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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 433 · 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 30 children, 16 play cricket, 13 play football and 6 play both. How many play neither of the two?
  2. 2.In a group of 29 children, 18 enjoy drawing, 8 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  3. 3.In a group of 31 children, 18 like mangoes, 12 like bananas and 9 like both. How many like only bananas?
  4. 4.In a group of 50 children, 24 like mangoes, 25 like bananas and 8 like both. How many like only bananas?
  5. 5.In a group of 46 children, 21 play chess, 25 play carrom and 11 play both. How many play neither of the two?
  6. 6.In a group of 37 children, 18 sing Hindi songs, 8 sing English songs and 4 sing both. How many sing exactly one of the two?
  7. 7.In a group of 26 children, 14 sing Hindi songs, 14 sing English songs and 4 sing both. How many sing only Hindi songs?
  8. 8.In a group of 46 children, 26 sing Hindi songs, 16 sing English songs and 11 sing both. How many sing only Hindi songs?
  9. 9.In a group of 27 children, 22 play cricket, 8 play football and 4 play both. How many play exactly one of the two?
  10. 10.In a group of 32 children, 16 play cricket, 18 play football and 5 play both. How many play only cricket?
  11. 11.In a group of 25 children, 14 like mangoes, 13 like bananas and 10 like both. How many like only mangoes?
  12. 12.In a group of 44 children, 27 like mangoes, 21 like bananas and 7 like both. How many like neither of the two?
  13. 13.In a group of 37 children, 10 enjoy drawing, 15 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  14. 14.In a group of 31 children, 22 play cricket, 15 play football and 9 play both. How many play neither of the two?
  15. 15.In a group of 35 grown-ups, 14 drink tea, 17 drink coffee and 2 drink both. How many drink at least one of the two?
  16. 16.In a group of 26 children, 9 play chess, 17 play carrom and 3 play both. How many play at least one of the two?
  17. 17.In a group of 40 children, 24 play cricket, 11 play football and 8 play both. How many play only cricket?
  18. 18.In a group of 29 children, 15 sing Hindi songs, 14 sing English songs and 5 sing both. How many sing at least one of the two?
  19. 19.In a group of 39 children, 20 enjoy drawing, 18 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  20. 20.In a group of 25 children, 16 play cricket, 13 play football and 9 play both. How many play exactly one of the two?
  21. 21.In a group of 34 children, 15 play cricket, 12 play football and 5 play both. How many play at least one of the two?
  22. 22.In a group of 49 children, 24 play cricket, 23 play football and 4 play both. How many play at least one of the two?
  23. 23.In a group of 20 grown-ups, 8 drink tea, 9 drink coffee and 2 drink both. How many drink exactly one of the two?
  24. 24.In a group of 22 children, 6 sing Hindi songs, 17 sing English songs and 2 sing both. How many sing exactly one of the two?
  25. 25.In a group of 27 children, 18 play chess, 15 play carrom and 12 play both. How many play only chess?
  26. 26.In a group of 34 grown-ups, 5 drink tea, 17 drink coffee and 2 drink both. How many drink neither of the two?
  27. 27.In a group of 37 children, 30 play chess, 14 play carrom and 10 play both. How many play only chess?
  28. 28.In a group of 44 children, 25 enjoy drawing, 16 enjoy dancing and 12 enjoy both. How many enjoy exactly one of the two?
  29. 29.In a group of 20 children, 13 play chess, 13 play carrom and 7 play both. How many play exactly one of the two?
  30. 30.In a group of 53 children, 29 play cricket, 29 play football and 11 play both. How many play only football?
  31. 31.In a group of 39 children, 19 enjoy drawing, 20 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  32. 32.In a group of 41 children, 19 play cricket, 19 play football and 12 play both. How many play exactly one of the two?
  33. 33.In a group of 45 children, 28 enjoy drawing, 16 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  34. 34.In a group of 29 children, 16 play cricket, 10 play football and 5 play both. How many play at least one of the two?
  35. 35.In a group of 36 children, 14 play cricket, 30 play football and 11 play both. How many play at least one of the two?
  36. 36.In a group of 44 children, 15 enjoy drawing, 25 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  37. 37.In a group of 23 children, 7 enjoy drawing, 7 enjoy dancing and 2 enjoy both. How many enjoy at least one of the two?
  38. 38.In a group of 51 grown-ups, 21 drink tea, 22 drink coffee and 3 drink both. How many drink exactly one of the two?
  39. 39.In a group of 42 children, 18 enjoy drawing, 25 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  40. 40.In a group of 25 children, 14 play chess, 16 play carrom and 7 play both. How many play neither of the two?

Answer key

  1. 7
  2. 6
  3. 3
  4. 17
  5. 11
  6. 18
  7. 10
  8. 15
  9. 22
  10. 11
  11. 4
  12. 3
  13. 13
  14. 3
  15. 29
  16. 23
  17. 16
  18. 24
  19. 9
  20. 11
  21. 22
  22. 43
  23. 13
  24. 19
  25. 6
  26. 14
  27. 20
  28. 17
  29. 12
  30. 18
  31. 7
  32. 14
  33. 20
  34. 21
  35. 33
  36. 7
  37. 12
  38. 37
  39. 34
  40. 2

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