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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 49 · 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 40 children, 19 play cricket, 19 play football and 6 play both. How many play exactly one of the two?
  2. 2.In a group of 29 children, 8 play chess, 14 play carrom and 4 play both. How many play exactly one of the two?
  3. 3.In a group of 43 children, 28 enjoy drawing, 25 enjoy dancing and 11 enjoy both. How many enjoy only drawing?
  4. 4.In a group of 44 children, 19 play chess, 23 play carrom and 7 play both. How many play only chess?
  5. 5.In a group of 29 children, 9 play cricket, 18 play football and 6 play both. How many play only cricket?
  6. 6.In a group of 19 children, 11 enjoy drawing, 10 enjoy dancing and 6 enjoy both. How many enjoy only dancing?
  7. 7.In a group of 35 children, 20 play cricket, 6 play football and 2 play both. How many play at least one of the two?
  8. 8.In a group of 35 children, 11 enjoy drawing, 25 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  9. 9.In a group of 28 children, 17 like mangoes, 10 like bananas and 7 like both. How many like only mangoes?
  10. 10.In a group of 21 children, 11 play cricket, 10 play football and 6 play both. How many play exactly one of the two?
  11. 11.In a group of 36 children, 9 enjoy drawing, 25 enjoy dancing and 5 enjoy both. How many enjoy only dancing?
  12. 12.In a group of 32 children, 20 enjoy drawing, 12 enjoy dancing and 5 enjoy both. How many enjoy exactly one of the two?
  13. 13.In a group of 52 children, 22 enjoy drawing, 28 enjoy dancing and 11 enjoy both. How many enjoy at least one of the two?
  14. 14.In a group of 37 children, 28 sing Hindi songs, 17 sing English songs and 9 sing both. How many sing only Hindi songs?
  15. 15.In a group of 53 children, 26 like mangoes, 32 like bananas and 12 like both. How many like only mangoes?
  16. 16.In a group of 31 children, 20 play cricket, 11 play football and 4 play both. How many play neither of the two?
  17. 17.In a group of 44 children, 17 like mangoes, 20 like bananas and 8 like both. How many like neither of the two?
  18. 18.In a group of 39 children, 31 enjoy drawing, 16 enjoy dancing and 12 enjoy both. How many enjoy at least one of the two?
  19. 19.In a group of 23 children, 11 play cricket, 13 play football and 2 play both. How many play only football?
  20. 20.In a group of 20 grown-ups, 15 drink tea, 16 drink coffee and 12 drink both. How many drink exactly one of the two?
  21. 21.In a group of 43 children, 9 play chess, 21 play carrom and 2 play both. How many play neither of the two?
  22. 22.In a group of 46 grown-ups, 29 drink tea, 23 drink coffee and 9 drink both. How many drink neither of the two?
  23. 23.In a group of 47 children, 21 play cricket, 23 play football and 5 play both. How many play only cricket?
  24. 24.In a group of 24 children, 15 play chess, 11 play carrom and 5 play both. How many play at least one of the two?
  25. 25.In a group of 43 children, 17 sing Hindi songs, 17 sing English songs and 5 sing both. How many sing only English songs?
  26. 26.In a group of 37 children, 27 like mangoes, 14 like bananas and 7 like both. How many like exactly one of the two?
  27. 27.In a group of 29 children, 13 sing Hindi songs, 14 sing English songs and 2 sing both. How many sing exactly one of the two?
  28. 28.In a group of 55 children, 29 sing Hindi songs, 21 sing English songs and 10 sing both. How many sing at least one of the two?
  29. 29.In a group of 41 children, 30 play cricket, 17 play football and 11 play both. How many play exactly one of the two?
  30. 30.In a group of 39 children, 23 play chess, 16 play carrom and 9 play both. How many play neither of the two?
  31. 31.In a group of 38 children, 22 like mangoes, 18 like bananas and 9 like both. How many like only bananas?
  32. 32.In a group of 17 children, 10 play cricket, 8 play football and 5 play both. How many play neither of the two?
  33. 33.In a group of 33 children, 16 enjoy drawing, 14 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  34. 34.In a group of 37 children, 14 play chess, 17 play carrom and 2 play both. How many play neither of the two?
  35. 35.In a group of 38 children, 15 play chess, 15 play carrom and 7 play both. How many play exactly one of the two?
  36. 36.In a group of 38 children, 14 play cricket, 13 play football and 2 play both. How many play at least one of the two?
  37. 37.In a group of 32 children, 17 play cricket, 14 play football and 3 play both. How many play only football?
  38. 38.In a group of 26 children, 20 play chess, 15 play carrom and 11 play both. How many play only carrom?
  39. 39.In a group of 40 children, 17 play cricket, 15 play football and 4 play both. How many play at least one of the two?
  40. 40.In a group of 45 grown-ups, 25 drink tea, 26 drink coffee and 12 drink both. How many drink at least one of the two?

Answer key

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

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