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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 188 · 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 16 children, 7 enjoy drawing, 7 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  2. 2.In a group of 32 children, 22 play chess, 7 play carrom and 2 play both. How many play exactly one of the two?
  3. 3.In a group of 40 children, 11 like mangoes, 19 like bananas and 2 like both. How many like neither of the two?
  4. 4.In a group of 41 children, 26 play chess, 16 play carrom and 9 play both. How many play only carrom?
  5. 5.In a group of 46 children, 20 enjoy drawing, 14 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  6. 6.In a group of 55 children, 28 sing Hindi songs, 32 sing English songs and 12 sing both. How many sing at least one of the two?
  7. 7.In a group of 53 children, 31 play cricket, 27 play football and 12 play both. How many play only cricket?
  8. 8.In a group of 43 children, 16 play chess, 25 play carrom and 6 play both. How many play at least one of the two?
  9. 9.In a group of 23 grown-ups, 19 drink tea, 15 drink coffee and 12 drink both. How many drink only tea?
  10. 10.In a group of 31 children, 23 enjoy drawing, 9 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  11. 11.In a group of 37 children, 23 sing Hindi songs, 15 sing English songs and 3 sing both. How many sing neither of the two?
  12. 12.In a group of 30 children, 14 like mangoes, 22 like bananas and 8 like both. How many like only mangoes?
  13. 13.In a group of 33 children, 23 enjoy drawing, 16 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  14. 14.In a group of 44 children, 22 play chess, 12 play carrom and 3 play both. How many play neither of the two?
  15. 15.In a group of 46 children, 21 play chess, 18 play carrom and 7 play both. How many play at least one of the two?
  16. 16.In a group of 43 children, 23 play cricket, 25 play football and 9 play both. How many play neither of the two?
  17. 17.In a group of 51 children, 22 play chess, 21 play carrom and 5 play both. How many play neither of the two?
  18. 18.In a group of 35 children, 15 play cricket, 20 play football and 9 play both. How many play exactly one of the two?
  19. 19.In a group of 46 children, 28 sing Hindi songs, 22 sing English songs and 11 sing both. How many sing only Hindi songs?
  20. 20.In a group of 44 children, 28 enjoy drawing, 11 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  21. 21.In a group of 49 children, 17 like mangoes, 23 like bananas and 5 like both. How many like only bananas?
  22. 22.In a group of 21 grown-ups, 11 drink tea, 14 drink coffee and 6 drink both. How many drink neither of the two?
  23. 23.In a group of 27 children, 6 enjoy drawing, 13 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  24. 24.In a group of 27 children, 13 play chess, 15 play carrom and 8 play both. How many play only chess?
  25. 25.In a group of 31 grown-ups, 14 drink tea, 17 drink coffee and 6 drink both. How many drink at least one of the two?
  26. 26.In a group of 37 children, 20 enjoy drawing, 17 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  27. 27.In a group of 42 children, 20 play cricket, 24 play football and 4 play both. How many play only football?
  28. 28.In a group of 31 children, 15 play chess, 16 play carrom and 10 play both. How many play neither of the two?
  29. 29.In a group of 42 children, 24 sing Hindi songs, 18 sing English songs and 7 sing both. How many sing only English songs?
  30. 30.In a group of 33 grown-ups, 23 drink tea, 17 drink coffee and 11 drink both. How many drink only coffee?
  31. 31.In a group of 29 children, 8 play cricket, 20 play football and 3 play both. How many play at least one of the two?
  32. 32.In a group of 39 children, 15 sing Hindi songs, 19 sing English songs and 7 sing both. How many sing only English songs?
  33. 33.In a group of 37 children, 11 play cricket, 18 play football and 4 play both. How many play only football?
  34. 34.In a group of 32 children, 19 play chess, 17 play carrom and 11 play both. How many play only chess?
  35. 35.In a group of 32 children, 18 play chess, 14 play carrom and 3 play both. How many play only carrom?
  36. 36.In a group of 31 grown-ups, 14 drink tea, 17 drink coffee and 10 drink both. How many drink at least one of the two?
  37. 37.In a group of 42 children, 17 enjoy drawing, 19 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  38. 38.In a group of 37 children, 21 enjoy drawing, 17 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  39. 39.In a group of 30 children, 25 enjoy drawing, 8 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  40. 40.In a group of 35 children, 16 enjoy drawing, 19 enjoy dancing and 11 enjoy both. How many enjoy only drawing?

Answer key

  1. 5
  2. 25
  3. 12
  4. 7
  5. 18
  6. 48
  7. 19
  8. 35
  9. 7
  10. 5
  11. 2
  12. 6
  13. 2
  14. 13
  15. 32
  16. 4
  17. 13
  18. 17
  19. 17
  20. 20
  21. 18
  22. 2
  23. 4
  24. 5
  25. 25
  26. 11
  27. 20
  28. 10
  29. 11
  30. 6
  31. 25
  32. 12
  33. 14
  34. 8
  35. 11
  36. 21
  37. 15
  38. 10
  39. 2
  40. 5

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