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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 100 · 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 children, 12 sing Hindi songs, 24 sing English songs and 7 sing both. How many sing neither of the two?
  2. 2.In a group of 39 children, 23 like mangoes, 12 like bananas and 8 like both. How many like only mangoes?
  3. 3.In a group of 36 children, 18 enjoy drawing, 21 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  4. 4.In a group of 42 children, 13 like mangoes, 22 like bananas and 2 like both. How many like exactly one of the two?
  5. 5.In a group of 51 children, 27 play cricket, 22 play football and 10 play both. How many play neither of the two?
  6. 6.In a group of 33 children, 17 like mangoes, 14 like bananas and 3 like both. How many like only bananas?
  7. 7.In a group of 28 children, 19 enjoy drawing, 14 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  8. 8.In a group of 45 children, 26 enjoy drawing, 17 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  9. 9.In a group of 25 children, 9 play cricket, 5 play football and 2 play both. How many play exactly one of the two?
  10. 10.In a group of 42 children, 20 play chess, 27 play carrom and 8 play both. How many play only chess?
  11. 11.In a group of 31 children, 22 play chess, 12 play carrom and 5 play both. How many play at least one of the two?
  12. 12.In a group of 38 grown-ups, 19 drink tea, 13 drink coffee and 7 drink both. How many drink at least one of the two?
  13. 13.In a group of 38 children, 21 play cricket, 20 play football and 10 play both. How many play at least one of the two?
  14. 14.In a group of 50 children, 28 play chess, 27 play carrom and 10 play both. How many play only carrom?
  15. 15.In a group of 43 children, 22 sing Hindi songs, 11 sing English songs and 4 sing both. How many sing only Hindi songs?
  16. 16.In a group of 35 children, 22 play cricket, 13 play football and 3 play both. How many play neither of the two?
  17. 17.In a group of 45 children, 29 play cricket, 17 play football and 11 play both. How many play at least one of the two?
  18. 18.In a group of 23 children, 8 play chess, 11 play carrom and 5 play both. How many play neither of the two?
  19. 19.In a group of 33 children, 16 play chess, 18 play carrom and 4 play both. How many play exactly one of the two?
  20. 20.In a group of 37 children, 18 play chess, 13 play carrom and 9 play both. How many play exactly one of the two?
  21. 21.In a group of 32 children, 12 like mangoes, 26 like bananas and 8 like both. How many like at least one of the two?
  22. 22.In a group of 32 children, 24 enjoy drawing, 14 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  23. 23.In a group of 34 children, 16 play cricket, 9 play football and 2 play both. How many play exactly one of the two?
  24. 24.In a group of 50 children, 23 play cricket, 19 play football and 5 play both. How many play only football?
  25. 25.In a group of 31 children, 17 enjoy drawing, 11 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  26. 26.In a group of 35 children, 26 play cricket, 14 play football and 6 play both. How many play neither of the two?
  27. 27.In a group of 23 children, 7 sing Hindi songs, 15 sing English songs and 3 sing both. How many sing neither of the two?
  28. 28.In a group of 27 children, 5 play chess, 21 play carrom and 2 play both. How many play only chess?
  29. 29.In a group of 45 children, 26 play chess, 22 play carrom and 6 play both. How many play only carrom?
  30. 30.In a group of 27 children, 16 play cricket, 15 play football and 6 play both. How many play only cricket?
  31. 31.In a group of 27 children, 20 sing Hindi songs, 10 sing English songs and 7 sing both. How many sing only Hindi songs?
  32. 32.In a group of 29 grown-ups, 13 drink tea, 9 drink coffee and 2 drink both. How many drink at least one of the two?
  33. 33.In a group of 30 children, 8 play chess, 20 play carrom and 2 play both. How many play at least one of the two?
  34. 34.In a group of 16 children, 9 enjoy drawing, 10 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  35. 35.In a group of 46 grown-ups, 15 drink tea, 28 drink coffee and 10 drink both. How many drink neither of the two?
  36. 36.In a group of 44 children, 19 enjoy drawing, 24 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  37. 37.In a group of 45 grown-ups, 24 drink tea, 31 drink coffee and 11 drink both. How many drink exactly one of the two?
  38. 38.In a group of 34 children, 13 enjoy drawing, 9 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  39. 39.In a group of 44 children, 18 play cricket, 21 play football and 4 play both. How many play only cricket?
  40. 40.In a group of 52 grown-ups, 25 drink tea, 21 drink coffee and 7 drink both. How many drink at least one of the two?

Answer key

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

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