.In a group of 34 children, 16 like mangoes, 9 like bananas and 6 like both. How many like only bananas?
  16. 16.In a group of 54 children, 29 enjoy drawing, 27 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  17. 17.In a group of 25 children, 16 play cricket, 16 play football and 11 play both. How many play only cricket?
  18. 18.In a group of 30 children, 12 play chess, 9 play carrom and 3 play both. How many play neither of the two?
  19. 19.In a group of 52 children, 20 enjoy drawing, 28 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  20. 20.In a group of 22 children, 17 play chess, 13 play carrom and 10 play both. How many play only carrom?
  21. 21.In a group of 45 children, 26 sing Hindi songs, 16 sing English songs and 12 sing both. How many sing only English songs?
  22. 22.In a group of 31 children, 15 sing Hindi songs, 15 sing English songs and 10 sing both. How many sing exactly one of the two?
  23. 23.In a group of 32 grown-ups, 25 drink tea, 11 drink coffee and 8 drink both. How many drink only tea?
  24. 24.In a group of 32 children, 12 play cricket, 13 play football and 5 play both. How many play only cricket?
  25. 25.In a group of 29 children, 12 play cricket, 17 play football and 4 play both. How many play at least one of the two?
  26. 26.In a group of 36 grown-ups, 20 drink tea, 17 drink coffee and 12 drink both. How many drink exactly one of the two?
  27. 27.In a group of 47 children, 23 enjoy drawing, 25 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  28. 28.In a group of 33 children, 15 play cricket, 27 play football and 11 play both. How many play at least one of the two?
  29. 29.In a group of 51 children, 29 sing Hindi songs, 18 sing English songs and 10 sing both. How many sing only English songs?
  30. 30.In a group of 38 children, 31 play cricket, 16 play football and 11 play both. How many play only football?
  31. 31.In a group of 60 children, 25 sing Hindi songs, 29 sing English songs and 9 sing both. How many sing neither of the two?
  32. 32.In a group of 29 children, 6 sing Hindi songs, 13 sing English songs and 3 sing both. How many sing at least one of the two?
  33. 33.In a group of 48 children, 14 sing Hindi songs, 30 sing English songs and 10 sing both. How many sing neither of the two?
  34. 34.In a group of 40 children, 11 enjoy drawing, 23 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  35. 35.In a group of 26 children, 15 enjoy drawing, 21 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  36. 36.In a group of 48 children, 21 play chess, 31 play carrom and 11 play both. How many play only chess?
  37. 37.In a group of 26 children, 17 play cricket, 10 play football and 4 play both. How many play only cricket?
  38. 38.In a group of 45 children, 15 enjoy drawing, 19 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  39. 39.In a group of 47 children, 24 enjoy drawing, 15 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  40. 40.In a group of 48 children, 30 play chess, 19 play carrom and 10 play both. How many play exactly one of the two?

Answer key

  1. 1
  2. 13
  3. 14
  4. 18
  5. 5
  6. 37
  7. 7
  8. 5
  9. 16
  10. 42
  11. 4
  12. 7
  13. 23
  14. 44
  15. 3
  16. 32
  17. 5
  18. 12
  19. 20
  20. 3
  21. 4
  22. 10
  23. 17
  24. 7
  25. 25
  26. 13
  27. 17
  28. 31
  29. 8
  30. 5
  31. 15
  32. 16
  33. 14
  34. 14
  35. 14
  36. 10
  37. 13
  38. 32
  39. 20
  40. 29

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