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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 409 · 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 52 children, 29 play cricket, 18 play football and 10 play both. How many play only football?
  2. 2.In a group of 18 children, 8 enjoy drawing, 8 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  3. 3.In a group of 34 children, 14 sing Hindi songs, 16 sing English songs and 7 sing both. How many sing exactly one of the two?
  4. 4.In a group of 44 children, 24 enjoy drawing, 19 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  5. 5.In a group of 34 children, 16 like mangoes, 12 like bananas and 5 like both. How many like only mangoes?
  6. 6.In a group of 39 children, 15 sing Hindi songs, 22 sing English songs and 9 sing both. How many sing only Hindi songs?
  7. 7.In a group of 25 children, 21 enjoy drawing, 10 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  8. 8.In a group of 25 children, 11 sing Hindi songs, 12 sing English songs and 8 sing both. How many sing at least one of the two?
  9. 9.In a group of 37 children, 17 play chess, 21 play carrom and 6 play both. How many play exactly one of the two?
  10. 10.In a group of 24 children, 14 sing Hindi songs, 9 sing English songs and 6 sing both. How many sing at least one of the two?
  11. 11.In a group of 47 children, 14 sing Hindi songs, 28 sing English songs and 8 sing both. How many sing exactly one of the two?
  12. 12.In a group of 18 children, 6 like mangoes, 7 like bananas and 3 like both. How many like neither of the two?
  13. 13.In a group of 40 children, 18 like mangoes, 26 like bananas and 6 like both. How many like only mangoes?
  14. 14.In a group of 44 children, 17 play cricket, 26 play football and 11 play both. How many play exactly one of the two?
  15. 15.In a group of 24 children, 15 play cricket, 19 play football and 11 play both. How many play only football?
  16. 16.In a group of 37 children, 19 play cricket, 20 play football and 4 play both. How many play exactly one of the two?
  17. 17.In a group of 44 children, 14 sing Hindi songs, 20 sing English songs and 3 sing both. How many sing at least one of the two?
  18. 18.In a group of 20 children, 13 sing Hindi songs, 14 sing English songs and 10 sing both. How many sing only Hindi songs?
  19. 19.In a group of 37 children, 15 enjoy drawing, 22 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  20. 20.In a group of 35 children, 15 sing Hindi songs, 26 sing English songs and 11 sing both. How many sing only Hindi songs?
  21. 21.In a group of 31 children, 13 play cricket, 25 play football and 10 play both. How many play neither of the two?
  22. 22.In a group of 37 grown-ups, 15 drink tea, 25 drink coffee and 9 drink both. How many drink only coffee?
  23. 23.In a group of 36 children, 22 play chess, 16 play carrom and 11 play both. How many play only carrom?
  24. 24.In a group of 42 grown-ups, 8 drink tea, 23 drink coffee and 4 drink both. How many drink at least one of the two?
  25. 25.In a group of 32 children, 14 enjoy drawing, 10 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  26. 26.In a group of 40 grown-ups, 28 drink tea, 18 drink coffee and 12 drink both. How many drink at least one of the two?
  27. 27.In a group of 34 children, 22 play cricket, 17 play football and 10 play both. How many play at least one of the two?
  28. 28.In a group of 31 children, 15 enjoy drawing, 14 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  29. 29.In a group of 28 children, 17 play cricket, 15 play football and 8 play both. How many play neither of the two?
  30. 30.In a group of 37 children, 23 sing Hindi songs, 20 sing English songs and 9 sing both. How many sing only English songs?
  31. 31.In a group of 47 grown-ups, 24 drink tea, 27 drink coffee and 8 drink both. How many drink only coffee?
  32. 32.In a group of 43 children, 21 play chess, 28 play carrom and 11 play both. How many play at least one of the two?
  33. 33.In a group of 34 children, 22 play chess, 8 play carrom and 5 play both. How many play at least one of the two?
  34. 34.In a group of 29 children, 16 enjoy drawing, 14 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?
  35. 35.In a group of 33 children, 10 play chess, 20 play carrom and 7 play both. How many play only carrom?
  36. 36.In a group of 35 grown-ups, 28 drink tea, 16 drink coffee and 12 drink both. How many drink neither of the two?
  37. 37.In a group of 26 children, 16 like mangoes, 11 like bananas and 7 like both. How many like only mangoes?
  38. 38.In a group of 34 children, 12 play cricket, 14 play football and 7 play both. How many play only cricket?
  39. 39.In a group of 35 children, 10 play chess, 14 play carrom and 4 play both. How many play exactly one of the two?
  40. 40.In a group of 39 grown-ups, 22 drink tea, 15 drink coffee and 9 drink both. How many drink at least one of the two?

Answer key

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

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