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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 196 · 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, 22 play cricket, 19 play football and 5 play both. How many play only football?
  2. 2.In a group of 44 children, 22 play cricket, 28 play football and 11 play both. How many play at least one of the two?
  3. 3.In a group of 31 children, 16 sing Hindi songs, 11 sing English songs and 7 sing both. How many sing at least one of the two?
  4. 4.In a group of 43 children, 25 like mangoes, 16 like bananas and 7 like both. How many like neither of the two?
  5. 5.In a group of 35 children, 18 play cricket, 10 play football and 3 play both. How many play only cricket?
  6. 6.In a group of 32 children, 14 sing Hindi songs, 22 sing English songs and 5 sing both. How many sing at least one of the two?
  7. 7.In a group of 23 children, 9 play chess, 17 play carrom and 4 play both. How many play neither of the two?
  8. 8.In a group of 42 children, 17 like mangoes, 25 like bananas and 10 like both. How many like exactly one of the two?
  9. 9.In a group of 38 children, 19 play chess, 22 play carrom and 12 play both. How many play only chess?
  10. 10.In a group of 47 children, 17 like mangoes, 26 like bananas and 9 like both. How many like only mangoes?
  11. 11.In a group of 32 children, 7 enjoy drawing, 14 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  12. 12.In a group of 30 children, 23 play cricket, 9 play football and 6 play both. How many play only cricket?
  13. 13.In a group of 36 children, 26 sing Hindi songs, 15 sing English songs and 10 sing both. How many sing at least one of the two?
  14. 14.In a group of 30 children, 14 play cricket, 16 play football and 9 play both. How many play exactly one of the two?
  15. 15.In a group of 43 children, 27 sing Hindi songs, 18 sing English songs and 8 sing both. How many sing exactly one of the two?
  16. 16.In a group of 34 children, 21 enjoy drawing, 6 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  17. 17.In a group of 52 children, 24 like mangoes, 29 like bananas and 9 like both. How many like exactly one of the two?
  18. 18.In a group of 36 grown-ups, 12 drink tea, 25 drink coffee and 5 drink both. How many drink only coffee?
  19. 19.In a group of 36 children, 16 play cricket, 9 play football and 4 play both. How many play only cricket?
  20. 20.In a group of 35 children, 16 like mangoes, 16 like bananas and 2 like both. How many like only mangoes?
  21. 21.In a group of 18 children, 6 enjoy drawing, 11 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  22. 22.In a group of 51 children, 27 enjoy drawing, 27 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  23. 23.In a group of 36 children, 18 like mangoes, 19 like bananas and 11 like both. How many like exactly one of the two?
  24. 24.In a group of 41 grown-ups, 18 drink tea, 31 drink coffee and 11 drink both. How many drink only coffee?
  25. 25.In a group of 37 children, 19 sing Hindi songs, 21 sing English songs and 7 sing both. How many sing exactly one of the two?
  26. 26.In a group of 27 grown-ups, 9 drink tea, 7 drink coffee and 3 drink both. How many drink only tea?
  27. 27.In a group of 40 grown-ups, 12 drink tea, 17 drink coffee and 2 drink both. How many drink only tea?
  28. 28.In a group of 27 children, 16 enjoy drawing, 14 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  29. 29.In a group of 30 children, 17 play cricket, 23 play football and 11 play both. How many play exactly one of the two?
  30. 30.In a group of 38 children, 21 play cricket, 8 play football and 2 play both. How many play exactly one of the two?
  31. 31.In a group of 52 children, 28 like mangoes, 21 like bananas and 11 like both. How many like only mangoes?
  32. 32.In a group of 31 children, 23 play cricket, 7 play football and 4 play both. How many play only cricket?
  33. 33.In a group of 27 children, 15 enjoy drawing, 16 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  34. 34.In a group of 55 children, 26 like mangoes, 25 like bananas and 7 like both. How many like exactly one of the two?
  35. 35.In a group of 33 children, 19 like mangoes, 8 like bananas and 3 like both. How many like only mangoes?
  36. 36.In a group of 31 children, 15 sing Hindi songs, 12 sing English songs and 2 sing both. How many sing only Hindi songs?
  37. 37.In a group of 21 children, 12 like mangoes, 16 like bananas and 9 like both. How many like exactly one of the two?
  38. 38.In a group of 44 children, 24 sing Hindi songs, 29 sing English songs and 12 sing both. How many sing neither of the two?
  39. 39.In a group of 30 grown-ups, 12 drink tea, 8 drink coffee and 2 drink both. How many drink only coffee?
  40. 40.In a group of 44 children, 13 play cricket, 29 play football and 10 play both. How many play neither of the two?

Answer key

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

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