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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 4 · 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 29 children, 19 sing Hindi songs, 12 sing English songs and 8 sing both. How many sing only English songs?
  2. 2.In a group of 31 children, 18 sing Hindi songs, 5 sing English songs and 2 sing both. How many sing exactly one of the two?
  3. 3.In a group of 34 children, 10 enjoy drawing, 17 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  4. 4.In a group of 48 grown-ups, 14 drink tea, 25 drink coffee and 5 drink both. How many drink neither of the two?
  5. 5.In a group of 44 children, 22 sing Hindi songs, 16 sing English songs and 5 sing both. How many sing only Hindi songs?
  6. 6.In a group of 24 children, 5 play chess, 19 play carrom and 2 play both. How many play exactly one of the two?
  7. 7.In a group of 36 children, 15 play chess, 29 play carrom and 12 play both. How many play at least one of the two?
  8. 8.In a group of 37 children, 28 sing Hindi songs, 19 sing English songs and 11 sing both. How many sing neither of the two?
  9. 9.In a group of 48 children, 26 play chess, 17 play carrom and 9 play both. How many play only chess?
  10. 10.In a group of 21 children, 8 play chess, 13 play carrom and 3 play both. How many play only chess?
  11. 11.In a group of 33 children, 12 sing Hindi songs, 18 sing English songs and 5 sing both. How many sing only English songs?
  12. 12.In a group of 38 children, 25 play chess, 23 play carrom and 11 play both. How many play neither of the two?
  13. 13.In a group of 18 children, 6 sing Hindi songs, 7 sing English songs and 2 sing both. How many sing at least one of the two?
  14. 14.In a group of 22 children, 6 play chess, 17 play carrom and 2 play both. How many play neither of the two?
  15. 15.In a group of 36 children, 24 enjoy drawing, 15 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  16. 16.In a group of 56 children, 26 play chess, 24 play carrom and 8 play both. How many play neither of the two?
  17. 17.In a group of 46 children, 24 play cricket, 30 play football and 11 play both. How many play only football?
  18. 18.In a group of 35 children, 14 play cricket, 28 play football and 8 play both. How many play only cricket?
  19. 19.In a group of 43 children, 23 sing Hindi songs, 20 sing English songs and 4 sing both. How many sing at least one of the two?
  20. 20.In a group of 33 children, 12 play cricket, 22 play football and 2 play both. How many play only football?
  21. 21.In a group of 26 children, 10 play chess, 10 play carrom and 3 play both. How many play neither of the two?
  22. 22.In a group of 48 children, 17 play cricket, 22 play football and 2 play both. How many play neither of the two?
  23. 23.In a group of 29 children, 5 like mangoes, 14 like bananas and 2 like both. How many like only mangoes?
  24. 24.In a group of 32 children, 14 like mangoes, 15 like bananas and 4 like both. How many like exactly one of the two?
  25. 25.In a group of 49 children, 32 play cricket, 27 play football and 12 play both. How many play only cricket?
  26. 26.In a group of 32 children, 11 sing Hindi songs, 17 sing English songs and 5 sing both. How many sing only English songs?
  27. 27.In a group of 46 children, 19 play cricket, 23 play football and 7 play both. How many play exactly one of the two?
  28. 28.In a group of 41 children, 11 sing Hindi songs, 21 sing English songs and 2 sing both. How many sing at least one of the two?
  29. 29.In a group of 23 children, 14 like mangoes, 11 like bananas and 8 like both. How many like only mangoes?
  30. 30.In a group of 28 children, 10 play chess, 8 play carrom and 4 play both. How many play only carrom?
  31. 31.In a group of 58 children, 30 enjoy drawing, 26 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  32. 32.In a group of 39 children, 10 play cricket, 20 play football and 6 play both. How many play exactly one of the two?
  33. 33.In a group of 23 grown-ups, 15 drink tea, 14 drink coffee and 7 drink both. How many drink only coffee?
  34. 34.In a group of 42 grown-ups, 15 drink tea, 31 drink coffee and 12 drink both. How many drink at least one of the two?
  35. 35.In a group of 32 children, 16 enjoy drawing, 15 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  36. 36.In a group of 51 children, 19 play cricket, 21 play football and 3 play both. How many play only cricket?
  37. 37.In a group of 51 children, 21 enjoy drawing, 26 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  38. 38.In a group of 50 children, 18 enjoy drawing, 29 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  39. 39.In a group of 31 children, 16 enjoy drawing, 11 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  40. 40.In a group of 40 children, 13 like mangoes, 18 like bananas and 4 like both. How many like exactly one of the two?

Answer key

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

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