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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 682 · 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 44 children, 16 sing Hindi songs, 27 sing English songs and 12 sing both. How many sing exactly one of the two?
  2. 2.In a group of 33 children, 18 play chess, 13 play carrom and 5 play both. How many play neither of the two?
  3. 3.In a group of 34 children, 19 play chess, 17 play carrom and 3 play both. How many play only chess?
  4. 4.In a group of 54 children, 23 like mangoes, 25 like bananas and 6 like both. How many like only bananas?
  5. 5.In a group of 33 children, 27 play chess, 15 play carrom and 12 play both. How many play neither of the two?
  6. 6.In a group of 38 children, 16 play chess, 19 play carrom and 12 play both. How many play only chess?
  7. 7.In a group of 32 children, 11 play cricket, 18 play football and 4 play both. How many play only cricket?
  8. 8.In a group of 16 children, 7 enjoy drawing, 10 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  9. 9.In a group of 34 children, 23 enjoy drawing, 14 enjoy dancing and 10 enjoy both. How many enjoy at least one of the two?
  10. 10.In a group of 44 grown-ups, 16 drink tea, 24 drink coffee and 5 drink both. How many drink at least one of the two?
  11. 11.In a group of 49 grown-ups, 19 drink tea, 22 drink coffee and 4 drink both. How many drink only tea?
  12. 12.In a group of 46 children, 16 like mangoes, 18 like bananas and 3 like both. How many like at least one of the two?
  13. 13.In a group of 51 children, 32 sing Hindi songs, 28 sing English songs and 12 sing both. How many sing only Hindi songs?
  14. 14.In a group of 34 children, 9 play chess, 21 play carrom and 4 play both. How many play exactly one of the two?
  15. 15.In a group of 23 children, 16 sing Hindi songs, 11 sing English songs and 7 sing both. How many sing only Hindi songs?
  16. 16.In a group of 30 children, 21 like mangoes, 14 like bananas and 9 like both. How many like only bananas?
  17. 17.In a group of 20 grown-ups, 6 drink tea, 12 drink coffee and 3 drink both. How many drink only coffee?
  18. 18.In a group of 35 grown-ups, 21 drink tea, 16 drink coffee and 10 drink both. How many drink only tea?
  19. 19.In a group of 32 children, 21 sing Hindi songs, 19 sing English songs and 12 sing both. How many sing only English songs?
  20. 20.In a group of 32 children, 23 enjoy drawing, 15 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  21. 21.In a group of 36 children, 18 play chess, 11 play carrom and 8 play both. How many play neither of the two?
  22. 22.In a group of 26 children, 10 play cricket, 15 play football and 2 play both. How many play neither of the two?
  23. 23.In a group of 29 children, 5 sing Hindi songs, 15 sing English songs and 2 sing both. How many sing at least one of the two?
  24. 24.In a group of 24 children, 5 sing Hindi songs, 9 sing English songs and 2 sing both. How many sing at least one of the two?
  25. 25.In a group of 35 children, 15 play cricket, 11 play football and 3 play both. How many play neither of the two?
  26. 26.In a group of 43 children, 17 like mangoes, 22 like bananas and 6 like both. How many like at least one of the two?
  27. 27.In a group of 44 children, 24 enjoy drawing, 23 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  28. 28.In a group of 31 children, 18 enjoy drawing, 14 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  29. 29.In a group of 28 children, 16 enjoy drawing, 22 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  30. 30.In a group of 36 children, 11 enjoy drawing, 22 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  31. 31.In a group of 47 children, 29 like mangoes, 26 like bananas and 10 like both. How many like only mangoes?
  32. 32.In a group of 34 children, 19 sing Hindi songs, 16 sing English songs and 12 sing both. How many sing at least one of the two?
  33. 33.In a group of 40 grown-ups, 19 drink tea, 18 drink coffee and 9 drink both. How many drink exactly one of the two?
  34. 34.In a group of 48 children, 19 enjoy drawing, 31 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  35. 35.In a group of 44 grown-ups, 27 drink tea, 14 drink coffee and 9 drink both. How many drink at least one of the two?
  36. 36.In a group of 37 children, 7 sing Hindi songs, 20 sing English songs and 2 sing both. How many sing only Hindi songs?
  37. 37.In a group of 43 children, 12 enjoy drawing, 24 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  38. 38.In a group of 34 children, 9 play chess, 13 play carrom and 3 play both. How many play at least one of the two?
  39. 39.In a group of 47 children, 29 like mangoes, 26 like bananas and 10 like both. How many like at least one of the two?
  40. 40.In a group of 53 children, 26 play chess, 28 play carrom and 11 play both. How many play only chess?

Answer key

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

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