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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 555 · 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 42 children, 24 sing Hindi songs, 11 sing English songs and 8 sing both. How many sing exactly one of the two?
  2. 2.In a group of 38 children, 15 play cricket, 30 play football and 12 play both. How many play exactly one of the two?
  3. 3.In a group of 41 children, 27 enjoy drawing, 13 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  4. 4.In a group of 23 children, 18 play chess, 10 play carrom and 7 play both. How many play exactly one of the two?
  5. 5.In a group of 22 children, 11 play chess, 12 play carrom and 2 play both. How many play neither of the two?
  6. 6.In a group of 43 children, 25 like mangoes, 24 like bananas and 7 like both. How many like only mangoes?
  7. 7.In a group of 34 children, 11 play chess, 16 play carrom and 3 play both. How many play neither of the two?
  8. 8.In a group of 57 children, 25 like mangoes, 30 like bananas and 10 like both. How many like neither of the two?
  9. 9.In a group of 42 grown-ups, 23 drink tea, 9 drink coffee and 3 drink both. How many drink only tea?
  10. 10.In a group of 27 children, 20 sing Hindi songs, 12 sing English songs and 6 sing both. How many sing only Hindi songs?
  11. 11.In a group of 33 children, 15 sing Hindi songs, 15 sing English songs and 4 sing both. How many sing at least one of the two?
  12. 12.In a group of 33 grown-ups, 19 drink tea, 9 drink coffee and 4 drink both. How many drink only coffee?
  13. 13.In a group of 35 children, 17 play chess, 9 play carrom and 5 play both. How many play only carrom?
  14. 14.In a group of 44 grown-ups, 20 drink tea, 22 drink coffee and 12 drink both. How many drink exactly one of the two?
  15. 15.In a group of 31 children, 15 like mangoes, 15 like bananas and 8 like both. How many like only mangoes?
  16. 16.In a group of 44 children, 13 play chess, 25 play carrom and 5 play both. How many play only carrom?
  17. 17.In a group of 36 children, 21 enjoy drawing, 7 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  18. 18.In a group of 41 children, 15 enjoy drawing, 29 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  19. 19.In a group of 31 children, 19 play cricket, 18 play football and 7 play both. How many play at least one of the two?
  20. 20.In a group of 24 children, 17 play chess, 15 play carrom and 12 play both. How many play exactly one of the two?
  21. 21.In a group of 47 children, 28 play cricket, 25 play football and 11 play both. How many play only football?
  22. 22.In a group of 20 children, 11 play cricket, 11 play football and 8 play both. How many play only football?
  23. 23.In a group of 25 children, 19 like mangoes, 16 like bananas and 11 like both. How many like exactly one of the two?
  24. 24.In a group of 43 children, 17 enjoy drawing, 21 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  25. 25.In a group of 34 children, 15 play chess, 11 play carrom and 4 play both. How many play neither of the two?
  26. 26.In a group of 32 grown-ups, 12 drink tea, 17 drink coffee and 5 drink both. How many drink only tea?
  27. 27.In a group of 42 children, 24 sing Hindi songs, 9 sing English songs and 4 sing both. How many sing only English songs?
  28. 28.In a group of 41 children, 16 like mangoes, 19 like bananas and 7 like both. How many like at least one of the two?
  29. 29.In a group of 23 children, 18 enjoy drawing, 6 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  30. 30.In a group of 45 children, 23 like mangoes, 18 like bananas and 7 like both. How many like exactly one of the two?
  31. 31.In a group of 57 children, 32 like mangoes, 28 like bananas and 12 like both. How many like neither of the two?
  32. 32.In a group of 36 grown-ups, 8 drink tea, 20 drink coffee and 3 drink both. How many drink only tea?
  33. 33.In a group of 45 grown-ups, 15 drink tea, 25 drink coffee and 9 drink both. How many drink only tea?
  34. 34.In a group of 51 children, 30 sing Hindi songs, 19 sing English songs and 11 sing both. How many sing only Hindi songs?
  35. 35.In a group of 47 children, 25 enjoy drawing, 18 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  36. 36.In a group of 36 grown-ups, 12 drink tea, 25 drink coffee and 6 drink both. How many drink at least one of the two?
  37. 37.In a group of 26 children, 16 sing Hindi songs, 9 sing English songs and 2 sing both. How many sing exactly one of the two?
  38. 38.In a group of 42 children, 14 sing Hindi songs, 25 sing English songs and 10 sing both. How many sing only English songs?
  39. 39.In a group of 38 children, 16 sing Hindi songs, 22 sing English songs and 11 sing both. How many sing neither of the two?
  40. 40.In a group of 21 grown-ups, 7 drink tea, 12 drink coffee and 3 drink both. How many drink exactly one of the two?

Answer key

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

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