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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 183 · 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 21 children, 16 enjoy drawing, 7 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  2. 2.In a group of 24 children, 9 like mangoes, 15 like bananas and 4 like both. How many like neither of the two?
  3. 3.In a group of 48 children, 23 enjoy drawing, 22 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  4. 4.In a group of 24 children, 15 sing Hindi songs, 7 sing English songs and 3 sing both. How many sing neither of the two?
  5. 5.In a group of 28 children, 11 sing Hindi songs, 21 sing English songs and 5 sing both. How many sing at least one of the two?
  6. 6.In a group of 31 children, 17 sing Hindi songs, 14 sing English songs and 7 sing both. How many sing exactly one of the two?
  7. 7.In a group of 30 children, 22 enjoy drawing, 14 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  8. 8.In a group of 32 children, 14 enjoy drawing, 21 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  9. 9.In a group of 44 children, 20 play chess, 23 play carrom and 9 play both. How many play exactly one of the two?
  10. 10.In a group of 19 children, 10 sing Hindi songs, 5 sing English songs and 2 sing both. How many sing only English songs?
  11. 11.In a group of 39 grown-ups, 24 drink tea, 14 drink coffee and 11 drink both. How many drink neither of the two?
  12. 12.In a group of 42 children, 24 sing Hindi songs, 17 sing English songs and 12 sing both. How many sing neither of the two?
  13. 13.In a group of 28 children, 8 like mangoes, 10 like bananas and 4 like both. How many like only mangoes?
  14. 14.In a group of 30 children, 22 play cricket, 14 play football and 11 play both. How many play at least one of the two?
  15. 15.In a group of 28 children, 15 play cricket, 24 play football and 12 play both. How many play exactly one of the two?
  16. 16.In a group of 30 children, 12 play cricket, 18 play football and 2 play both. How many play exactly one of the two?
  17. 17.In a group of 32 children, 21 enjoy drawing, 17 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  18. 18.In a group of 51 children, 19 like mangoes, 19 like bananas and 2 like both. How many like neither of the two?
  19. 19.In a group of 55 children, 26 play cricket, 27 play football and 7 play both. How many play only football?
  20. 20.In a group of 23 children, 17 play cricket, 9 play football and 5 play both. How many play at least one of the two?
  21. 21.In a group of 42 children, 23 play chess, 14 play carrom and 6 play both. How many play at least one of the two?
  22. 22.In a group of 40 children, 24 play chess, 19 play carrom and 11 play both. How many play only chess?
  23. 23.In a group of 26 grown-ups, 9 drink tea, 6 drink coffee and 3 drink both. How many drink neither of the two?
  24. 24.In a group of 26 children, 14 play chess, 13 play carrom and 8 play both. How many play only chess?
  25. 25.In a group of 41 grown-ups, 24 drink tea, 8 drink coffee and 5 drink both. How many drink neither of the two?
  26. 26.In a group of 28 children, 11 like mangoes, 11 like bananas and 8 like both. How many like neither of the two?
  27. 27.In a group of 62 children, 29 play cricket, 28 play football and 9 play both. How many play exactly one of the two?
  28. 28.In a group of 37 children, 27 like mangoes, 12 like bananas and 9 like both. How many like only bananas?
  29. 29.In a group of 43 grown-ups, 13 drink tea, 23 drink coffee and 6 drink both. How many drink exactly one of the two?
  30. 30.In a group of 33 children, 16 play chess, 14 play carrom and 3 play both. How many play at least one of the two?
  31. 31.In a group of 26 children, 7 enjoy drawing, 16 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  32. 32.In a group of 39 children, 16 sing Hindi songs, 23 sing English songs and 5 sing both. How many sing exactly one of the two?
  33. 33.In a group of 38 grown-ups, 16 drink tea, 20 drink coffee and 3 drink both. How many drink only tea?
  34. 34.In a group of 44 children, 13 sing Hindi songs, 25 sing English songs and 7 sing both. How many sing exactly one of the two?
  35. 35.In a group of 41 children, 22 play cricket, 17 play football and 8 play both. How many play only football?
  36. 36.In a group of 34 children, 22 enjoy drawing, 19 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  37. 37.In a group of 42 children, 21 play cricket, 28 play football and 11 play both. How many play only cricket?
  38. 38.In a group of 27 children, 9 play chess, 17 play carrom and 6 play both. How many play neither of the two?
  39. 39.In a group of 24 children, 7 sing Hindi songs, 8 sing English songs and 4 sing both. How many sing exactly one of the two?
  40. 40.In a group of 31 children, 13 enjoy drawing, 15 enjoy dancing and 10 enjoy both. How many enjoy only drawing?

Answer key

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

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