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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 584 · 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 54 children, 32 enjoy drawing, 27 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  2. 2.In a group of 47 grown-ups, 25 drink tea, 13 drink coffee and 5 drink both. How many drink exactly one of the two?
  3. 3.In a group of 48 children, 21 play chess, 19 play carrom and 3 play both. How many play neither of the two?
  4. 4.In a group of 42 children, 23 enjoy drawing, 14 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  5. 5.In a group of 30 children, 11 like mangoes, 14 like bananas and 2 like both. How many like only bananas?
  6. 6.In a group of 31 children, 14 play cricket, 9 play football and 5 play both. How many play at least one of the two?
  7. 7.In a group of 26 children, 10 enjoy drawing, 8 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  8. 8.In a group of 23 children, 11 like mangoes, 8 like bananas and 4 like both. How many like only bananas?
  9. 9.In a group of 27 grown-ups, 11 drink tea, 9 drink coffee and 2 drink both. How many drink only tea?
  10. 10.In a group of 43 children, 17 like mangoes, 20 like bananas and 9 like both. How many like exactly one of the two?
  11. 11.In a group of 16 children, 7 sing Hindi songs, 5 sing English songs and 2 sing both. How many sing neither of the two?
  12. 12.In a group of 56 children, 24 play cricket, 28 play football and 8 play both. How many play exactly one of the two?
  13. 13.In a group of 33 children, 18 enjoy drawing, 12 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  14. 14.In a group of 29 children, 12 play chess, 12 play carrom and 3 play both. How many play only chess?
  15. 15.In a group of 31 children, 19 sing Hindi songs, 12 sing English songs and 2 sing both. How many sing at least one of the two?
  16. 16.In a group of 31 children, 11 play chess, 7 play carrom and 2 play both. How many play neither of the two?
  17. 17.In a group of 31 children, 24 play cricket, 13 play football and 9 play both. How many play only football?
  18. 18.In a group of 32 children, 9 play chess, 17 play carrom and 4 play both. How many play only carrom?
  19. 19.In a group of 15 children, 7 play chess, 7 play carrom and 4 play both. How many play exactly one of the two?
  20. 20.In a group of 36 children, 17 play chess, 19 play carrom and 4 play both. How many play exactly one of the two?
  21. 21.In a group of 55 children, 22 sing Hindi songs, 20 sing English songs and 2 sing both. How many sing only Hindi songs?
  22. 22.In a group of 39 children, 13 enjoy drawing, 21 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  23. 23.In a group of 43 children, 29 play cricket, 12 play football and 9 play both. How many play exactly one of the two?
  24. 24.In a group of 35 children, 19 play cricket, 8 play football and 2 play both. How many play only football?
  25. 25.In a group of 37 children, 15 sing Hindi songs, 16 sing English songs and 3 sing both. How many sing only Hindi songs?
  26. 26.In a group of 18 children, 10 play cricket, 7 play football and 4 play both. How many play only football?
  27. 27.In a group of 34 grown-ups, 6 drink tea, 16 drink coffee and 2 drink both. How many drink exactly one of the two?
  28. 28.In a group of 19 children, 9 play chess, 9 play carrom and 4 play both. How many play only carrom?
  29. 29.In a group of 49 children, 17 sing Hindi songs, 31 sing English songs and 12 sing both. How many sing only English songs?
  30. 30.In a group of 46 children, 20 play chess, 26 play carrom and 10 play both. How many play neither of the two?
  31. 31.In a group of 48 children, 14 play cricket, 23 play football and 4 play both. How many play at least one of the two?
  32. 32.In a group of 41 children, 19 like mangoes, 20 like bananas and 10 like both. How many like only bananas?
  33. 33.In a group of 29 children, 8 play chess, 22 play carrom and 5 play both. How many play only chess?
  34. 34.In a group of 36 children, 18 like mangoes, 8 like bananas and 4 like both. How many like only mangoes?
  35. 35.In a group of 42 children, 15 sing Hindi songs, 24 sing English songs and 7 sing both. How many sing only English songs?
  36. 36.In a group of 29 children, 12 enjoy drawing, 14 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  37. 37.In a group of 50 children, 26 play chess, 25 play carrom and 10 play both. How many play at least one of the two?
  38. 38.In a group of 33 children, 16 enjoy drawing, 17 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  39. 39.In a group of 32 children, 10 play chess, 16 play carrom and 7 play both. How many play only chess?
  40. 40.In a group of 32 children, 12 play chess, 22 play carrom and 9 play both. How many play only chess?

Answer key

  1. 20
  2. 28
  3. 11
  4. 21
  5. 12
  6. 18
  7. 6
  8. 4
  9. 9
  10. 19
  11. 6
  12. 36
  13. 10
  14. 9
  15. 29
  16. 15
  17. 4
  18. 13
  19. 6
  20. 28
  21. 20
  22. 30
  23. 23
  24. 6
  25. 12
  26. 3
  27. 18
  28. 5
  29. 19
  30. 10
  31. 33
  32. 10
  33. 3
  34. 14
  35. 17
  36. 10
  37. 41
  38. 7
  39. 3
  40. 3

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