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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 126 · 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, 25 play cricket, 9 play football and 6 play both. How many play neither of the two?
  2. 2.In a group of 40 children, 16 enjoy drawing, 22 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  3. 3.In a group of 48 children, 32 sing Hindi songs, 24 sing English songs and 12 sing both. How many sing only English songs?
  4. 4.In a group of 21 children, 7 play cricket, 13 play football and 4 play both. How many play at least one of the two?
  5. 5.In a group of 41 children, 28 enjoy drawing, 19 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  6. 6.In a group of 42 children, 21 sing Hindi songs, 11 sing English songs and 4 sing both. How many sing at least one of the two?
  7. 7.In a group of 27 children, 9 play cricket, 20 play football and 6 play both. How many play at least one of the two?
  8. 8.In a group of 33 children, 15 play cricket, 15 play football and 12 play both. How many play only football?
  9. 9.In a group of 36 grown-ups, 17 drink tea, 24 drink coffee and 12 drink both. How many drink only coffee?
  10. 10.In a group of 31 children, 19 like mangoes, 17 like bananas and 10 like both. How many like only bananas?
  11. 11.In a group of 36 children, 14 like mangoes, 20 like bananas and 6 like both. How many like only mangoes?
  12. 12.In a group of 38 children, 19 play cricket, 13 play football and 9 play both. How many play only football?
  13. 13.In a group of 30 grown-ups, 24 drink tea, 15 drink coffee and 10 drink both. How many drink at least one of the two?
  14. 14.In a group of 32 children, 16 like mangoes, 11 like bananas and 5 like both. How many like only bananas?
  15. 15.In a group of 30 children, 22 play cricket, 14 play football and 7 play both. How many play neither of the two?
  16. 16.In a group of 23 children, 13 enjoy drawing, 12 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  17. 17.In a group of 33 children, 12 play cricket, 16 play football and 4 play both. How many play at least one of the two?
  18. 18.In a group of 25 children, 17 play cricket, 8 play football and 2 play both. How many play neither of the two?
  19. 19.In a group of 18 children, 10 play chess, 13 play carrom and 7 play both. How many play exactly one of the two?
  20. 20.In a group of 41 children, 18 like mangoes, 15 like bananas and 4 like both. How many like only mangoes?
  21. 21.In a group of 33 children, 19 play chess, 14 play carrom and 6 play both. How many play at least one of the two?
  22. 22.In a group of 35 grown-ups, 22 drink tea, 10 drink coffee and 3 drink both. How many drink only coffee?
  23. 23.In a group of 49 children, 15 like mangoes, 30 like bananas and 10 like both. How many like exactly one of the two?
  24. 24.In a group of 34 children, 11 play cricket, 25 play football and 7 play both. How many play neither of the two?
  25. 25.In a group of 28 children, 13 play chess, 12 play carrom and 5 play both. How many play exactly one of the two?
  26. 26.In a group of 43 children, 26 play chess, 24 play carrom and 12 play both. How many play at least one of the two?
  27. 27.In a group of 25 children, 6 play chess, 21 play carrom and 3 play both. How many play at least one of the two?
  28. 28.In a group of 18 grown-ups, 8 drink tea, 8 drink coffee and 2 drink both. How many drink at least one of the two?
  29. 29.In a group of 23 grown-ups, 16 drink tea, 5 drink coffee and 2 drink both. How many drink only coffee?
  30. 30.In a group of 28 children, 6 like mangoes, 17 like bananas and 3 like both. How many like exactly one of the two?
  31. 31.In a group of 39 children, 22 play cricket, 15 play football and 8 play both. How many play only cricket?
  32. 32.In a group of 36 children, 16 play cricket, 22 play football and 5 play both. How many play at least one of the two?
  33. 33.In a group of 31 children, 23 play cricket, 14 play football and 11 play both. How many play only cricket?
  34. 34.In a group of 54 children, 25 play chess, 23 play carrom and 9 play both. How many play at least one of the two?
  35. 35.In a group of 40 children, 24 enjoy drawing, 23 enjoy dancing and 10 enjoy both. How many enjoy at least one of the two?
  36. 36.In a group of 25 children, 14 like mangoes, 14 like bananas and 8 like both. How many like exactly one of the two?
  37. 37.In a group of 24 children, 6 like mangoes, 16 like bananas and 3 like both. How many like only mangoes?
  38. 38.In a group of 56 grown-ups, 28 drink tea, 24 drink coffee and 11 drink both. How many drink neither of the two?
  39. 39.In a group of 41 children, 28 enjoy drawing, 16 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  40. 40.In a group of 57 children, 25 sing Hindi songs, 25 sing English songs and 5 sing both. How many sing at least one of the two?

Answer key

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

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