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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 349 · 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, 19 sing Hindi songs, 9 sing English songs and 6 sing both. How many sing neither of the two?
  2. 2.In a group of 36 children, 20 enjoy drawing, 17 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  3. 3.In a group of 21 children, 14 play chess, 13 play carrom and 9 play both. How many play only chess?
  4. 4.In a group of 18 children, 8 play chess, 12 play carrom and 4 play both. How many play neither of the two?
  5. 5.In a group of 19 children, 15 play chess, 10 play carrom and 7 play both. How many play exactly one of the two?
  6. 6.In a group of 35 children, 10 play cricket, 22 play football and 5 play both. How many play exactly one of the two?
  7. 7.In a group of 50 children, 23 play cricket, 26 play football and 8 play both. How many play only cricket?
  8. 8.In a group of 30 children, 18 play cricket, 9 play football and 5 play both. How many play exactly one of the two?
  9. 9.In a group of 13 children, 6 play cricket, 7 play football and 3 play both. How many play exactly one of the two?
  10. 10.In a group of 26 grown-ups, 18 drink tea, 7 drink coffee and 3 drink both. How many drink only tea?
  11. 11.In a group of 41 grown-ups, 20 drink tea, 21 drink coffee and 7 drink both. How many drink only coffee?
  12. 12.In a group of 43 children, 20 enjoy drawing, 22 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  13. 13.In a group of 42 children, 25 enjoy drawing, 24 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  14. 14.In a group of 50 children, 27 play cricket, 28 play football and 8 play both. How many play neither of the two?
  15. 15.In a group of 40 children, 17 enjoy drawing, 29 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  16. 16.In a group of 38 children, 25 play cricket, 12 play football and 6 play both. How many play at least one of the two?
  17. 17.In a group of 21 grown-ups, 11 drink tea, 13 drink coffee and 6 drink both. How many drink only coffee?
  18. 18.In a group of 36 children, 20 play chess, 13 play carrom and 2 play both. How many play only carrom?
  19. 19.In a group of 23 grown-ups, 9 drink tea, 18 drink coffee and 6 drink both. How many drink exactly one of the two?
  20. 20.In a group of 29 children, 16 play chess, 13 play carrom and 4 play both. How many play at least one of the two?
  21. 21.In a group of 34 grown-ups, 13 drink tea, 10 drink coffee and 2 drink both. How many drink only coffee?
  22. 22.In a group of 36 children, 29 like mangoes, 13 like bananas and 9 like both. How many like only mangoes?
  23. 23.In a group of 27 children, 14 sing Hindi songs, 15 sing English songs and 6 sing both. How many sing neither of the two?
  24. 24.In a group of 39 children, 22 enjoy drawing, 21 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  25. 25.In a group of 37 children, 17 play chess, 10 play carrom and 5 play both. How many play neither of the two?
  26. 26.In a group of 33 children, 11 play cricket, 19 play football and 6 play both. How many play neither of the two?
  27. 27.In a group of 51 children, 26 play cricket, 24 play football and 11 play both. How many play at least one of the two?
  28. 28.In a group of 35 children, 9 like mangoes, 14 like bananas and 3 like both. How many like exactly one of the two?
  29. 29.In a group of 33 children, 23 play chess, 10 play carrom and 6 play both. How many play only carrom?
  30. 30.In a group of 33 children, 23 like mangoes, 9 like bananas and 4 like both. How many like exactly one of the two?
  31. 31.In a group of 55 children, 24 play cricket, 21 play football and 4 play both. How many play neither of the two?
  32. 32.In a group of 40 children, 19 play cricket, 21 play football and 3 play both. How many play only cricket?
  33. 33.In a group of 32 children, 10 play chess, 19 play carrom and 3 play both. How many play exactly one of the two?
  34. 34.In a group of 26 grown-ups, 11 drink tea, 10 drink coffee and 5 drink both. How many drink exactly one of the two?
  35. 35.In a group of 32 children, 19 enjoy drawing, 9 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  36. 36.In a group of 26 children, 6 play chess, 14 play carrom and 2 play both. How many play only carrom?
  37. 37.In a group of 44 children, 24 sing Hindi songs, 23 sing English songs and 5 sing both. How many sing at least one of the two?
  38. 38.In a group of 29 children, 18 enjoy drawing, 11 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  39. 39.In a group of 27 grown-ups, 8 drink tea, 14 drink coffee and 5 drink both. How many drink only coffee?
  40. 40.In a group of 27 children, 10 like mangoes, 6 like bananas and 2 like both. How many like exactly one of the two?

Answer key

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

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