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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 578 · 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 31 children, 20 play chess, 19 play carrom and 12 play both. How many play exactly one of the two?
  2. 2.In a group of 45 children, 17 play chess, 26 play carrom and 12 play both. How many play at least one of the two?
  3. 3.In a group of 30 grown-ups, 16 drink tea, 19 drink coffee and 9 drink both. How many drink neither of the two?
  4. 4.In a group of 44 children, 22 like mangoes, 20 like bananas and 4 like both. How many like only bananas?
  5. 5.In a group of 43 children, 30 enjoy drawing, 17 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  6. 6.In a group of 53 children, 24 play cricket, 24 play football and 9 play both. How many play only cricket?
  7. 7.In a group of 32 children, 25 sing Hindi songs, 14 sing English songs and 9 sing both. How many sing exactly one of the two?
  8. 8.In a group of 38 grown-ups, 30 drink tea, 16 drink coffee and 11 drink both. How many drink only coffee?
  9. 9.In a group of 38 children, 14 sing Hindi songs, 21 sing English songs and 2 sing both. How many sing neither of the two?
  10. 10.In a group of 30 children, 18 sing Hindi songs, 15 sing English songs and 4 sing both. How many sing only English songs?
  11. 11.In a group of 29 children, 9 play cricket, 8 play football and 2 play both. How many play only cricket?
  12. 12.In a group of 40 grown-ups, 32 drink tea, 17 drink coffee and 12 drink both. How many drink only tea?
  13. 13.In a group of 29 children, 12 play chess, 12 play carrom and 6 play both. How many play at least one of the two?
  14. 14.In a group of 28 children, 20 like mangoes, 12 like bananas and 6 like both. How many like only mangoes?
  15. 15.In a group of 44 children, 23 like mangoes, 19 like bananas and 10 like both. How many like at least one of the two?
  16. 16.In a group of 41 children, 14 like mangoes, 20 like bananas and 8 like both. How many like only bananas?
  17. 17.In a group of 51 children, 30 play cricket, 19 play football and 12 play both. How many play neither of the two?
  18. 18.In a group of 24 children, 16 enjoy drawing, 15 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  19. 19.In a group of 30 children, 19 like mangoes, 13 like bananas and 6 like both. How many like only bananas?
  20. 20.In a group of 33 children, 10 enjoy drawing, 20 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  21. 21.In a group of 35 children, 19 enjoy drawing, 7 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  22. 22.In a group of 36 children, 27 like mangoes, 17 like bananas and 9 like both. How many like neither of the two?
  23. 23.In a group of 24 children, 15 sing Hindi songs, 15 sing English songs and 8 sing both. How many sing exactly one of the two?
  24. 24.In a group of 51 children, 30 play chess, 22 play carrom and 12 play both. How many play neither of the two?
  25. 25.In a group of 30 children, 14 sing Hindi songs, 21 sing English songs and 8 sing both. How many sing neither of the two?
  26. 26.In a group of 27 children, 19 play chess, 14 play carrom and 9 play both. How many play only carrom?
  27. 27.In a group of 35 children, 29 play chess, 17 play carrom and 12 play both. How many play only carrom?
  28. 28.In a group of 36 children, 20 enjoy drawing, 13 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  29. 29.In a group of 36 children, 17 like mangoes, 18 like bananas and 8 like both. How many like only mangoes?
  30. 30.In a group of 38 children, 15 play cricket, 16 play football and 3 play both. How many play only football?
  31. 31.In a group of 29 children, 17 sing Hindi songs, 7 sing English songs and 4 sing both. How many sing only English songs?
  32. 32.In a group of 37 children, 7 like mangoes, 20 like bananas and 3 like both. How many like exactly one of the two?
  33. 33.In a group of 43 children, 17 play chess, 20 play carrom and 9 play both. How many play exactly one of the two?
  34. 34.In a group of 40 children, 28 play chess, 14 play carrom and 11 play both. How many play only carrom?
  35. 35.In a group of 47 children, 29 like mangoes, 24 like bananas and 11 like both. How many like only bananas?
  36. 36.In a group of 43 children, 27 sing Hindi songs, 22 sing English songs and 9 sing both. How many sing only Hindi songs?
  37. 37.In a group of 35 children, 7 play chess, 18 play carrom and 4 play both. How many play at least one of the two?
  38. 38.In a group of 33 children, 12 play cricket, 9 play football and 3 play both. How many play only cricket?
  39. 39.In a group of 34 grown-ups, 13 drink tea, 16 drink coffee and 9 drink both. How many drink exactly one of the two?
  40. 40.In a group of 17 children, 12 like mangoes, 10 like bananas and 6 like both. How many like only bananas?

Answer key

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

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