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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 17 · 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 33 children, 11 like mangoes, 19 like bananas and 2 like both. How many like neither of the two?
  2. 2.In a group of 27 children, 9 enjoy drawing, 10 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  3. 3.In a group of 15 children, 6 like mangoes, 9 like bananas and 2 like both. How many like exactly one of the two?
  4. 4.In a group of 43 children, 26 play cricket, 22 play football and 8 play both. How many play only football?
  5. 5.In a group of 43 children, 25 like mangoes, 14 like bananas and 9 like both. How many like only mangoes?
  6. 6.In a group of 30 children, 13 like mangoes, 23 like bananas and 7 like both. How many like at least one of the two?
  7. 7.In a group of 26 children, 11 sing Hindi songs, 21 sing English songs and 8 sing both. How many sing exactly one of the two?
  8. 8.In a group of 29 children, 14 enjoy drawing, 14 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  9. 9.In a group of 37 children, 22 sing Hindi songs, 17 sing English songs and 5 sing both. How many sing only Hindi songs?
  10. 10.In a group of 36 children, 27 like mangoes, 18 like bananas and 11 like both. How many like only bananas?
  11. 11.In a group of 30 children, 15 sing Hindi songs, 16 sing English songs and 11 sing both. How many sing only English songs?
  12. 12.In a group of 32 children, 9 sing Hindi songs, 24 sing English songs and 6 sing both. How many sing neither of the two?
  13. 13.In a group of 46 grown-ups, 27 drink tea, 13 drink coffee and 8 drink both. How many drink only tea?
  14. 14.In a group of 37 children, 12 like mangoes, 21 like bananas and 6 like both. How many like neither of the two?
  15. 15.In a group of 35 grown-ups, 11 drink tea, 22 drink coffee and 2 drink both. How many drink neither of the two?
  16. 16.In a group of 41 children, 20 enjoy drawing, 17 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  17. 17.In a group of 43 children, 19 enjoy drawing, 24 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  18. 18.In a group of 32 children, 20 play cricket, 10 play football and 3 play both. How many play only football?
  19. 19.In a group of 30 children, 12 play cricket, 14 play football and 9 play both. How many play exactly one of the two?
  20. 20.In a group of 31 children, 10 play cricket, 16 play football and 3 play both. How many play at least one of the two?
  21. 21.In a group of 37 grown-ups, 14 drink tea, 28 drink coffee and 8 drink both. How many drink at least one of the two?
  22. 22.In a group of 30 children, 23 sing Hindi songs, 13 sing English songs and 8 sing both. How many sing exactly one of the two?
  23. 23.In a group of 22 children, 12 like mangoes, 6 like bananas and 2 like both. How many like only bananas?
  24. 24.In a group of 51 grown-ups, 24 drink tea, 20 drink coffee and 6 drink both. How many drink neither of the two?
  25. 25.In a group of 52 children, 26 play chess, 28 play carrom and 9 play both. How many play only chess?
  26. 26.In a group of 31 children, 15 play chess, 22 play carrom and 9 play both. How many play only carrom?
  27. 27.In a group of 32 children, 15 sing Hindi songs, 17 sing English songs and 5 sing both. How many sing only English songs?
  28. 28.In a group of 42 children, 23 sing Hindi songs, 24 sing English songs and 8 sing both. How many sing at least one of the two?
  29. 29.In a group of 26 children, 11 play cricket, 5 play football and 2 play both. How many play only football?
  30. 30.In a group of 19 children, 8 play cricket, 15 play football and 5 play both. How many play exactly one of the two?
  31. 31.In a group of 36 children, 25 play chess, 18 play carrom and 11 play both. How many play neither of the two?
  32. 32.In a group of 57 children, 29 play chess, 29 play carrom and 11 play both. How many play only chess?
  33. 33.In a group of 35 children, 13 play cricket, 16 play football and 8 play both. How many play only football?
  34. 34.In a group of 27 children, 16 enjoy drawing, 16 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  35. 35.In a group of 51 children, 19 play chess, 22 play carrom and 4 play both. How many play at least one of the two?
  36. 36.In a group of 47 children, 12 play cricket, 29 play football and 9 play both. How many play only cricket?
  37. 37.In a group of 34 children, 12 play cricket, 19 play football and 2 play both. How many play exactly one of the two?
  38. 38.In a group of 56 children, 24 like mangoes, 21 like bananas and 4 like both. How many like only bananas?
  39. 39.In a group of 32 children, 14 enjoy drawing, 14 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  40. 40.In a group of 28 children, 14 like mangoes, 11 like bananas and 4 like both. How many like neither of the two?

Answer key

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

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