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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 389 · 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 35 children, 17 play cricket, 22 play football and 5 play both. How many play neither of the two?
  2. 2.In a group of 38 children, 15 enjoy drawing, 23 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  3. 3.In a group of 15 children, 6 play cricket, 11 play football and 3 play both. How many play at least one of the two?
  4. 4.In a group of 41 children, 11 play chess, 21 play carrom and 5 play both. How many play at least one of the two?
  5. 5.In a group of 35 children, 19 play chess, 16 play carrom and 12 play both. How many play only carrom?
  6. 6.In a group of 37 children, 12 enjoy drawing, 17 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  7. 7.In a group of 40 children, 17 play chess, 29 play carrom and 10 play both. How many play neither of the two?
  8. 8.In a group of 16 children, 5 enjoy drawing, 9 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  9. 9.In a group of 29 children, 18 play chess, 10 play carrom and 4 play both. How many play at least one of the two?
  10. 10.In a group of 37 children, 20 play chess, 13 play carrom and 5 play both. How many play at least one of the two?
  11. 11.In a group of 42 children, 17 play chess, 28 play carrom and 8 play both. How many play only carrom?
  12. 12.In a group of 46 grown-ups, 22 drink tea, 31 drink coffee and 11 drink both. How many drink at least one of the two?
  13. 13.In a group of 27 grown-ups, 12 drink tea, 15 drink coffee and 2 drink both. How many drink neither of the two?
  14. 14.In a group of 37 children, 22 play cricket, 15 play football and 6 play both. How many play only football?
  15. 15.In a group of 46 children, 25 sing Hindi songs, 32 sing English songs and 12 sing both. How many sing only English songs?
  16. 16.In a group of 44 children, 20 sing Hindi songs, 22 sing English songs and 8 sing both. How many sing only Hindi songs?
  17. 17.In a group of 36 children, 27 like mangoes, 16 like bananas and 11 like both. How many like at least one of the two?
  18. 18.In a group of 32 grown-ups, 8 drink tea, 18 drink coffee and 3 drink both. How many drink at least one of the two?
  19. 19.In a group of 40 grown-ups, 19 drink tea, 26 drink coffee and 7 drink both. How many drink only tea?
  20. 20.In a group of 32 children, 25 enjoy drawing, 16 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  21. 21.In a group of 38 children, 19 like mangoes, 14 like bananas and 4 like both. How many like only mangoes?
  22. 22.In a group of 41 children, 16 play chess, 23 play carrom and 6 play both. How many play only chess?
  23. 23.In a group of 38 children, 22 like mangoes, 13 like bananas and 3 like both. How many like only bananas?
  24. 24.In a group of 36 children, 18 play chess, 28 play carrom and 12 play both. How many play only carrom?
  25. 25.In a group of 32 grown-ups, 19 drink tea, 13 drink coffee and 8 drink both. How many drink only coffee?
  26. 26.In a group of 43 children, 22 enjoy drawing, 18 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  27. 27.In a group of 26 children, 18 sing Hindi songs, 13 sing English songs and 10 sing both. How many sing at least one of the two?
  28. 28.In a group of 24 grown-ups, 13 drink tea, 12 drink coffee and 8 drink both. How many drink only tea?
  29. 29.In a group of 44 children, 25 play cricket, 13 play football and 8 play both. How many play exactly one of the two?
  30. 30.In a group of 32 children, 15 like mangoes, 24 like bananas and 10 like both. How many like only mangoes?
  31. 31.In a group of 55 children, 28 like mangoes, 27 like bananas and 12 like both. How many like only bananas?
  32. 32.In a group of 37 children, 10 like mangoes, 25 like bananas and 5 like both. How many like only mangoes?
  33. 33.In a group of 27 children, 15 enjoy drawing, 22 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  34. 34.In a group of 48 children, 14 play cricket, 24 play football and 5 play both. How many play only football?
  35. 35.In a group of 25 children, 11 sing Hindi songs, 16 sing English songs and 6 sing both. How many sing only English songs?
  36. 36.In a group of 33 children, 9 play cricket, 23 play football and 3 play both. How many play exactly one of the two?
  37. 37.In a group of 26 children, 14 enjoy drawing, 16 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  38. 38.In a group of 38 children, 12 sing Hindi songs, 20 sing English songs and 2 sing both. How many sing at least one of the two?
  39. 39.In a group of 12 children, 8 play chess, 5 play carrom and 2 play both. How many play only carrom?
  40. 40.In a group of 35 children, 15 play cricket, 23 play football and 8 play both. How many play only football?

Answer key

  1. 1
  2. 29
  3. 14
  4. 27
  5. 4
  6. 6
  7. 4
  8. 3
  9. 24
  10. 28
  11. 20
  12. 42
  13. 2
  14. 9
  15. 20
  16. 12
  17. 32
  18. 23
  19. 12
  20. 14
  21. 15
  22. 10
  23. 10
  24. 16
  25. 5
  26. 33
  27. 21
  28. 5
  29. 22
  30. 5
  31. 15
  32. 5
  33. 26
  34. 19
  35. 10
  36. 26
  37. 6
  38. 30
  39. 3
  40. 15

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