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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 16 · 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 50 children, 28 play cricket, 27 play football and 11 play both. How many play exactly one of the two?
  2. 2.In a group of 35 grown-ups, 12 drink tea, 20 drink coffee and 8 drink both. How many drink only tea?
  3. 3.In a group of 35 children, 9 sing Hindi songs, 24 sing English songs and 6 sing both. How many sing exactly one of the two?
  4. 4.In a group of 40 children, 17 play cricket, 24 play football and 12 play both. How many play only cricket?
  5. 5.In a group of 42 children, 28 play cricket, 20 play football and 11 play both. How many play neither of the two?
  6. 6.In a group of 38 children, 13 play chess, 17 play carrom and 6 play both. How many play only chess?
  7. 7.In a group of 20 children, 14 play cricket, 10 play football and 7 play both. How many play only football?
  8. 8.In a group of 31 grown-ups, 10 drink tea, 8 drink coffee and 2 drink both. How many drink neither of the two?
  9. 9.In a group of 50 children, 19 sing Hindi songs, 20 sing English songs and 3 sing both. How many sing exactly one of the two?
  10. 10.In a group of 23 children, 11 sing Hindi songs, 6 sing English songs and 3 sing both. How many sing neither of the two?
  11. 11.In a group of 40 children, 10 sing Hindi songs, 27 sing English songs and 7 sing both. How many sing neither of the two?
  12. 12.In a group of 43 children, 23 enjoy drawing, 18 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  13. 13.In a group of 26 children, 15 like mangoes, 9 like bananas and 5 like both. How many like only mangoes?
  14. 14.In a group of 27 children, 12 like mangoes, 9 like bananas and 3 like both. How many like only mangoes?
  15. 15.In a group of 44 children, 16 enjoy drawing, 21 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  16. 16.In a group of 59 children, 27 sing Hindi songs, 27 sing English songs and 10 sing both. How many sing only Hindi songs?
  17. 17.In a group of 49 children, 25 sing Hindi songs, 22 sing English songs and 9 sing both. How many sing exactly one of the two?
  18. 18.In a group of 53 children, 20 play chess, 26 play carrom and 8 play both. How many play neither of the two?
  19. 19.In a group of 36 children, 22 like mangoes, 21 like bananas and 9 like both. How many like only bananas?
  20. 20.In a group of 37 children, 19 play cricket, 16 play football and 3 play both. How many play neither of the two?
  21. 21.In a group of 39 children, 18 like mangoes, 18 like bananas and 12 like both. How many like at least one of the two?
  22. 22.In a group of 51 children, 28 play cricket, 28 play football and 12 play both. How many play at least one of the two?
  23. 23.In a group of 32 children, 12 play cricket, 10 play football and 5 play both. How many play only cricket?
  24. 24.In a group of 36 children, 13 like mangoes, 24 like bananas and 10 like both. How many like at least one of the two?
  25. 25.In a group of 45 children, 23 play chess, 24 play carrom and 7 play both. How many play exactly one of the two?
  26. 26.In a group of 32 grown-ups, 20 drink tea, 13 drink coffee and 6 drink both. How many drink at least one of the two?
  27. 27.In a group of 42 children, 15 like mangoes, 15 like bananas and 3 like both. How many like exactly one of the two?
  28. 28.In a group of 37 children, 14 like mangoes, 20 like bananas and 7 like both. How many like only mangoes?
  29. 29.In a group of 49 children, 20 play cricket, 28 play football and 12 play both. How many play neither of the two?
  30. 30.In a group of 37 children, 20 play chess, 15 play carrom and 4 play both. How many play at least one of the two?
  31. 31.In a group of 43 children, 14 enjoy drawing, 20 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  32. 32.In a group of 46 children, 17 enjoy drawing, 32 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  33. 33.In a group of 25 children, 8 play cricket, 20 play football and 5 play both. How many play only cricket?
  34. 34.In a group of 38 grown-ups, 27 drink tea, 17 drink coffee and 10 drink both. How many drink at least one of the two?
  35. 35.In a group of 42 children, 13 play chess, 24 play carrom and 6 play both. How many play at least one of the two?
  36. 36.In a group of 39 children, 24 sing Hindi songs, 10 sing English songs and 7 sing both. How many sing neither of the two?
  37. 37.In a group of 32 children, 25 like mangoes, 14 like bananas and 9 like both. How many like at least one of the two?
  38. 38.In a group of 41 children, 22 like mangoes, 14 like bananas and 2 like both. How many like neither of the two?
  39. 39.In a group of 38 children, 23 play chess, 24 play carrom and 12 play both. How many play exactly one of the two?
  40. 40.In a group of 43 children, 25 sing Hindi songs, 23 sing English songs and 10 sing both. How many sing at least one of the two?

Answer key

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

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