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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 607 · 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 36 children, 15 like mangoes, 21 like bananas and 9 like both. How many like exactly one of the two?
  2. 2.In a group of 24 children, 16 sing Hindi songs, 19 sing English songs and 12 sing both. How many sing only Hindi songs?
  3. 3.In a group of 30 children, 13 sing Hindi songs, 19 sing English songs and 9 sing both. How many sing only English songs?
  4. 4.In a group of 38 children, 18 play chess, 14 play carrom and 7 play both. How many play neither of the two?
  5. 5.In a group of 41 children, 23 enjoy drawing, 12 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  6. 6.In a group of 27 grown-ups, 15 drink tea, 17 drink coffee and 7 drink both. How many drink only tea?
  7. 7.In a group of 22 children, 18 like mangoes, 8 like bananas and 5 like both. How many like only mangoes?
  8. 8.In a group of 50 grown-ups, 21 drink tea, 25 drink coffee and 5 drink both. How many drink exactly one of the two?
  9. 9.In a group of 34 children, 17 sing Hindi songs, 12 sing English songs and 4 sing both. How many sing only Hindi songs?
  10. 10.In a group of 14 children, 9 play cricket, 9 play football and 5 play both. How many play exactly one of the two?
  11. 11.In a group of 32 children, 7 play chess, 16 play carrom and 3 play both. How many play only carrom?
  12. 12.In a group of 25 children, 19 enjoy drawing, 13 enjoy dancing and 10 enjoy both. How many enjoy at least one of the two?
  13. 13.In a group of 45 children, 19 play cricket, 30 play football and 10 play both. How many play at least one of the two?
  14. 14.In a group of 43 grown-ups, 15 drink tea, 17 drink coffee and 2 drink both. How many drink at least one of the two?
  15. 15.In a group of 27 children, 16 like mangoes, 8 like bananas and 4 like both. How many like only mangoes?
  16. 16.In a group of 47 children, 22 play chess, 23 play carrom and 6 play both. How many play only carrom?
  17. 17.In a group of 44 grown-ups, 21 drink tea, 24 drink coffee and 4 drink both. How many drink only tea?
  18. 18.In a group of 52 children, 24 sing Hindi songs, 27 sing English songs and 10 sing both. How many sing neither of the two?
  19. 19.In a group of 35 children, 29 like mangoes, 14 like bananas and 9 like both. How many like only bananas?
  20. 20.In a group of 34 children, 17 like mangoes, 10 like bananas and 4 like both. How many like at least one of the two?
  21. 21.In a group of 31 children, 13 enjoy drawing, 18 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  22. 22.In a group of 26 children, 21 like mangoes, 8 like bananas and 5 like both. How many like only mangoes?
  23. 23.In a group of 42 children, 18 enjoy drawing, 16 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  24. 24.In a group of 19 children, 14 play cricket, 8 play football and 5 play both. How many play only football?
  25. 25.In a group of 24 children, 13 enjoy drawing, 9 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  26. 26.In a group of 35 children, 12 like mangoes, 19 like bananas and 6 like both. How many like at least one of the two?
  27. 27.In a group of 31 children, 22 play chess, 14 play carrom and 7 play both. How many play neither of the two?
  28. 28.In a group of 31 children, 11 enjoy drawing, 25 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?
  29. 29.In a group of 34 children, 20 sing Hindi songs, 20 sing English songs and 7 sing both. How many sing exactly one of the two?
  30. 30.In a group of 25 children, 14 play cricket, 11 play football and 2 play both. How many play only cricket?
  31. 31.In a group of 30 children, 19 sing Hindi songs, 11 sing English songs and 2 sing both. How many sing only English songs?
  32. 32.In a group of 30 children, 12 play cricket, 24 play football and 7 play both. How many play at least one of the two?
  33. 33.In a group of 36 children, 16 play chess, 9 play carrom and 2 play both. How many play only chess?
  34. 34.In a group of 28 children, 14 enjoy drawing, 15 enjoy dancing and 8 enjoy both. How many enjoy neither of the two?
  35. 35.In a group of 35 children, 24 play cricket, 10 play football and 6 play both. How many play only cricket?
  36. 36.In a group of 35 grown-ups, 14 drink tea, 16 drink coffee and 8 drink both. How many drink at least one of the two?
  37. 37.In a group of 57 children, 24 sing Hindi songs, 31 sing English songs and 12 sing both. How many sing only English songs?
  38. 38.In a group of 25 children, 18 like mangoes, 7 like bananas and 2 like both. How many like only bananas?
  39. 39.In a group of 36 children, 27 play cricket, 16 play football and 10 play both. How many play exactly one of the two?
  40. 40.In a group of 25 children, 13 play cricket, 10 play football and 2 play both. How many play neither of the two?

Answer key

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

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