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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 176 · 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 41 grown-ups, 20 drink tea, 29 drink coffee and 9 drink both. How many drink exactly one of the two?
  2. 2.In a group of 49 grown-ups, 25 drink tea, 26 drink coffee and 8 drink both. How many drink exactly one of the two?
  3. 3.In a group of 38 children, 25 sing Hindi songs, 13 sing English songs and 5 sing both. How many sing neither of the two?
  4. 4.In a group of 53 children, 27 like mangoes, 27 like bananas and 10 like both. How many like at least one of the two?
  5. 5.In a group of 50 children, 29 enjoy drawing, 23 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  6. 6.In a group of 42 children, 23 sing Hindi songs, 22 sing English songs and 11 sing both. How many sing only English songs?
  7. 7.In a group of 33 children, 11 play chess, 20 play carrom and 7 play both. How many play exactly one of the two?
  8. 8.In a group of 49 grown-ups, 24 drink tea, 18 drink coffee and 6 drink both. How many drink only tea?
  9. 9.In a group of 40 children, 19 enjoy drawing, 19 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  10. 10.In a group of 20 children, 8 play chess, 13 play carrom and 5 play both. How many play only carrom?
  11. 11.In a group of 56 children, 26 enjoy drawing, 26 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  12. 12.In a group of 46 children, 21 play chess, 25 play carrom and 5 play both. How many play only chess?
  13. 13.In a group of 26 children, 18 enjoy drawing, 10 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  14. 14.In a group of 23 grown-ups, 8 drink tea, 11 drink coffee and 2 drink both. How many drink only tea?
  15. 15.In a group of 45 children, 17 play cricket, 25 play football and 6 play both. How many play neither of the two?
  16. 16.In a group of 32 children, 20 play cricket, 8 play football and 3 play both. How many play neither of the two?
  17. 17.In a group of 37 children, 11 enjoy drawing, 24 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  18. 18.In a group of 22 children, 11 like mangoes, 7 like bananas and 4 like both. How many like only mangoes?
  19. 19.In a group of 40 children, 22 play cricket, 8 play football and 2 play both. How many play neither of the two?
  20. 20.In a group of 38 children, 26 like mangoes, 14 like bananas and 9 like both. How many like only mangoes?
  21. 21.In a group of 42 children, 20 play chess, 27 play carrom and 12 play both. How many play exactly one of the two?
  22. 22.In a group of 39 children, 20 sing Hindi songs, 21 sing English songs and 6 sing both. How many sing only Hindi songs?
  23. 23.In a group of 24 children, 9 enjoy drawing, 13 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  24. 24.In a group of 32 children, 12 like mangoes, 16 like bananas and 7 like both. How many like neither of the two?
  25. 25.In a group of 51 children, 25 play chess, 22 play carrom and 6 play both. How many play exactly one of the two?
  26. 26.In a group of 37 children, 23 like mangoes, 13 like bananas and 7 like both. How many like only bananas?
  27. 27.In a group of 33 children, 19 enjoy drawing, 14 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  28. 28.In a group of 34 children, 15 play cricket, 25 play football and 8 play both. How many play only cricket?
  29. 29.In a group of 38 children, 24 like mangoes, 16 like bananas and 11 like both. How many like neither of the two?
  30. 30.In a group of 32 children, 12 play cricket, 21 play football and 8 play both. How many play only cricket?
  31. 31.In a group of 47 children, 25 play chess, 20 play carrom and 5 play both. How many play neither of the two?
  32. 32.In a group of 52 children, 24 play cricket, 25 play football and 8 play both. How many play neither of the two?
  33. 33.In a group of 30 children, 13 play cricket, 7 play football and 3 play both. How many play only cricket?
  34. 34.In a group of 39 children, 8 play chess, 21 play carrom and 3 play both. How many play at least one of the two?
  35. 35.In a group of 49 children, 28 enjoy drawing, 29 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  36. 36.In a group of 30 children, 13 play chess, 15 play carrom and 5 play both. How many play exactly one of the two?
  37. 37.In a group of 27 children, 13 sing Hindi songs, 17 sing English songs and 5 sing both. How many sing only Hindi songs?
  38. 38.In a group of 42 children, 21 like mangoes, 20 like bananas and 5 like both. How many like exactly one of the two?
  39. 39.In a group of 43 children, 15 sing Hindi songs, 27 sing English songs and 9 sing both. How many sing only English songs?
  40. 40.In a group of 45 children, 28 sing Hindi songs, 23 sing English songs and 12 sing both. How many sing at least one of the two?

Answer key

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

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