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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 116 · 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 49 children, 25 play chess, 26 play carrom and 11 play both. How many play neither of the two?
  2. 2.In a group of 37 children, 23 play chess, 14 play carrom and 4 play both. How many play only chess?
  3. 3.In a group of 38 grown-ups, 9 drink tea, 21 drink coffee and 3 drink both. How many drink neither of the two?
  4. 4.In a group of 32 children, 14 play cricket, 13 play football and 2 play both. How many play at least one of the two?
  5. 5.In a group of 38 grown-ups, 26 drink tea, 20 drink coffee and 11 drink both. How many drink neither of the two?
  6. 6.In a group of 48 children, 20 enjoy drawing, 20 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  7. 7.In a group of 34 children, 23 play chess, 6 play carrom and 3 play both. How many play at least one of the two?
  8. 8.In a group of 37 children, 23 play cricket, 21 play football and 11 play both. How many play exactly one of the two?
  9. 9.In a group of 27 children, 16 play cricket, 13 play football and 3 play both. How many play at least one of the two?
  10. 10.In a group of 32 children, 20 play chess, 10 play carrom and 2 play both. How many play only carrom?
  11. 11.In a group of 20 children, 9 enjoy drawing, 11 enjoy dancing and 5 enjoy both. How many enjoy at least one of the two?
  12. 12.In a group of 29 children, 11 sing Hindi songs, 14 sing English songs and 8 sing both. How many sing only Hindi songs?
  13. 13.In a group of 37 children, 18 enjoy drawing, 25 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  14. 14.In a group of 31 children, 21 play cricket, 16 play football and 9 play both. How many play neither of the two?
  15. 15.In a group of 48 children, 21 sing Hindi songs, 22 sing English songs and 7 sing both. How many sing at least one of the two?
  16. 16.In a group of 25 grown-ups, 16 drink tea, 10 drink coffee and 6 drink both. How many drink only tea?
  17. 17.In a group of 41 children, 25 sing Hindi songs, 15 sing English songs and 5 sing both. How many sing at least one of the two?
  18. 18.In a group of 28 grown-ups, 19 drink tea, 8 drink coffee and 4 drink both. How many drink only coffee?
  19. 19.In a group of 31 children, 18 sing Hindi songs, 12 sing English songs and 2 sing both. How many sing exactly one of the two?
  20. 20.In a group of 34 children, 14 like mangoes, 23 like bananas and 5 like both. How many like only bananas?
  21. 21.In a group of 44 children, 15 sing Hindi songs, 29 sing English songs and 12 sing both. How many sing neither of the two?
  22. 22.In a group of 34 children, 9 play chess, 13 play carrom and 2 play both. How many play exactly one of the two?
  23. 23.In a group of 33 children, 27 like mangoes, 13 like bananas and 8 like both. How many like only bananas?
  24. 24.In a group of 42 children, 16 sing Hindi songs, 19 sing English songs and 2 sing both. How many sing only Hindi songs?
  25. 25.In a group of 28 children, 9 play chess, 14 play carrom and 6 play both. How many play only chess?
  26. 26.In a group of 31 children, 13 sing Hindi songs, 17 sing English songs and 2 sing both. How many sing only Hindi songs?
  27. 27.In a group of 34 children, 22 like mangoes, 10 like bananas and 4 like both. How many like at least one of the two?
  28. 28.In a group of 41 children, 17 play cricket, 24 play football and 11 play both. How many play at least one of the two?
  29. 29.In a group of 29 grown-ups, 18 drink tea, 14 drink coffee and 5 drink both. How many drink only tea?
  30. 30.In a group of 51 children, 19 like mangoes, 20 like bananas and 2 like both. How many like exactly one of the two?
  31. 31.In a group of 47 children, 21 enjoy drawing, 18 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  32. 32.In a group of 35 children, 25 play chess, 10 play carrom and 7 play both. How many play neither of the two?
  33. 33.In a group of 30 children, 25 play cricket, 12 play football and 8 play both. How many play only football?
  34. 34.In a group of 39 grown-ups, 13 drink tea, 24 drink coffee and 4 drink both. How many drink neither of the two?
  35. 35.In a group of 33 grown-ups, 24 drink tea, 14 drink coffee and 8 drink both. How many drink at least one of the two?
  36. 36.In a group of 37 children, 23 sing Hindi songs, 15 sing English songs and 3 sing both. How many sing at least one of the two?
  37. 37.In a group of 48 children, 25 sing Hindi songs, 25 sing English songs and 12 sing both. How many sing only Hindi songs?
  38. 38.In a group of 42 children, 16 sing Hindi songs, 17 sing English songs and 4 sing both. How many sing exactly one of the two?
  39. 39.In a group of 43 children, 20 play chess, 21 play carrom and 3 play both. How many play neither of the two?
  40. 40.In a group of 38 children, 17 play cricket, 29 play football and 12 play both. How many play exactly one of the two?

Answer key

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

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