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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 195 · 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 39 grown-ups, 9 drink tea, 23 drink coffee and 5 drink both. How many drink exactly one of the two?
  2. 2.In a group of 36 children, 20 sing Hindi songs, 14 sing English songs and 10 sing both. How many sing exactly one of the two?
  3. 3.In a group of 20 children, 10 like mangoes, 9 like bananas and 5 like both. How many like only mangoes?
  4. 4.In a group of 38 children, 15 play cricket, 16 play football and 3 play both. How many play only football?
  5. 5.In a group of 41 children, 12 like mangoes, 24 like bananas and 6 like both. How many like only mangoes?
  6. 6.In a group of 41 children, 18 enjoy drawing, 19 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  7. 7.In a group of 44 children, 19 sing Hindi songs, 23 sing English songs and 7 sing both. How many sing only English songs?
  8. 8.In a group of 28 children, 24 play cricket, 12 play football and 9 play both. How many play neither of the two?
  9. 9.In a group of 26 children, 17 enjoy drawing, 12 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  10. 10.In a group of 38 children, 19 play cricket, 22 play football and 7 play both. How many play only football?
  11. 11.In a group of 31 grown-ups, 15 drink tea, 15 drink coffee and 11 drink both. How many drink exactly one of the two?
  12. 12.In a group of 44 children, 24 enjoy drawing, 20 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  13. 13.In a group of 31 children, 8 sing Hindi songs, 17 sing English songs and 4 sing both. How many sing at least one of the two?
  14. 14.In a group of 31 children, 12 sing Hindi songs, 6 sing English songs and 2 sing both. How many sing neither of the two?
  15. 15.In a group of 42 children, 11 enjoy drawing, 24 enjoy dancing and 7 enjoy both. How many enjoy only drawing?
  16. 16.In a group of 24 children, 10 sing Hindi songs, 19 sing English songs and 6 sing both. How many sing exactly one of the two?
  17. 17.In a group of 39 children, 18 sing Hindi songs, 19 sing English songs and 3 sing both. How many sing neither of the two?
  18. 18.In a group of 27 children, 22 enjoy drawing, 9 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  19. 19.In a group of 29 children, 22 play cricket, 13 play football and 9 play both. How many play neither of the two?
  20. 20.In a group of 38 children, 8 enjoy drawing, 19 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  21. 21.In a group of 25 children, 14 play chess, 12 play carrom and 2 play both. How many play at least one of the two?
  22. 22.In a group of 45 children, 13 enjoy drawing, 21 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  23. 23.In a group of 36 children, 19 sing Hindi songs, 17 sing English songs and 7 sing both. How many sing neither of the two?
  24. 24.In a group of 28 children, 10 play cricket, 18 play football and 3 play both. How many play only football?
  25. 25.In a group of 36 grown-ups, 25 drink tea, 9 drink coffee and 6 drink both. How many drink neither of the two?
  26. 26.In a group of 48 children, 23 play cricket, 19 play football and 8 play both. How many play only cricket?
  27. 27.In a group of 49 children, 25 play chess, 29 play carrom and 10 play both. How many play only chess?
  28. 28.In a group of 43 children, 11 play chess, 21 play carrom and 3 play both. How many play neither of the two?
  29. 29.In a group of 55 children, 25 sing Hindi songs, 23 sing English songs and 8 sing both. How many sing at least one of the two?
  30. 30.In a group of 36 children, 27 play chess, 10 play carrom and 7 play both. How many play neither of the two?
  31. 31.In a group of 42 children, 12 like mangoes, 19 like bananas and 4 like both. How many like neither of the two?
  32. 32.In a group of 27 grown-ups, 9 drink tea, 9 drink coffee and 3 drink both. How many drink only coffee?
  33. 33.In a group of 45 children, 10 play cricket, 25 play football and 5 play both. How many play only cricket?
  34. 34.In a group of 27 children, 15 play chess, 19 play carrom and 9 play both. How many play at least one of the two?
  35. 35.In a group of 33 children, 19 sing Hindi songs, 10 sing English songs and 3 sing both. How many sing at least one of the two?
  36. 36.In a group of 43 children, 16 play cricket, 25 play football and 9 play both. How many play only football?
  37. 37.In a group of 33 children, 13 play cricket, 16 play football and 2 play both. How many play neither of the two?
  38. 38.In a group of 35 children, 7 like mangoes, 17 like bananas and 3 like both. How many like neither of the two?
  39. 39.In a group of 55 children, 24 play cricket, 30 play football and 11 play both. How many play only football?
  40. 40.In a group of 37 children, 21 play cricket, 25 play football and 11 play both. How many play only football?

Answer key

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

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