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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 466 · 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 31 children, 14 play chess, 22 play carrom and 7 play both. How many play only carrom?
  2. 2.In a group of 38 children, 14 play cricket, 23 play football and 9 play both. How many play only cricket?
  3. 3.In a group of 36 children, 14 like mangoes, 23 like bananas and 7 like both. How many like at least one of the two?
  4. 4.In a group of 34 children, 14 play chess, 14 play carrom and 3 play both. How many play only chess?
  5. 5.In a group of 26 children, 20 play cricket, 10 play football and 5 play both. How many play exactly one of the two?
  6. 6.In a group of 57 children, 28 play chess, 29 play carrom and 12 play both. How many play neither of the two?
  7. 7.In a group of 32 children, 18 play chess, 16 play carrom and 9 play both. How many play exactly one of the two?
  8. 8.In a group of 42 children, 18 play chess, 20 play carrom and 9 play both. How many play only carrom?
  9. 9.In a group of 17 children, 9 sing Hindi songs, 10 sing English songs and 3 sing both. How many sing at least one of the two?
  10. 10.In a group of 30 children, 20 enjoy drawing, 13 enjoy dancing and 8 enjoy both. How many enjoy at least one of the two?
  11. 11.In a group of 35 children, 18 like mangoes, 17 like bananas and 2 like both. How many like at least one of the two?
  12. 12.In a group of 35 children, 12 sing Hindi songs, 24 sing English songs and 5 sing both. How many sing only Hindi songs?
  13. 13.In a group of 26 children, 19 like mangoes, 16 like bananas and 12 like both. How many like only bananas?
  14. 14.In a group of 32 children, 16 sing Hindi songs, 7 sing English songs and 4 sing both. How many sing only Hindi songs?
  15. 15.In a group of 47 children, 23 play cricket, 19 play football and 8 play both. How many play exactly one of the two?
  16. 16.In a group of 44 children, 16 enjoy drawing, 24 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  17. 17.In a group of 39 children, 23 sing Hindi songs, 18 sing English songs and 8 sing both. How many sing at least one of the two?
  18. 18.In a group of 12 grown-ups, 7 drink tea, 5 drink coffee and 2 drink both. How many drink only tea?
  19. 19.In a group of 18 children, 8 enjoy drawing, 11 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?
  20. 20.In a group of 41 children, 19 play cricket, 27 play football and 9 play both. How many play neither of the two?
  21. 21.In a group of 52 children, 27 like mangoes, 23 like bananas and 8 like both. How many like only mangoes?
  22. 22.In a group of 43 children, 19 play chess, 27 play carrom and 8 play both. How many play only chess?
  23. 23.In a group of 40 children, 23 play cricket, 25 play football and 12 play both. How many play only football?
  24. 24.In a group of 19 children, 13 enjoy drawing, 15 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  25. 25.In a group of 17 grown-ups, 9 drink tea, 9 drink coffee and 4 drink both. How many drink only coffee?
  26. 26.In a group of 32 grown-ups, 10 drink tea, 12 drink coffee and 5 drink both. How many drink only coffee?
  27. 27.In a group of 19 children, 9 like mangoes, 11 like bananas and 2 like both. How many like only mangoes?
  28. 28.In a group of 26 children, 19 play chess, 14 play carrom and 8 play both. How many play exactly one of the two?
  29. 29.In a group of 22 children, 11 enjoy drawing, 12 enjoy dancing and 4 enjoy both. How many enjoy only dancing?
  30. 30.In a group of 33 children, 24 like mangoes, 10 like bananas and 5 like both. How many like only mangoes?
  31. 31.In a group of 17 children, 8 enjoy drawing, 5 enjoy dancing and 2 enjoy both. How many enjoy neither of the two?
  32. 32.In a group of 33 children, 13 like mangoes, 19 like bananas and 5 like both. How many like only bananas?
  33. 33.In a group of 46 children, 22 enjoy drawing, 17 enjoy dancing and 6 enjoy both. How many enjoy only drawing?
  34. 34.In a group of 46 children, 23 sing Hindi songs, 11 sing English songs and 3 sing both. How many sing neither of the two?
  35. 35.In a group of 20 children, 8 play cricket, 9 play football and 2 play both. How many play only cricket?
  36. 36.In a group of 48 children, 21 sing Hindi songs, 23 sing English songs and 8 sing both. How many sing exactly one of the two?
  37. 37.In a group of 47 children, 27 play chess, 25 play carrom and 10 play both. How many play at least one of the two?
  38. 38.In a group of 24 children, 12 sing Hindi songs, 5 sing English songs and 2 sing both. How many sing at least one of the two?
  39. 39.In a group of 26 children, 19 like mangoes, 12 like bananas and 6 like both. How many like neither of the two?
  40. 40.In a group of 27 children, 9 enjoy drawing, 22 enjoy dancing and 6 enjoy both. How many enjoy neither of the two?

Answer key

  1. 15
  2. 5
  3. 30
  4. 11
  5. 20
  6. 12
  7. 16
  8. 11
  9. 16
  10. 25
  11. 33
  12. 7
  13. 4
  14. 12
  15. 26
  16. 12
  17. 33
  18. 5
  19. 4
  20. 4
  21. 19
  22. 11
  23. 13
  24. 8
  25. 5
  26. 7
  27. 7
  28. 17
  29. 8
  30. 19
  31. 6
  32. 14
  33. 16
  34. 15
  35. 6
  36. 28
  37. 42
  38. 15
  39. 1
  40. 2

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