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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 574 · 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 28 children, 8 play cricket, 20 play football and 2 play both. How many play at least one of the two?
  2. 2.In a group of 32 children, 21 play chess, 11 play carrom and 3 play both. How many play exactly one of the two?
  3. 3.In a group of 51 children, 22 enjoy drawing, 26 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  4. 4.In a group of 27 children, 18 play chess, 6 play carrom and 2 play both. How many play only chess?
  5. 5.In a group of 26 children, 7 like mangoes, 7 like bananas and 3 like both. How many like only mangoes?
  6. 6.In a group of 25 children, 12 play chess, 21 play carrom and 9 play both. How many play exactly one of the two?
  7. 7.In a group of 25 children, 9 like mangoes, 11 like bananas and 6 like both. How many like neither of the two?
  8. 8.In a group of 46 children, 24 enjoy drawing, 29 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  9. 9.In a group of 38 children, 18 like mangoes, 23 like bananas and 4 like both. How many like only mangoes?
  10. 10.In a group of 42 children, 25 play cricket, 15 play football and 11 play both. How many play only football?
  11. 11.In a group of 30 children, 8 play cricket, 14 play football and 2 play both. How many play only cricket?
  12. 12.In a group of 56 children, 27 like mangoes, 24 like bananas and 9 like both. How many like neither of the two?
  13. 13.In a group of 47 children, 22 sing Hindi songs, 21 sing English songs and 6 sing both. How many sing at least one of the two?
  14. 14.In a group of 26 children, 7 enjoy drawing, 18 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  15. 15.In a group of 41 children, 14 play chess, 16 play carrom and 4 play both. How many play only carrom?
  16. 16.In a group of 29 grown-ups, 18 drink tea, 10 drink coffee and 3 drink both. How many drink exactly one of the two?
  17. 17.In a group of 48 children, 24 play chess, 24 play carrom and 10 play both. How many play at least one of the two?
  18. 18.In a group of 38 children, 18 like mangoes, 23 like bananas and 8 like both. How many like only bananas?
  19. 19.In a group of 54 children, 25 sing Hindi songs, 30 sing English songs and 11 sing both. How many sing at least one of the two?
  20. 20.In a group of 41 children, 24 sing Hindi songs, 17 sing English songs and 6 sing both. How many sing at least one of the two?
  21. 21.In a group of 28 grown-ups, 19 drink tea, 11 drink coffee and 5 drink both. How many drink only tea?
  22. 22.In a group of 52 children, 24 enjoy drawing, 26 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  23. 23.In a group of 46 children, 18 play chess, 23 play carrom and 6 play both. How many play neither of the two?
  24. 24.In a group of 21 children, 9 play chess, 12 play carrom and 4 play both. How many play only chess?
  25. 25.In a group of 54 children, 20 play chess, 21 play carrom and 2 play both. How many play neither of the two?
  26. 26.In a group of 39 children, 18 enjoy drawing, 23 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  27. 27.In a group of 45 children, 21 play cricket, 26 play football and 8 play both. How many play at least one of the two?
  28. 28.In a group of 36 children, 21 play cricket, 17 play football and 10 play both. How many play at least one of the two?
  29. 29.In a group of 36 children, 13 enjoy drawing, 24 enjoy dancing and 9 enjoy both. How many enjoy neither of the two?
  30. 30.In a group of 33 children, 21 play chess, 21 play carrom and 12 play both. How many play exactly one of the two?
  31. 31.In a group of 38 children, 23 like mangoes, 8 like bananas and 3 like both. How many like only mangoes?
  32. 32.In a group of 37 children, 28 sing Hindi songs, 16 sing English songs and 10 sing both. How many sing only English songs?
  33. 33.In a group of 39 children, 15 play chess, 15 play carrom and 3 play both. How many play exactly one of the two?
  34. 34.In a group of 38 children, 17 play cricket, 16 play football and 4 play both. How many play only cricket?
  35. 35.In a group of 27 children, 14 play chess, 7 play carrom and 3 play both. How many play exactly one of the two?
  36. 36.In a group of 41 children, 17 like mangoes, 15 like bananas and 2 like both. How many like exactly one of the two?
  37. 37.In a group of 32 children, 12 enjoy drawing, 19 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  38. 38.In a group of 34 children, 10 sing Hindi songs, 13 sing English songs and 3 sing both. How many sing only English songs?
  39. 39.In a group of 50 grown-ups, 30 drink tea, 17 drink coffee and 11 drink both. How many drink neither of the two?
  40. 40.In a group of 20 grown-ups, 9 drink tea, 6 drink coffee and 3 drink both. How many drink at least one of the two?

Answer key

  1. 26
  2. 26
  3. 20
  4. 16
  5. 4
  6. 15
  7. 11
  8. 33
  9. 14
  10. 4
  11. 6
  12. 14
  13. 37
  14. 16
  15. 12
  16. 22
  17. 38
  18. 15
  19. 44
  20. 35
  21. 14
  22. 28
  23. 11
  24. 5
  25. 15
  26. 12
  27. 39
  28. 28
  29. 8
  30. 18
  31. 20
  32. 6
  33. 24
  34. 13
  35. 15
  36. 28
  37. 25
  38. 10
  39. 14
  40. 12

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