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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 612 · 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 32 children, 21 play chess, 16 play carrom and 12 play both. How many play neither of the two?
  2. 2.In a group of 34 children, 22 play cricket, 14 play football and 8 play both. How many play neither of the two?
  3. 3.In a group of 35 children, 20 enjoy drawing, 14 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  4. 4.In a group of 24 children, 12 like mangoes, 15 like bananas and 4 like both. How many like only bananas?
  5. 5.In a group of 43 children, 26 sing Hindi songs, 17 sing English songs and 8 sing both. How many sing at least one of the two?
  6. 6.In a group of 30 children, 18 play cricket, 10 play football and 6 play both. How many play at least one of the two?
  7. 7.In a group of 33 children, 18 play cricket, 17 play football and 6 play both. How many play only football?
  8. 8.In a group of 31 children, 20 play cricket, 13 play football and 6 play both. How many play neither of the two?
  9. 9.In a group of 27 children, 7 play cricket, 13 play football and 2 play both. How many play only cricket?
  10. 10.In a group of 26 children, 9 play chess, 16 play carrom and 4 play both. How many play neither of the two?
  11. 11.In a group of 41 children, 13 like mangoes, 20 like bananas and 4 like both. How many like only bananas?
  12. 12.In a group of 26 children, 21 play cricket, 11 play football and 8 play both. How many play at least one of the two?
  13. 13.In a group of 43 children, 21 play cricket, 17 play football and 8 play both. How many play at least one of the two?
  14. 14.In a group of 34 children, 29 enjoy drawing, 12 enjoy dancing and 9 enjoy both. How many enjoy exactly one of the two?
  15. 15.In a group of 40 children, 19 enjoy drawing, 20 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  16. 16.In a group of 44 children, 27 play chess, 18 play carrom and 12 play both. How many play only carrom?
  17. 17.In a group of 27 children, 10 play chess, 18 play carrom and 6 play both. How many play at least one of the two?
  18. 18.In a group of 36 children, 22 play cricket, 6 play football and 3 play both. How many play only cricket?
  19. 19.In a group of 38 children, 16 enjoy drawing, 27 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  20. 20.In a group of 26 children, 15 enjoy drawing, 16 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  21. 21.In a group of 38 children, 19 enjoy drawing, 12 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  22. 22.In a group of 54 children, 23 enjoy drawing, 29 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  23. 23.In a group of 39 children, 9 like mangoes, 18 like bananas and 2 like both. How many like exactly one of the two?
  24. 24.In a group of 53 children, 23 like mangoes, 21 like bananas and 3 like both. How many like only bananas?
  25. 25.In a group of 33 children, 20 enjoy drawing, 16 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  26. 26.In a group of 55 children, 23 sing Hindi songs, 21 sing English songs and 3 sing both. How many sing only Hindi songs?
  27. 27.In a group of 24 grown-ups, 18 drink tea, 8 drink coffee and 4 drink both. How many drink neither of the two?
  28. 28.In a group of 52 children, 25 play cricket, 22 play football and 6 play both. How many play at least one of the two?
  29. 29.In a group of 25 children, 19 enjoy drawing, 12 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  30. 30.In a group of 26 children, 21 play chess, 6 play carrom and 2 play both. How many play exactly one of the two?
  31. 31.In a group of 37 children, 24 play cricket, 13 play football and 4 play both. How many play exactly one of the two?
  32. 32.In a group of 42 children, 17 like mangoes, 30 like bananas and 10 like both. How many like only bananas?
  33. 33.In a group of 47 children, 25 play chess, 24 play carrom and 7 play both. How many play neither of the two?
  34. 34.In a group of 36 children, 16 like mangoes, 14 like bananas and 5 like both. How many like exactly one of the two?
  35. 35.In a group of 32 children, 14 enjoy drawing, 15 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  36. 36.In a group of 29 grown-ups, 9 drink tea, 11 drink coffee and 2 drink both. How many drink only tea?
  37. 37.In a group of 46 children, 22 like mangoes, 20 like bananas and 4 like both. How many like only mangoes?
  38. 38.In a group of 52 children, 29 play chess, 20 play carrom and 12 play both. How many play neither of the two?
  39. 39.In a group of 31 children, 12 play chess, 17 play carrom and 5 play both. How many play exactly one of the two?
  40. 40.In a group of 32 children, 16 enjoy drawing, 14 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?

Answer key

  1. 7
  2. 6
  3. 27
  4. 11
  5. 35
  6. 22
  7. 11
  8. 4
  9. 5
  10. 5
  11. 16
  12. 24
  13. 30
  14. 23
  15. 28
  16. 6
  17. 22
  18. 19
  19. 31
  20. 22
  21. 27
  22. 13
  23. 23
  24. 18
  25. 10
  26. 20
  27. 2
  28. 41
  29. 15
  30. 23
  31. 29
  32. 20
  33. 5
  34. 20
  35. 5
  36. 7
  37. 18
  38. 15
  39. 19
  40. 9

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