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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 94 · 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 37 children, 18 enjoy drawing, 14 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  2. 2.In a group of 34 grown-ups, 11 drink tea, 16 drink coffee and 7 drink both. How many drink neither of the two?
  3. 3.In a group of 53 children, 20 like mangoes, 29 like bananas and 11 like both. How many like exactly one of the two?
  4. 4.In a group of 39 children, 21 play cricket, 12 play football and 7 play both. How many play neither of the two?
  5. 5.In a group of 21 children, 9 play chess, 16 play carrom and 5 play both. How many play at least one of the two?
  6. 6.In a group of 52 children, 22 play chess, 21 play carrom and 3 play both. How many play only chess?
  7. 7.In a group of 25 children, 8 play cricket, 19 play football and 3 play both. How many play only cricket?
  8. 8.In a group of 46 children, 31 enjoy drawing, 16 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  9. 9.In a group of 46 children, 28 play cricket, 17 play football and 11 play both. How many play neither of the two?
  10. 10.In a group of 31 children, 15 play chess, 24 play carrom and 12 play both. How many play only carrom?
  11. 11.In a group of 31 children, 9 sing Hindi songs, 15 sing English songs and 2 sing both. How many sing only English songs?
  12. 12.In a group of 35 children, 18 play chess, 27 play carrom and 11 play both. How many play at least one of the two?
  13. 13.In a group of 34 children, 21 enjoy drawing, 8 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  14. 14.In a group of 53 children, 25 play chess, 23 play carrom and 5 play both. How many play neither of the two?
  15. 15.In a group of 35 children, 23 enjoy drawing, 20 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  16. 16.In a group of 41 children, 15 sing Hindi songs, 14 sing English songs and 3 sing both. How many sing exactly one of the two?
  17. 17.In a group of 46 children, 16 play cricket, 24 play football and 7 play both. How many play at least one of the two?
  18. 18.In a group of 34 children, 16 play chess, 6 play carrom and 3 play both. How many play exactly one of the two?
  19. 19.In a group of 47 children, 21 like mangoes, 19 like bananas and 2 like both. How many like at least one of the two?
  20. 20.In a group of 36 grown-ups, 17 drink tea, 18 drink coffee and 4 drink both. How many drink exactly one of the two?
  21. 21.In a group of 35 children, 15 play cricket, 16 play football and 10 play both. How many play neither of the two?
  22. 22.In a group of 25 children, 16 sing Hindi songs, 11 sing English songs and 5 sing both. How many sing only English songs?
  23. 23.In a group of 24 children, 6 like mangoes, 16 like bananas and 3 like both. How many like exactly one of the two?
  24. 24.In a group of 47 children, 24 play cricket, 29 play football and 12 play both. How many play at least one of the two?
  25. 25.In a group of 42 children, 21 enjoy drawing, 28 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  26. 26.In a group of 23 children, 7 play cricket, 5 play football and 2 play both. How many play only cricket?
  27. 27.In a group of 45 children, 25 play cricket, 12 play football and 5 play both. How many play at least one of the two?
  28. 28.In a group of 37 grown-ups, 20 drink tea, 27 drink coffee and 11 drink both. How many drink at least one of the two?
  29. 29.In a group of 60 children, 26 enjoy drawing, 28 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  30. 30.In a group of 43 children, 21 play cricket, 19 play football and 8 play both. How many play only football?
  31. 31.In a group of 40 children, 26 play chess, 16 play carrom and 11 play both. How many play exactly one of the two?
  32. 32.In a group of 59 children, 26 play chess, 28 play carrom and 8 play both. How many play neither of the two?
  33. 33.In a group of 51 grown-ups, 18 drink tea, 24 drink coffee and 4 drink both. How many drink only tea?
  34. 34.In a group of 46 children, 30 play chess, 19 play carrom and 12 play both. How many play exactly one of the two?
  35. 35.In a group of 36 grown-ups, 19 drink tea, 17 drink coffee and 3 drink both. How many drink neither of the two?
  36. 36.In a group of 38 children, 15 like mangoes, 21 like bananas and 9 like both. How many like only bananas?
  37. 37.In a group of 35 children, 11 like mangoes, 16 like bananas and 5 like both. How many like neither of the two?
  38. 38.In a group of 33 children, 8 like mangoes, 16 like bananas and 2 like both. How many like at least one of the two?
  39. 39.In a group of 42 children, 19 play cricket, 22 play football and 2 play both. How many play exactly one of the two?
  40. 40.In a group of 46 children, 20 play chess, 17 play carrom and 2 play both. How many play neither of the two?

Answer key

  1. 14
  2. 14
  3. 27
  4. 13
  5. 20
  6. 19
  7. 5
  8. 5
  9. 12
  10. 12
  11. 13
  12. 34
  13. 27
  14. 10
  15. 11
  16. 23
  17. 33
  18. 16
  19. 38
  20. 27
  21. 14
  22. 6
  23. 16
  24. 41
  25. 9
  26. 5
  27. 32
  28. 36
  29. 45
  30. 11
  31. 20
  32. 13
  33. 14
  34. 25
  35. 3
  36. 12
  37. 13
  38. 22
  39. 37
  40. 11

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