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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 169 · 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 38 children, 21 sing Hindi songs, 14 sing English songs and 11 sing both. How many sing neither of the two?
  2. 2.In a group of 30 children, 19 play chess, 19 play carrom and 9 play both. How many play only chess?
  3. 3.In a group of 16 children, 7 play cricket, 9 play football and 2 play both. How many play exactly one of the two?
  4. 4.In a group of 48 children, 26 play cricket, 17 play football and 8 play both. How many play only football?
  5. 5.In a group of 29 children, 19 sing Hindi songs, 12 sing English songs and 5 sing both. How many sing only English songs?
  6. 6.In a group of 43 children, 10 play cricket, 24 play football and 4 play both. How many play neither of the two?
  7. 7.In a group of 36 children, 22 like mangoes, 22 like bananas and 10 like both. How many like at least one of the two?
  8. 8.In a group of 38 grown-ups, 15 drink tea, 22 drink coffee and 2 drink both. How many drink exactly one of the two?
  9. 9.In a group of 39 children, 23 like mangoes, 10 like bananas and 3 like both. How many like only mangoes?
  10. 10.In a group of 42 children, 12 enjoy drawing, 28 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  11. 11.In a group of 45 children, 25 like mangoes, 29 like bananas and 11 like both. How many like at least one of the two?
  12. 12.In a group of 29 children, 21 like mangoes, 18 like bananas and 11 like both. How many like only bananas?
  13. 13.In a group of 27 children, 15 sing Hindi songs, 12 sing English songs and 3 sing both. How many sing only English songs?
  14. 14.In a group of 20 children, 10 like mangoes, 13 like bananas and 7 like both. How many like neither of the two?
  15. 15.In a group of 38 children, 8 play cricket, 22 play football and 4 play both. How many play at least one of the two?
  16. 16.In a group of 22 children, 11 play cricket, 13 play football and 4 play both. How many play only football?
  17. 17.In a group of 26 grown-ups, 21 drink tea, 12 drink coffee and 9 drink both. How many drink at least one of the two?
  18. 18.In a group of 29 children, 8 like mangoes, 15 like bananas and 5 like both. How many like at least one of the two?
  19. 19.In a group of 37 children, 25 sing Hindi songs, 9 sing English songs and 6 sing both. How many sing only English songs?
  20. 20.In a group of 41 children, 17 enjoy drawing, 18 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  21. 21.In a group of 46 grown-ups, 25 drink tea, 24 drink coffee and 11 drink both. How many drink exactly one of the two?
  22. 22.In a group of 39 children, 23 sing Hindi songs, 22 sing English songs and 9 sing both. How many sing neither of the two?
  23. 23.In a group of 30 children, 9 play chess, 15 play carrom and 2 play both. How many play neither of the two?
  24. 24.In a group of 51 children, 21 enjoy drawing, 29 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  25. 25.In a group of 40 children, 28 like mangoes, 20 like bananas and 12 like both. How many like exactly one of the two?
  26. 26.In a group of 24 children, 16 like mangoes, 8 like bananas and 3 like both. How many like only bananas?
  27. 27.In a group of 36 grown-ups, 21 drink tea, 9 drink coffee and 5 drink both. How many drink exactly one of the two?
  28. 28.In a group of 44 children, 18 enjoy drawing, 18 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  29. 29.In a group of 27 children, 9 like mangoes, 13 like bananas and 4 like both. How many like only bananas?
  30. 30.In a group of 37 children, 10 play cricket, 18 play football and 3 play both. How many play exactly one of the two?
  31. 31.In a group of 46 children, 29 play cricket, 26 play football and 11 play both. How many play only football?
  32. 32.In a group of 46 children, 13 sing Hindi songs, 29 sing English songs and 10 sing both. How many sing neither of the two?
  33. 33.In a group of 42 children, 16 enjoy drawing, 28 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  34. 34.In a group of 23 children, 13 play cricket, 9 play football and 5 play both. How many play exactly one of the two?
  35. 35.In a group of 28 children, 18 like mangoes, 20 like bananas and 12 like both. How many like exactly one of the two?
  36. 36.In a group of 30 children, 23 play cricket, 17 play football and 11 play both. How many play exactly one of the two?
  37. 37.In a group of 23 children, 10 play chess, 11 play carrom and 2 play both. How many play neither of the two?
  38. 38.In a group of 39 children, 23 play cricket, 12 play football and 8 play both. How many play only cricket?
  39. 39.In a group of 34 children, 5 play chess, 19 play carrom and 2 play both. How many play only chess?
  40. 40.In a group of 19 children, 12 enjoy drawing, 10 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?

Answer key

  1. 14
  2. 10
  3. 12
  4. 9
  5. 7
  6. 13
  7. 34
  8. 33
  9. 20
  10. 20
  11. 43
  12. 7
  13. 9
  14. 4
  15. 26
  16. 9
  17. 24
  18. 18
  19. 3
  20. 33
  21. 27
  22. 3
  23. 8
  24. 38
  25. 24
  26. 5
  27. 20
  28. 16
  29. 9
  30. 22
  31. 15
  32. 14
  33. 20
  34. 12
  35. 14
  36. 18
  37. 4
  38. 15
  39. 3
  40. 18

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