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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 166 · 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 40 children, 18 play cricket, 23 play football and 5 play both. How many play only football?
  2. 2.In a group of 32 children, 10 play chess, 23 play carrom and 3 play both. How many play only carrom?
  3. 3.In a group of 31 children, 22 enjoy drawing, 8 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  4. 4.In a group of 22 grown-ups, 8 drink tea, 15 drink coffee and 5 drink both. How many drink exactly one of the two?
  5. 5.In a group of 35 children, 10 enjoy drawing, 16 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  6. 6.In a group of 39 children, 21 sing Hindi songs, 17 sing English songs and 9 sing both. How many sing at least one of the two?
  7. 7.In a group of 31 children, 17 play cricket, 19 play football and 6 play both. How many play only cricket?
  8. 8.In a group of 21 children, 14 play cricket, 11 play football and 8 play both. How many play neither of the two?
  9. 9.In a group of 25 children, 7 play cricket, 20 play football and 4 play both. How many play at least one of the two?
  10. 10.In a group of 14 grown-ups, 6 drink tea, 7 drink coffee and 2 drink both. How many drink only tea?
  11. 11.In a group of 36 children, 9 sing Hindi songs, 24 sing English songs and 4 sing both. How many sing only English songs?
  12. 12.In a group of 39 children, 17 play chess, 25 play carrom and 8 play both. How many play at least one of the two?
  13. 13.In a group of 35 children, 17 play chess, 21 play carrom and 9 play both. How many play exactly one of the two?
  14. 14.In a group of 33 children, 10 like mangoes, 19 like bananas and 7 like both. How many like only bananas?
  15. 15.In a group of 41 grown-ups, 22 drink tea, 9 drink coffee and 3 drink both. How many drink neither of the two?
  16. 16.In a group of 29 children, 19 enjoy drawing, 9 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  17. 17.In a group of 32 children, 12 enjoy drawing, 22 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  18. 18.In a group of 61 children, 28 play cricket, 26 play football and 8 play both. How many play only football?
  19. 19.In a group of 47 children, 24 play chess, 18 play carrom and 5 play both. How many play only carrom?
  20. 20.In a group of 62 children, 27 play cricket, 27 play football and 7 play both. How many play neither of the two?
  21. 21.In a group of 41 children, 25 sing Hindi songs, 17 sing English songs and 8 sing both. How many sing exactly one of the two?
  22. 22.In a group of 47 children, 22 sing Hindi songs, 20 sing English songs and 10 sing both. How many sing only English songs?
  23. 23.In a group of 49 children, 30 like mangoes, 25 like bananas and 10 like both. How many like neither of the two?
  24. 24.In a group of 36 children, 25 play chess, 17 play carrom and 8 play both. How many play at least one of the two?
  25. 25.In a group of 44 children, 25 enjoy drawing, 15 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  26. 26.In a group of 38 children, 13 enjoy drawing, 21 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  27. 27.In a group of 37 children, 20 like mangoes, 9 like bananas and 2 like both. How many like only mangoes?
  28. 28.In a group of 33 children, 13 sing Hindi songs, 26 sing English songs and 10 sing both. How many sing at least one of the two?
  29. 29.In a group of 36 children, 13 enjoy drawing, 27 enjoy dancing and 8 enjoy both. How many enjoy exactly one of the two?
  30. 30.In a group of 42 children, 15 play chess, 19 play carrom and 4 play both. How many play only chess?
  31. 31.In a group of 29 children, 15 sing Hindi songs, 15 sing English songs and 10 sing both. How many sing neither of the two?
  32. 32.In a group of 28 children, 18 enjoy drawing, 15 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  33. 33.In a group of 37 children, 19 sing Hindi songs, 26 sing English songs and 12 sing both. How many sing at least one of the two?
  34. 34.In a group of 30 children, 9 enjoy drawing, 17 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  35. 35.In a group of 43 children, 17 enjoy drawing, 19 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  36. 36.In a group of 33 grown-ups, 9 drink tea, 24 drink coffee and 4 drink both. How many drink exactly one of the two?
  37. 37.In a group of 36 children, 15 play cricket, 24 play football and 8 play both. How many play only cricket?
  38. 38.In a group of 50 children, 30 sing Hindi songs, 17 sing English songs and 10 sing both. How many sing neither of the two?
  39. 39.In a group of 43 children, 12 like mangoes, 24 like bananas and 5 like both. How many like at least one of the two?
  40. 40.In a group of 34 children, 13 enjoy drawing, 23 enjoy dancing and 10 enjoy both. How many enjoy at least one of the two?

Answer key

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

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