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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 136 · 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 15 children, 6 enjoy drawing, 6 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  2. 2.In a group of 38 children, 24 sing Hindi songs, 14 sing English songs and 7 sing both. How many sing neither of the two?
  3. 3.In a group of 45 children, 14 play chess, 28 play carrom and 9 play both. How many play exactly one of the two?
  4. 4.In a group of 41 children, 27 enjoy drawing, 21 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  5. 5.In a group of 48 children, 21 play chess, 21 play carrom and 5 play both. How many play exactly one of the two?
  6. 6.In a group of 31 children, 15 sing Hindi songs, 9 sing English songs and 3 sing both. How many sing at least one of the two?
  7. 7.In a group of 42 children, 17 play chess, 13 play carrom and 3 play both. How many play only carrom?
  8. 8.In a group of 26 children, 15 like mangoes, 9 like bananas and 4 like both. How many like only bananas?
  9. 9.In a group of 33 children, 21 like mangoes, 11 like bananas and 6 like both. How many like at least one of the two?
  10. 10.In a group of 40 children, 16 play chess, 30 play carrom and 12 play both. How many play at least one of the two?
  11. 11.In a group of 47 children, 19 sing Hindi songs, 25 sing English songs and 6 sing both. How many sing only English songs?
  12. 12.In a group of 38 children, 18 play cricket, 28 play football and 11 play both. How many play only football?
  13. 13.In a group of 47 children, 20 play cricket, 19 play football and 6 play both. How many play neither of the two?
  14. 14.In a group of 32 children, 23 enjoy drawing, 12 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  15. 15.In a group of 43 children, 23 like mangoes, 16 like bananas and 3 like both. How many like neither of the two?
  16. 16.In a group of 31 children, 24 like mangoes, 14 like bananas and 10 like both. How many like only mangoes?
  17. 17.In a group of 38 children, 18 enjoy drawing, 28 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  18. 18.In a group of 25 children, 17 play chess, 15 play carrom and 8 play both. How many play at least one of the two?
  19. 19.In a group of 29 children, 6 sing Hindi songs, 21 sing English songs and 2 sing both. How many sing only English songs?
  20. 20.In a group of 36 children, 22 play cricket, 15 play football and 2 play both. How many play only football?
  21. 21.In a group of 48 children, 28 sing Hindi songs, 25 sing English songs and 9 sing both. How many sing at least one of the two?
  22. 22.In a group of 33 children, 9 sing Hindi songs, 14 sing English songs and 4 sing both. How many sing at least one of the two?
  23. 23.In a group of 23 children, 15 enjoy drawing, 14 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  24. 24.In a group of 34 grown-ups, 11 drink tea, 24 drink coffee and 8 drink both. How many drink exactly one of the two?
  25. 25.In a group of 42 children, 20 like mangoes, 16 like bananas and 5 like both. How many like only mangoes?
  26. 26.In a group of 31 grown-ups, 14 drink tea, 20 drink coffee and 11 drink both. How many drink only tea?
  27. 27.In a group of 36 children, 20 sing Hindi songs, 14 sing English songs and 3 sing both. How many sing only Hindi songs?
  28. 28.In a group of 58 children, 26 play cricket, 28 play football and 9 play both. How many play at least one of the two?
  29. 29.In a group of 53 children, 22 sing Hindi songs, 24 sing English songs and 7 sing both. How many sing only Hindi songs?
  30. 30.In a group of 24 children, 15 enjoy drawing, 5 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  31. 31.In a group of 25 children, 21 enjoy drawing, 12 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  32. 32.In a group of 35 children, 22 like mangoes, 14 like bananas and 9 like both. How many like at least one of the two?
  33. 33.In a group of 29 children, 11 play cricket, 12 play football and 3 play both. How many play only football?
  34. 34.In a group of 19 children, 14 play cricket, 13 play football and 10 play both. How many play only cricket?
  35. 35.In a group of 32 grown-ups, 9 drink tea, 17 drink coffee and 2 drink both. How many drink only coffee?
  36. 36.In a group of 42 grown-ups, 11 drink tea, 21 drink coffee and 2 drink both. How many drink exactly one of the two?
  37. 37.In a group of 26 children, 20 like mangoes, 14 like bananas and 10 like both. How many like neither of the two?
  38. 38.In a group of 44 children, 17 like mangoes, 23 like bananas and 11 like both. How many like only bananas?
  39. 39.In a group of 46 children, 19 play cricket, 25 play football and 8 play both. How many play exactly one of the two?
  40. 40.In a group of 44 children, 30 sing Hindi songs, 22 sing English songs and 11 sing both. How many sing exactly one of the two?

Answer key

  1. 8
  2. 7
  3. 24
  4. 16
  5. 32
  6. 21
  7. 10
  8. 5
  9. 26
  10. 34
  11. 19
  12. 17
  13. 14
  14. 3
  15. 7
  16. 14
  17. 22
  18. 24
  19. 19
  20. 13
  21. 44
  22. 19
  23. 7
  24. 19
  25. 15
  26. 3
  27. 17
  28. 45
  29. 15
  30. 13
  31. 3
  32. 27
  33. 9
  34. 4
  35. 15
  36. 28
  37. 2
  38. 12
  39. 28
  40. 30

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