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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 243 · 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 27 grown-ups, 19 drink tea, 11 drink coffee and 6 drink both. How many drink at least one of the two?
  2. 2.In a group of 53 grown-ups, 19 drink tea, 23 drink coffee and 3 drink both. How many drink exactly one of the two?
  3. 3.In a group of 32 children, 21 enjoy drawing, 22 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  4. 4.In a group of 19 children, 9 sing Hindi songs, 7 sing English songs and 3 sing both. How many sing only Hindi songs?
  5. 5.In a group of 32 children, 24 enjoy drawing, 14 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  6. 6.In a group of 55 children, 24 play chess, 29 play carrom and 12 play both. How many play neither of the two?
  7. 7.In a group of 32 children, 19 enjoy drawing, 22 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  8. 8.In a group of 40 children, 13 enjoy drawing, 14 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  9. 9.In a group of 28 grown-ups, 21 drink tea, 10 drink coffee and 7 drink both. How many drink neither of the two?
  10. 10.In a group of 19 grown-ups, 11 drink tea, 13 drink coffee and 6 drink both. How many drink exactly one of the two?
  11. 11.In a group of 25 children, 6 play cricket, 13 play football and 3 play both. How many play only cricket?
  12. 12.In a group of 36 children, 27 enjoy drawing, 16 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  13. 13.In a group of 35 children, 16 like mangoes, 10 like bananas and 3 like both. How many like at least one of the two?
  14. 14.In a group of 40 children, 21 enjoy drawing, 18 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  15. 15.In a group of 50 children, 24 like mangoes, 23 like bananas and 4 like both. How many like only mangoes?
  16. 16.In a group of 35 children, 23 sing Hindi songs, 18 sing English songs and 12 sing both. How many sing neither of the two?
  17. 17.In a group of 27 children, 12 play cricket, 11 play football and 3 play both. How many play only cricket?
  18. 18.In a group of 32 children, 22 enjoy drawing, 14 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  19. 19.In a group of 45 children, 26 play chess, 21 play carrom and 6 play both. How many play neither of the two?
  20. 20.In a group of 53 children, 27 enjoy drawing, 28 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  21. 21.In a group of 55 children, 21 like mangoes, 28 like bananas and 9 like both. How many like only mangoes?
  22. 22.In a group of 28 children, 12 like mangoes, 19 like bananas and 4 like both. How many like only mangoes?
  23. 23.In a group of 44 grown-ups, 19 drink tea, 24 drink coffee and 4 drink both. How many drink neither of the two?
  24. 24.In a group of 30 children, 10 sing Hindi songs, 11 sing English songs and 6 sing both. How many sing only Hindi songs?
  25. 25.In a group of 33 children, 15 enjoy drawing, 22 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  26. 26.In a group of 40 children, 24 enjoy drawing, 20 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  27. 27.In a group of 34 children, 13 like mangoes, 24 like bananas and 8 like both. How many like exactly one of the two?
  28. 28.In a group of 19 children, 9 play chess, 6 play carrom and 3 play both. How many play exactly one of the two?
  29. 29.In a group of 39 grown-ups, 10 drink tea, 24 drink coffee and 4 drink both. How many drink only coffee?
  30. 30.In a group of 38 children, 16 enjoy drawing, 20 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  31. 31.In a group of 41 children, 25 play cricket, 17 play football and 12 play both. How many play exactly one of the two?
  32. 32.In a group of 26 children, 20 play cricket, 12 play football and 8 play both. How many play neither of the two?
  33. 33.In a group of 60 children, 31 enjoy drawing, 31 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  34. 34.In a group of 42 children, 16 enjoy drawing, 22 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  35. 35.In a group of 44 children, 30 play chess, 23 play carrom and 10 play both. How many play at least one of the two?
  36. 36.In a group of 39 children, 13 like mangoes, 26 like bananas and 7 like both. How many like at least one of the two?
  37. 37.In a group of 14 children, 8 like mangoes, 10 like bananas and 5 like both. How many like only mangoes?
  38. 38.In a group of 38 children, 26 play chess, 22 play carrom and 11 play both. How many play neither of the two?
  39. 39.In a group of 34 children, 15 play cricket, 17 play football and 2 play both. How many play only football?
  40. 40.In a group of 26 children, 8 play cricket, 9 play football and 2 play both. How many play at least one of the two?

Answer key

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

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