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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 395 · 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 37 children, 14 play cricket, 30 play football and 10 play both. How many play exactly one of the two?
  2. 2.In a group of 37 children, 21 like mangoes, 14 like bananas and 8 like both. How many like only bananas?
  3. 3.In a group of 42 children, 31 enjoy drawing, 18 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  4. 4.In a group of 26 children, 9 sing Hindi songs, 12 sing English songs and 3 sing both. How many sing exactly one of the two?
  5. 5.In a group of 37 children, 21 play chess, 13 play carrom and 9 play both. How many play only chess?
  6. 6.In a group of 49 children, 21 enjoy drawing, 21 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  7. 7.In a group of 32 children, 7 like mangoes, 16 like bananas and 4 like both. How many like only bananas?
  8. 8.In a group of 32 children, 12 enjoy drawing, 12 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  9. 9.In a group of 44 children, 18 like mangoes, 21 like bananas and 5 like both. How many like only mangoes?
  10. 10.In a group of 22 children, 11 play chess, 11 play carrom and 8 play both. How many play only chess?
  11. 11.In a group of 36 children, 15 enjoy drawing, 27 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  12. 12.In a group of 32 children, 21 like mangoes, 7 like bananas and 2 like both. How many like only mangoes?
  13. 13.In a group of 40 children, 14 like mangoes, 20 like bananas and 9 like both. How many like neither of the two?
  14. 14.In a group of 47 grown-ups, 25 drink tea, 31 drink coffee and 12 drink both. How many drink at least one of the two?
  15. 15.In a group of 36 children, 21 sing Hindi songs, 10 sing English songs and 5 sing both. How many sing only English songs?
  16. 16.In a group of 32 children, 17 enjoy drawing, 14 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  17. 17.In a group of 15 children, 8 play cricket, 11 play football and 5 play both. How many play only cricket?
  18. 18.In a group of 42 children, 24 sing Hindi songs, 19 sing English songs and 6 sing both. How many sing neither of the two?
  19. 19.In a group of 43 children, 19 enjoy drawing, 17 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  20. 20.In a group of 29 children, 20 play cricket, 10 play football and 3 play both. How many play only cricket?
  21. 21.In a group of 38 children, 20 play chess, 18 play carrom and 12 play both. How many play only chess?
  22. 22.In a group of 31 children, 11 sing Hindi songs, 17 sing English songs and 4 sing both. How many sing at least one of the two?
  23. 23.In a group of 31 children, 7 play cricket, 19 play football and 2 play both. How many play neither of the two?
  24. 24.In a group of 29 children, 16 play cricket, 16 play football and 10 play both. How many play at least one of the two?
  25. 25.In a group of 39 children, 14 play cricket, 23 play football and 3 play both. How many play neither of the two?
  26. 26.In a group of 15 grown-ups, 9 drink tea, 9 drink coffee and 5 drink both. How many drink only coffee?
  27. 27.In a group of 31 children, 11 like mangoes, 14 like bananas and 6 like both. How many like exactly one of the two?
  28. 28.In a group of 37 children, 13 sing Hindi songs, 25 sing English songs and 6 sing both. How many sing neither of the two?
  29. 29.In a group of 36 children, 18 enjoy drawing, 17 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  30. 30.In a group of 47 children, 20 enjoy drawing, 19 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  31. 31.In a group of 33 grown-ups, 12 drink tea, 21 drink coffee and 6 drink both. How many drink only tea?
  32. 32.In a group of 27 children, 9 play chess, 21 play carrom and 5 play both. How many play exactly one of the two?
  33. 33.In a group of 36 children, 6 like mangoes, 20 like bananas and 2 like both. How many like exactly one of the two?
  34. 34.In a group of 28 children, 20 play cricket, 5 play football and 2 play both. How many play exactly one of the two?
  35. 35.In a group of 35 children, 12 like mangoes, 24 like bananas and 7 like both. How many like at least one of the two?
  36. 36.In a group of 24 children, 9 enjoy drawing, 14 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  37. 37.In a group of 40 children, 27 sing Hindi songs, 14 sing English songs and 10 sing both. How many sing only Hindi songs?
  38. 38.In a group of 29 children, 10 sing Hindi songs, 19 sing English songs and 4 sing both. How many sing only Hindi songs?
  39. 39.In a group of 44 children, 19 like mangoes, 22 like bananas and 11 like both. How many like neither of the two?
  40. 40.In a group of 30 children, 12 play chess, 10 play carrom and 2 play both. How many play neither of the two?

Answer key

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

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