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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 175 · 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 42 children, 15 play chess, 30 play carrom and 12 play both. How many play exactly one of the two?
  2. 2.In a group of 47 children, 16 play cricket, 23 play football and 6 play both. How many play exactly one of the two?
  3. 3.In a group of 31 children, 15 like mangoes, 12 like bananas and 7 like both. How many like only mangoes?
  4. 4.In a group of 39 children, 12 play cricket, 23 play football and 6 play both. How many play neither of the two?
  5. 5.In a group of 38 children, 19 play cricket, 22 play football and 6 play both. How many play neither of the two?
  6. 6.In a group of 40 children, 20 sing Hindi songs, 13 sing English songs and 5 sing both. How many sing at least one of the two?
  7. 7.In a group of 28 children, 15 like mangoes, 9 like bananas and 2 like both. How many like at least one of the two?
  8. 8.In a group of 45 children, 22 enjoy drawing, 13 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  9. 9.In a group of 31 children, 23 sing Hindi songs, 15 sing English songs and 9 sing both. How many sing exactly one of the two?
  10. 10.In a group of 17 children, 8 play chess, 11 play carrom and 5 play both. How many play at least one of the two?
  11. 11.In a group of 26 children, 15 enjoy drawing, 15 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  12. 12.In a group of 31 grown-ups, 13 drink tea, 9 drink coffee and 4 drink both. How many drink at least one of the two?
  13. 13.In a group of 38 children, 17 play cricket, 11 play football and 2 play both. How many play exactly one of the two?
  14. 14.In a group of 29 children, 11 enjoy drawing, 11 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  15. 15.In a group of 32 children, 18 sing Hindi songs, 9 sing English songs and 3 sing both. How many sing only English songs?
  16. 16.In a group of 47 children, 24 play cricket, 21 play football and 12 play both. How many play exactly one of the two?
  17. 17.In a group of 51 children, 23 enjoy drawing, 24 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  18. 18.In a group of 21 children, 8 play chess, 10 play carrom and 3 play both. How many play exactly one of the two?
  19. 19.In a group of 15 children, 10 sing Hindi songs, 9 sing English songs and 6 sing both. How many sing exactly one of the two?
  20. 20.In a group of 29 children, 21 play cricket, 11 play football and 4 play both. How many play only football?
  21. 21.In a group of 42 children, 31 sing Hindi songs, 14 sing English songs and 11 sing both. How many sing at least one of the two?
  22. 22.In a group of 37 children, 22 enjoy drawing, 19 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  23. 23.In a group of 35 children, 20 enjoy drawing, 16 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  24. 24.In a group of 19 grown-ups, 13 drink tea, 10 drink coffee and 5 drink both. How many drink only tea?
  25. 25.In a group of 30 children, 15 sing Hindi songs, 15 sing English songs and 10 sing both. How many sing neither of the two?
  26. 26.In a group of 31 children, 19 play chess, 9 play carrom and 2 play both. How many play only chess?
  27. 27.In a group of 32 children, 16 play chess, 18 play carrom and 12 play both. How many play only chess?
  28. 28.In a group of 40 grown-ups, 18 drink tea, 14 drink coffee and 2 drink both. How many drink exactly one of the two?
  29. 29.In a group of 40 children, 18 play cricket, 13 play football and 3 play both. How many play only football?
  30. 30.In a group of 33 children, 23 like mangoes, 16 like bananas and 7 like both. How many like only bananas?
  31. 31.In a group of 51 children, 25 sing Hindi songs, 27 sing English songs and 7 sing both. How many sing neither of the two?
  32. 32.In a group of 43 children, 19 enjoy drawing, 21 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  33. 33.In a group of 31 children, 20 play chess, 15 play carrom and 12 play both. How many play exactly one of the two?
  34. 34.In a group of 43 children, 19 sing Hindi songs, 27 sing English songs and 9 sing both. How many sing only Hindi songs?
  35. 35.In a group of 29 children, 13 play cricket, 23 play football and 10 play both. How many play neither of the two?
  36. 36.In a group of 52 children, 17 like mangoes, 26 like bananas and 6 like both. How many like only bananas?
  37. 37.In a group of 44 grown-ups, 26 drink tea, 14 drink coffee and 9 drink both. How many drink at least one of the two?
  38. 38.In a group of 48 children, 21 play chess, 29 play carrom and 12 play both. How many play exactly one of the two?
  39. 39.In a group of 37 children, 19 play cricket, 17 play football and 2 play both. How many play neither of the two?
  40. 40.In a group of 43 children, 28 play chess, 21 play carrom and 12 play both. How many play only chess?

Answer key

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

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