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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 340 · 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 39 children, 19 enjoy drawing, 19 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  2. 2.In a group of 32 children, 22 like mangoes, 14 like bananas and 7 like both. How many like only bananas?
  3. 3.In a group of 48 children, 30 sing Hindi songs, 27 sing English songs and 10 sing both. How many sing neither of the two?
  4. 4.In a group of 55 children, 22 enjoy drawing, 21 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  5. 5.In a group of 24 children, 15 play chess, 10 play carrom and 6 play both. How many play only carrom?
  6. 6.In a group of 29 children, 11 enjoy drawing, 12 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  7. 7.In a group of 41 children, 16 play cricket, 15 play football and 5 play both. How many play only football?
  8. 8.In a group of 53 children, 32 play chess, 20 play carrom and 12 play both. How many play exactly one of the two?
  9. 9.In a group of 48 children, 23 like mangoes, 24 like bananas and 5 like both. How many like neither of the two?
  10. 10.In a group of 38 children, 22 like mangoes, 16 like bananas and 2 like both. How many like only bananas?
  11. 11.In a group of 28 children, 6 play chess, 16 play carrom and 3 play both. How many play exactly one of the two?
  12. 12.In a group of 39 children, 16 like mangoes, 26 like bananas and 8 like both. How many like neither of the two?
  13. 13.In a group of 25 grown-ups, 13 drink tea, 13 drink coffee and 6 drink both. How many drink neither of the two?
  14. 14.In a group of 44 children, 23 play cricket, 23 play football and 7 play both. How many play neither of the two?
  15. 15.In a group of 52 children, 23 enjoy drawing, 18 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  16. 16.In a group of 39 children, 20 enjoy drawing, 15 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  17. 17.In a group of 41 children, 18 play cricket, 24 play football and 12 play both. How many play neither of the two?
  18. 18.In a group of 30 children, 17 enjoy drawing, 15 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  19. 19.In a group of 40 grown-ups, 27 drink tea, 19 drink coffee and 7 drink both. How many drink at least one of the two?
  20. 20.In a group of 37 children, 24 play chess, 19 play carrom and 10 play both. How many play only chess?
  21. 21.In a group of 32 grown-ups, 18 drink tea, 13 drink coffee and 6 drink both. How many drink only tea?
  22. 22.In a group of 53 children, 24 like mangoes, 23 like bananas and 7 like both. How many like neither of the two?
  23. 23.In a group of 29 children, 22 play chess, 6 play carrom and 2 play both. How many play neither of the two?
  24. 24.In a group of 32 children, 19 play chess, 21 play carrom and 10 play both. How many play exactly one of the two?
  25. 25.In a group of 42 children, 18 like mangoes, 14 like bananas and 4 like both. How many like exactly one of the two?
  26. 26.In a group of 48 children, 23 play cricket, 25 play football and 10 play both. How many play neither of the two?
  27. 27.In a group of 26 children, 15 play chess, 15 play carrom and 7 play both. How many play neither of the two?
  28. 28.In a group of 39 children, 21 like mangoes, 24 like bananas and 12 like both. How many like only mangoes?
  29. 29.In a group of 43 children, 16 enjoy drawing, 18 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  30. 30.In a group of 46 children, 22 sing Hindi songs, 23 sing English songs and 8 sing both. How many sing at least one of the two?
  31. 31.In a group of 39 grown-ups, 14 drink tea, 28 drink coffee and 8 drink both. How many drink neither of the two?
  32. 32.In a group of 23 children, 15 enjoy drawing, 12 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  33. 33.In a group of 42 children, 24 play cricket, 23 play football and 7 play both. How many play only cricket?
  34. 34.In a group of 45 children, 22 like mangoes, 24 like bananas and 4 like both. How many like exactly one of the two?
  35. 35.In a group of 25 children, 13 like mangoes, 10 like bananas and 2 like both. How many like only mangoes?
  36. 36.In a group of 28 children, 21 enjoy drawing, 17 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  37. 37.In a group of 32 children, 22 enjoy drawing, 7 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  38. 38.In a group of 33 children, 25 play cricket, 11 play football and 7 play both. How many play only football?
  39. 39.In a group of 43 grown-ups, 21 drink tea, 26 drink coffee and 7 drink both. How many drink neither of the two?
  40. 40.In a group of 41 children, 18 enjoy drawing, 16 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?

Answer key

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

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