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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 542 · 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 24 grown-ups, 5 drink tea, 11 drink coffee and 2 drink both. How many drink at least one of the two?
  2. 2.In a group of 26 children, 12 play chess, 12 play carrom and 8 play both. How many play neither of the two?
  3. 3.In a group of 38 children, 15 like mangoes, 18 like bananas and 5 like both. How many like at least one of the two?
  4. 4.In a group of 39 children, 16 sing Hindi songs, 31 sing English songs and 12 sing both. How many sing only English songs?
  5. 5.In a group of 43 children, 17 like mangoes, 28 like bananas and 8 like both. How many like at least one of the two?
  6. 6.In a group of 40 children, 29 like mangoes, 17 like bananas and 11 like both. How many like exactly one of the two?
  7. 7.In a group of 22 children, 14 enjoy drawing, 12 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  8. 8.In a group of 52 children, 29 enjoy drawing, 22 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  9. 9.In a group of 23 children, 7 play chess, 10 play carrom and 2 play both. How many play only chess?
  10. 10.In a group of 29 grown-ups, 11 drink tea, 14 drink coffee and 6 drink both. How many drink only coffee?
  11. 11.In a group of 41 children, 18 enjoy drawing, 24 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  12. 12.In a group of 49 grown-ups, 23 drink tea, 26 drink coffee and 11 drink both. How many drink neither of the two?
  13. 13.In a group of 21 children, 9 enjoy drawing, 13 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  14. 14.In a group of 34 children, 16 play cricket, 22 play football and 7 play both. How many play at least one of the two?
  15. 15.In a group of 39 children, 15 enjoy drawing, 16 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  16. 16.In a group of 41 children, 11 sing Hindi songs, 23 sing English songs and 3 sing both. How many sing only English songs?
  17. 17.In a group of 38 children, 18 like mangoes, 13 like bananas and 6 like both. How many like only mangoes?
  18. 18.In a group of 29 children, 17 play cricket, 13 play football and 9 play both. How many play exactly one of the two?
  19. 19.In a group of 46 grown-ups, 22 drink tea, 15 drink coffee and 2 drink both. How many drink only tea?
  20. 20.In a group of 36 children, 21 enjoy drawing, 11 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  21. 21.In a group of 40 children, 25 enjoy drawing, 18 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  22. 22.In a group of 31 grown-ups, 12 drink tea, 27 drink coffee and 9 drink both. How many drink only tea?
  23. 23.In a group of 49 grown-ups, 28 drink tea, 27 drink coffee and 12 drink both. How many drink only tea?
  24. 24.In a group of 34 grown-ups, 21 drink tea, 14 drink coffee and 9 drink both. How many drink neither of the two?
  25. 25.In a group of 27 children, 18 play cricket, 15 play football and 9 play both. How many play at least one of the two?
  26. 26.In a group of 27 children, 12 play cricket, 8 play football and 5 play both. How many play only football?
  27. 27.In a group of 34 children, 20 enjoy drawing, 11 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  28. 28.In a group of 35 children, 15 sing Hindi songs, 15 sing English songs and 8 sing both. How many sing only Hindi songs?
  29. 29.In a group of 23 children, 17 play cricket, 12 play football and 8 play both. How many play exactly one of the two?
  30. 30.In a group of 41 children, 23 play chess, 26 play carrom and 11 play both. How many play neither of the two?
  31. 31.In a group of 43 children, 26 sing Hindi songs, 23 sing English songs and 10 sing both. How many sing only Hindi songs?
  32. 32.In a group of 45 children, 19 play cricket, 20 play football and 9 play both. How many play neither of the two?
  33. 33.In a group of 42 children, 25 play cricket, 19 play football and 5 play both. How many play neither of the two?
  34. 34.In a group of 22 children, 14 play chess, 17 play carrom and 10 play both. How many play at least one of the two?
  35. 35.In a group of 33 children, 11 enjoy drawing, 12 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  36. 36.In a group of 51 children, 19 sing Hindi songs, 26 sing English songs and 8 sing both. How many sing only English songs?
  37. 37.In a group of 37 grown-ups, 14 drink tea, 26 drink coffee and 8 drink both. How many drink exactly one of the two?
  38. 38.In a group of 28 children, 15 enjoy drawing, 11 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  39. 39.In a group of 25 children, 16 play chess, 16 play carrom and 8 play both. How many play exactly one of the two?
  40. 40.In a group of 51 children, 21 sing Hindi songs, 28 sing English songs and 9 sing both. How many sing at least one of the two?

Answer key

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

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