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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 414 · 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 28 children, 15 sing Hindi songs, 20 sing English songs and 12 sing both. How many sing only Hindi songs?
  2. 2.In a group of 39 children, 18 like mangoes, 22 like bananas and 4 like both. How many like only mangoes?
  3. 3.In a group of 40 children, 25 play chess, 22 play carrom and 8 play both. How many play only chess?
  4. 4.In a group of 31 children, 7 play chess, 16 play carrom and 3 play both. How many play exactly one of the two?
  5. 5.In a group of 47 children, 27 play cricket, 25 play football and 7 play both. How many play at least one of the two?
  6. 6.In a group of 28 children, 14 enjoy drawing, 15 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  7. 7.In a group of 28 children, 16 play cricket, 16 play football and 10 play both. How many play only football?
  8. 8.In a group of 39 children, 23 like mangoes, 12 like bananas and 8 like both. How many like exactly one of the two?
  9. 9.In a group of 44 children, 24 sing Hindi songs, 19 sing English songs and 11 sing both. How many sing neither of the two?
  10. 10.In a group of 19 children, 8 like mangoes, 6 like bananas and 2 like both. How many like neither of the two?
  11. 11.In a group of 28 children, 14 enjoy drawing, 12 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  12. 12.In a group of 40 children, 18 enjoy drawing, 21 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  13. 13.In a group of 28 children, 10 enjoy drawing, 11 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  14. 14.In a group of 22 children, 6 enjoy drawing, 9 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  15. 15.In a group of 43 children, 24 play cricket, 30 play football and 12 play both. How many play at least one of the two?
  16. 16.In a group of 42 children, 22 enjoy drawing, 30 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  17. 17.In a group of 37 children, 17 play chess, 16 play carrom and 2 play both. How many play at least one of the two?
  18. 18.In a group of 42 grown-ups, 18 drink tea, 25 drink coffee and 5 drink both. How many drink exactly one of the two?
  19. 19.In a group of 25 children, 14 play cricket, 14 play football and 6 play both. How many play only football?
  20. 20.In a group of 46 children, 18 like mangoes, 32 like bananas and 12 like both. How many like only bananas?
  21. 21.In a group of 16 children, 6 play cricket, 7 play football and 3 play both. How many play exactly one of the two?
  22. 22.In a group of 26 children, 13 play cricket, 16 play football and 6 play both. How many play at least one of the two?
  23. 23.In a group of 50 children, 16 sing Hindi songs, 24 sing English songs and 4 sing both. How many sing exactly one of the two?
  24. 24.In a group of 43 grown-ups, 21 drink tea, 11 drink coffee and 2 drink both. How many drink only coffee?
  25. 25.In a group of 42 children, 17 enjoy drawing, 17 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  26. 26.In a group of 38 children, 14 play chess, 16 play carrom and 3 play both. How many play only carrom?
  27. 27.In a group of 36 grown-ups, 13 drink tea, 26 drink coffee and 9 drink both. How many drink at least one of the two?
  28. 28.In a group of 48 children, 18 like mangoes, 21 like bananas and 4 like both. How many like neither of the two?
  29. 29.In a group of 29 children, 16 sing Hindi songs, 14 sing English songs and 10 sing both. How many sing only Hindi songs?
  30. 30.In a group of 30 children, 6 play chess, 19 play carrom and 3 play both. How many play only chess?
  31. 31.In a group of 28 children, 16 enjoy drawing, 15 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  32. 32.In a group of 42 grown-ups, 22 drink tea, 9 drink coffee and 4 drink both. How many drink only coffee?
  33. 33.In a group of 30 children, 14 enjoy drawing, 16 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  34. 34.In a group of 39 children, 14 play chess, 22 play carrom and 7 play both. How many play neither of the two?
  35. 35.In a group of 48 children, 24 sing Hindi songs, 23 sing English songs and 5 sing both. How many sing exactly one of the two?
  36. 36.In a group of 43 children, 20 like mangoes, 17 like bananas and 2 like both. How many like neither of the two?
  37. 37.In a group of 16 children, 10 like mangoes, 7 like bananas and 2 like both. How many like only bananas?
  38. 38.In a group of 58 children, 29 play chess, 24 play carrom and 10 play both. How many play exactly one of the two?
  39. 39.In a group of 26 children, 11 sing Hindi songs, 11 sing English songs and 7 sing both. How many sing at least one of the two?
  40. 40.In a group of 28 children, 21 enjoy drawing, 12 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?

Answer key

  1. 3
  2. 14
  3. 17
  4. 17
  5. 45
  6. 12
  7. 6
  8. 19
  9. 12
  10. 7
  11. 24
  12. 28
  13. 19
  14. 10
  15. 42
  16. 18
  17. 31
  18. 33
  19. 8
  20. 20
  21. 7
  22. 23
  23. 32
  24. 9
  25. 27
  26. 13
  27. 30
  28. 13
  29. 6
  30. 3
  31. 9
  32. 5
  33. 11
  34. 10
  35. 37
  36. 8
  37. 5
  38. 33
  39. 15
  40. 2

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