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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 386 · 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 46 children, 24 play cricket, 28 play football and 12 play both. How many play only football?
  2. 2.In a group of 36 grown-ups, 14 drink tea, 26 drink coffee and 6 drink both. How many drink only coffee?
  3. 3.In a group of 29 children, 25 enjoy drawing, 9 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  4. 4.In a group of 49 children, 28 enjoy drawing, 17 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  5. 5.In a group of 19 children, 11 sing Hindi songs, 7 sing English songs and 4 sing both. How many sing only English songs?
  6. 6.In a group of 34 children, 17 like mangoes, 11 like bananas and 8 like both. How many like only mangoes?
  7. 7.In a group of 26 children, 11 play cricket, 9 play football and 3 play both. How many play neither of the two?
  8. 8.In a group of 42 children, 16 like mangoes, 19 like bananas and 2 like both. How many like neither of the two?
  9. 9.In a group of 40 children, 24 like mangoes, 18 like bananas and 12 like both. How many like only bananas?
  10. 10.In a group of 24 grown-ups, 18 drink tea, 12 drink coffee and 8 drink both. How many drink exactly one of the two?
  11. 11.In a group of 37 children, 23 like mangoes, 19 like bananas and 11 like both. How many like at least one of the two?
  12. 12.In a group of 35 children, 6 play chess, 18 play carrom and 3 play both. How many play only carrom?
  13. 13.In a group of 26 children, 9 like mangoes, 15 like bananas and 3 like both. How many like only bananas?
  14. 14.In a group of 56 children, 22 like mangoes, 31 like bananas and 12 like both. How many like exactly one of the two?
  15. 15.In a group of 26 children, 10 play cricket, 14 play football and 5 play both. How many play exactly one of the two?
  16. 16.In a group of 45 children, 12 enjoy drawing, 27 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  17. 17.In a group of 30 children, 14 like mangoes, 10 like bananas and 2 like both. How many like neither of the two?
  18. 18.In a group of 17 children, 6 like mangoes, 6 like bananas and 2 like both. How many like only bananas?
  19. 19.In a group of 43 children, 16 play cricket, 16 play football and 2 play both. How many play only cricket?
  20. 20.In a group of 51 children, 28 play cricket, 25 play football and 12 play both. How many play only football?
  21. 21.In a group of 34 children, 25 sing Hindi songs, 16 sing English songs and 9 sing both. How many sing only English songs?
  22. 22.In a group of 25 grown-ups, 8 drink tea, 9 drink coffee and 2 drink both. How many drink only coffee?
  23. 23.In a group of 45 grown-ups, 23 drink tea, 27 drink coffee and 8 drink both. How many drink at least one of the two?
  24. 24.In a group of 24 children, 13 play cricket, 10 play football and 6 play both. How many play at least one of the two?
  25. 25.In a group of 27 children, 19 play chess, 9 play carrom and 6 play both. How many play neither of the two?
  26. 26.In a group of 14 children, 5 enjoy drawing, 9 enjoy dancing and 2 enjoy both. How many enjoy exactly one of the two?
  27. 27.In a group of 42 children, 29 like mangoes, 17 like bananas and 10 like both. How many like neither of the two?
  28. 28.In a group of 37 children, 13 like mangoes, 19 like bananas and 9 like both. How many like only mangoes?
  29. 29.In a group of 24 children, 14 play cricket, 12 play football and 9 play both. How many play only cricket?
  30. 30.In a group of 25 children, 13 sing Hindi songs, 11 sing English songs and 8 sing both. How many sing exactly one of the two?
  31. 31.In a group of 53 children, 20 play chess, 32 play carrom and 12 play both. How many play at least one of the two?
  32. 32.In a group of 45 children, 28 play cricket, 27 play football and 11 play both. How many play neither of the two?
  33. 33.In a group of 29 children, 8 sing Hindi songs, 11 sing English songs and 2 sing both. How many sing exactly one of the two?
  34. 34.In a group of 41 children, 22 like mangoes, 15 like bananas and 2 like both. How many like exactly one of the two?
  35. 35.In a group of 15 grown-ups, 9 drink tea, 6 drink coffee and 3 drink both. How many drink neither of the two?
  36. 36.In a group of 31 children, 10 sing Hindi songs, 21 sing English songs and 7 sing both. How many sing at least one of the two?
  37. 37.In a group of 26 children, 16 enjoy drawing, 20 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  38. 38.In a group of 40 children, 15 sing Hindi songs, 31 sing English songs and 11 sing both. How many sing at least one of the two?
  39. 39.In a group of 39 children, 17 play chess, 24 play carrom and 5 play both. How many play only chess?
  40. 40.In a group of 34 children, 16 enjoy drawing, 16 enjoy dancing and 5 enjoy both. How many enjoy neither of the two?

Answer key

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

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