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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 365 · 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 35 grown-ups, 18 drink tea, 13 drink coffee and 4 drink both. How many drink at least one of the two?
  2. 2.In a group of 37 children, 19 play chess, 13 play carrom and 10 play both. How many play exactly one of the two?
  3. 3.In a group of 22 children, 8 sing Hindi songs, 14 sing English songs and 4 sing both. How many sing exactly one of the two?
  4. 4.In a group of 57 children, 25 play chess, 32 play carrom and 12 play both. How many play at least one of the two?
  5. 5.In a group of 64 children, 30 sing Hindi songs, 30 sing English songs and 11 sing both. How many sing only English songs?
  6. 6.In a group of 19 children, 10 enjoy drawing, 9 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  7. 7.In a group of 33 grown-ups, 10 drink tea, 17 drink coffee and 3 drink both. How many drink only coffee?
  8. 8.In a group of 22 children, 5 play chess, 5 play carrom and 2 play both. How many play only chess?
  9. 9.In a group of 37 children, 18 play cricket, 17 play football and 7 play both. How many play only cricket?
  10. 10.In a group of 42 children, 17 play cricket, 20 play football and 8 play both. How many play only football?
  11. 11.In a group of 43 grown-ups, 16 drink tea, 24 drink coffee and 4 drink both. How many drink only coffee?
  12. 12.In a group of 34 children, 16 like mangoes, 20 like bananas and 7 like both. How many like at least one of the two?
  13. 13.In a group of 40 children, 29 play chess, 15 play carrom and 10 play both. How many play only chess?
  14. 14.In a group of 23 children, 15 sing Hindi songs, 11 sing English songs and 8 sing both. How many sing at least one of the two?
  15. 15.In a group of 50 children, 15 play cricket, 24 play football and 4 play both. How many play only football?
  16. 16.In a group of 33 children, 15 like mangoes, 22 like bananas and 12 like both. How many like only mangoes?
  17. 17.In a group of 39 grown-ups, 30 drink tea, 15 drink coffee and 11 drink both. How many drink at least one of the two?
  18. 18.In a group of 25 children, 17 play cricket, 15 play football and 12 play both. How many play neither of the two?
  19. 19.In a group of 35 children, 29 like mangoes, 14 like bananas and 11 like both. How many like only bananas?
  20. 20.In a group of 47 children, 16 like mangoes, 21 like bananas and 3 like both. How many like only bananas?
  21. 21.In a group of 46 children, 20 play cricket, 18 play football and 6 play both. How many play neither of the two?
  22. 22.In a group of 32 children, 5 play cricket, 20 play football and 2 play both. How many play exactly one of the two?
  23. 23.In a group of 27 children, 14 play chess, 9 play carrom and 5 play both. How many play only chess?
  24. 24.In a group of 24 children, 15 play chess, 7 play carrom and 4 play both. How many play only carrom?
  25. 25.In a group of 49 children, 17 enjoy drawing, 30 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  26. 26.In a group of 40 children, 15 play cricket, 16 play football and 5 play both. How many play neither of the two?
  27. 27.In a group of 35 grown-ups, 15 drink tea, 20 drink coffee and 10 drink both. How many drink exactly one of the two?
  28. 28.In a group of 51 children, 24 sing Hindi songs, 26 sing English songs and 11 sing both. How many sing only English songs?
  29. 29.In a group of 34 children, 12 play cricket, 10 play football and 2 play both. How many play neither of the two?
  30. 30.In a group of 49 children, 22 enjoy drawing, 17 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  31. 31.In a group of 31 children, 7 like mangoes, 14 like bananas and 4 like both. How many like neither of the two?
  32. 32.In a group of 41 children, 29 play chess, 17 play carrom and 11 play both. How many play neither of the two?
  33. 33.In a group of 24 children, 15 like mangoes, 15 like bananas and 9 like both. How many like neither of the two?
  34. 34.In a group of 37 children, 17 play chess, 20 play carrom and 2 play both. How many play only carrom?
  35. 35.In a group of 41 children, 29 play cricket, 14 play football and 10 play both. How many play only football?
  36. 36.In a group of 45 children, 20 sing Hindi songs, 22 sing English songs and 4 sing both. How many sing only Hindi songs?
  37. 37.In a group of 40 children, 19 play cricket, 13 play football and 3 play both. How many play only cricket?
  38. 38.In a group of 42 children, 20 sing Hindi songs, 31 sing English songs and 11 sing both. How many sing only Hindi songs?
  39. 39.In a group of 42 children, 20 enjoy drawing, 21 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  40. 40.In a group of 24 children, 10 enjoy drawing, 8 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?

Answer key

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

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