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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 34 · 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 30 grown-ups, 9 drink tea, 19 drink coffee and 5 drink both. How many drink exactly one of the two?
  2. 2.In a group of 34 grown-ups, 16 drink tea, 9 drink coffee and 5 drink both. How many drink only tea?
  3. 3.In a group of 39 grown-ups, 16 drink tea, 18 drink coffee and 8 drink both. How many drink neither of the two?
  4. 4.In a group of 45 children, 14 enjoy drawing, 20 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  5. 5.In a group of 46 children, 11 play cricket, 26 play football and 6 play both. How many play at least one of the two?
  6. 6.In a group of 33 grown-ups, 16 drink tea, 26 drink coffee and 10 drink both. How many drink neither of the two?
  7. 7.In a group of 32 children, 12 play cricket, 23 play football and 9 play both. How many play neither of the two?
  8. 8.In a group of 22 children, 9 sing Hindi songs, 14 sing English songs and 5 sing both. How many sing exactly one of the two?
  9. 9.In a group of 45 grown-ups, 22 drink tea, 18 drink coffee and 4 drink both. How many drink only coffee?
  10. 10.In a group of 41 children, 22 play cricket, 9 play football and 3 play both. How many play exactly one of the two?
  11. 11.In a group of 43 children, 19 play chess, 17 play carrom and 3 play both. How many play neither of the two?
  12. 12.In a group of 27 children, 12 play cricket, 14 play football and 2 play both. How many play exactly one of the two?
  13. 13.In a group of 12 grown-ups, 7 drink tea, 8 drink coffee and 4 drink both. How many drink neither of the two?
  14. 14.In a group of 35 children, 20 like mangoes, 16 like bananas and 12 like both. How many like only bananas?
  15. 15.In a group of 44 children, 26 sing Hindi songs, 23 sing English songs and 7 sing both. How many sing only Hindi songs?
  16. 16.In a group of 26 grown-ups, 11 drink tea, 16 drink coffee and 3 drink both. How many drink exactly one of the two?
  17. 17.In a group of 39 children, 8 play cricket, 18 play football and 2 play both. How many play only football?
  18. 18.In a group of 33 children, 22 sing Hindi songs, 11 sing English songs and 7 sing both. How many sing neither of the two?
  19. 19.In a group of 27 children, 16 play chess, 16 play carrom and 11 play both. How many play only chess?
  20. 20.In a group of 31 children, 16 play cricket, 14 play football and 7 play both. How many play exactly one of the two?
  21. 21.In a group of 17 children, 8 play chess, 7 play carrom and 4 play both. How many play at least one of the two?
  22. 22.In a group of 38 children, 10 play cricket, 19 play football and 5 play both. How many play at least one of the two?
  23. 23.In a group of 46 children, 23 sing Hindi songs, 15 sing English songs and 7 sing both. How many sing only Hindi songs?
  24. 24.In a group of 41 children, 23 play cricket, 21 play football and 5 play both. How many play only football?
  25. 25.In a group of 54 children, 22 like mangoes, 26 like bananas and 8 like both. How many like neither of the two?
  26. 26.In a group of 25 children, 20 like mangoes, 11 like bananas and 8 like both. How many like only bananas?
  27. 27.In a group of 33 grown-ups, 14 drink tea, 15 drink coffee and 11 drink both. How many drink at least one of the two?
  28. 28.In a group of 31 children, 22 enjoy drawing, 9 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  29. 29.In a group of 35 children, 19 sing Hindi songs, 13 sing English songs and 7 sing both. How many sing only English songs?
  30. 30.In a group of 30 children, 6 like mangoes, 19 like bananas and 3 like both. How many like exactly one of the two?
  31. 31.In a group of 39 children, 27 enjoy drawing, 21 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  32. 32.In a group of 41 children, 20 play cricket, 22 play football and 2 play both. How many play neither of the two?
  33. 33.In a group of 40 children, 19 like mangoes, 19 like bananas and 12 like both. How many like neither of the two?
  34. 34.In a group of 33 children, 8 play chess, 16 play carrom and 4 play both. How many play only carrom?
  35. 35.In a group of 36 children, 24 play cricket, 12 play football and 8 play both. How many play exactly one of the two?
  36. 36.In a group of 36 children, 9 play chess, 19 play carrom and 2 play both. How many play at least one of the two?
  37. 37.In a group of 39 children, 16 like mangoes, 20 like bananas and 9 like both. How many like at least one of the two?
  38. 38.In a group of 28 children, 9 sing Hindi songs, 12 sing English songs and 6 sing both. How many sing at least one of the two?
  39. 39.In a group of 38 children, 13 like mangoes, 20 like bananas and 7 like both. How many like exactly one of the two?
  40. 40.In a group of 32 children, 19 enjoy drawing, 20 enjoy dancing and 8 enjoy both. How many enjoy only dancing?

Answer key

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

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