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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 625 · 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 43 children, 24 enjoy drawing, 14 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  2. 2.In a group of 48 grown-ups, 15 drink tea, 23 drink coffee and 4 drink both. How many drink only tea?
  3. 3.In a group of 33 children, 19 play cricket, 20 play football and 12 play both. How many play only cricket?
  4. 4.In a group of 36 children, 18 play chess, 13 play carrom and 5 play both. How many play only carrom?
  5. 5.In a group of 32 children, 17 sing Hindi songs, 10 sing English songs and 2 sing both. How many sing only English songs?
  6. 6.In a group of 16 children, 8 sing Hindi songs, 7 sing English songs and 4 sing both. How many sing only Hindi songs?
  7. 7.In a group of 41 children, 18 play cricket, 10 play football and 2 play both. How many play only football?
  8. 8.In a group of 27 children, 14 play cricket, 11 play football and 6 play both. How many play only cricket?
  9. 9.In a group of 41 children, 26 enjoy drawing, 18 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  10. 10.In a group of 36 children, 16 play chess, 19 play carrom and 5 play both. How many play only carrom?
  11. 11.In a group of 32 children, 21 like mangoes, 8 like bananas and 4 like both. How many like only mangoes?
  12. 12.In a group of 32 children, 15 play chess, 18 play carrom and 8 play both. How many play at least one of the two?
  13. 13.In a group of 14 children, 6 sing Hindi songs, 7 sing English songs and 2 sing both. How many sing at least one of the two?
  14. 14.In a group of 33 children, 18 enjoy drawing, 14 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  15. 15.In a group of 48 children, 23 sing Hindi songs, 21 sing English songs and 11 sing both. How many sing exactly one of the two?
  16. 16.In a group of 23 children, 15 sing Hindi songs, 7 sing English songs and 2 sing both. How many sing only Hindi songs?
  17. 17.In a group of 41 children, 25 play chess, 13 play carrom and 6 play both. How many play at least one of the two?
  18. 18.In a group of 33 grown-ups, 15 drink tea, 21 drink coffee and 4 drink both. How many drink at least one of the two?
  19. 19.In a group of 51 children, 32 play chess, 17 play carrom and 12 play both. How many play at least one of the two?
  20. 20.In a group of 27 children, 9 like mangoes, 15 like bananas and 5 like both. How many like neither of the two?
  21. 21.In a group of 32 children, 9 enjoy drawing, 14 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  22. 22.In a group of 55 children, 27 play chess, 25 play carrom and 8 play both. How many play at least one of the two?
  23. 23.In a group of 41 children, 23 enjoy drawing, 21 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  24. 24.In a group of 30 children, 20 like mangoes, 18 like bananas and 10 like both. How many like only bananas?
  25. 25.In a group of 47 children, 25 enjoy drawing, 17 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  26. 26.In a group of 23 children, 13 sing Hindi songs, 14 sing English songs and 6 sing both. How many sing at least one of the two?
  27. 27.In a group of 51 children, 32 enjoy drawing, 20 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  28. 28.In a group of 27 children, 10 play chess, 13 play carrom and 2 play both. How many play only chess?
  29. 29.In a group of 53 children, 23 play cricket, 24 play football and 7 play both. How many play only cricket?
  30. 30.In a group of 37 children, 14 enjoy drawing, 24 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  31. 31.In a group of 34 children, 23 enjoy drawing, 11 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  32. 32.In a group of 30 children, 19 like mangoes, 5 like bananas and 2 like both. How many like neither of the two?
  33. 33.In a group of 38 children, 17 enjoy drawing, 32 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  34. 34.In a group of 38 children, 17 play cricket, 17 play football and 3 play both. How many play only football?
  35. 35.In a group of 38 children, 16 play cricket, 30 play football and 12 play both. How many play only football?
  36. 36.In a group of 41 grown-ups, 25 drink tea, 18 drink coffee and 12 drink both. How many drink at least one of the two?
  37. 37.In a group of 32 children, 28 like mangoes, 11 like bananas and 8 like both. How many like only mangoes?
  38. 38.In a group of 33 children, 12 sing Hindi songs, 27 sing English songs and 7 sing both. How many sing only English songs?
  39. 39.In a group of 36 children, 13 play cricket, 18 play football and 9 play both. How many play exactly one of the two?
  40. 40.In a group of 42 children, 22 play chess, 9 play carrom and 2 play both. How many play at least one of the two?

Answer key

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

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