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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 296 · 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 children, 22 play chess, 20 play carrom and 4 play both. How many play exactly one of the two?
  2. 2.In a group of 33 children, 11 enjoy drawing, 22 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  3. 3.In a group of 58 children, 25 enjoy drawing, 29 enjoy dancing and 9 enjoy both. How many enjoy at least one of the two?
  4. 4.In a group of 27 children, 18 enjoy drawing, 17 enjoy dancing and 12 enjoy both. How many enjoy only dancing?
  5. 5.In a group of 29 children, 23 like mangoes, 15 like bananas and 11 like both. How many like only mangoes?
  6. 6.In a group of 40 children, 29 enjoy drawing, 14 enjoy dancing and 10 enjoy both. How many enjoy neither of the two?
  7. 7.In a group of 47 children, 26 sing Hindi songs, 18 sing English songs and 6 sing both. How many sing at least one of the two?
  8. 8.In a group of 46 children, 22 play cricket, 24 play football and 4 play both. How many play exactly one of the two?
  9. 9.In a group of 44 children, 18 play chess, 24 play carrom and 8 play both. How many play only carrom?
  10. 10.In a group of 43 children, 26 play chess, 18 play carrom and 8 play both. How many play at least one of the two?
  11. 11.In a group of 36 children, 20 sing Hindi songs, 25 sing English songs and 12 sing both. How many sing exactly one of the two?
  12. 12.In a group of 27 children, 8 sing Hindi songs, 23 sing English songs and 5 sing both. How many sing only English songs?
  13. 13.In a group of 40 children, 23 play chess, 22 play carrom and 10 play both. How many play at least one of the two?
  14. 14.In a group of 37 children, 15 play cricket, 21 play football and 11 play both. How many play at least one of the two?
  15. 15.In a group of 23 children, 9 play chess, 10 play carrom and 4 play both. How many play only chess?
  16. 16.In a group of 38 children, 19 play chess, 30 play carrom and 12 play both. How many play neither of the two?
  17. 17.In a group of 53 children, 30 enjoy drawing, 22 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  18. 18.In a group of 37 children, 16 enjoy drawing, 17 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  19. 19.In a group of 30 children, 6 like mangoes, 23 like bananas and 3 like both. How many like exactly one of the two?
  20. 20.In a group of 42 children, 27 play chess, 13 play carrom and 10 play both. How many play only chess?
  21. 21.In a group of 39 children, 14 play chess, 25 play carrom and 6 play both. How many play only carrom?
  22. 22.In a group of 45 children, 26 play chess, 23 play carrom and 11 play both. How many play neither of the two?
  23. 23.In a group of 27 children, 18 enjoy drawing, 8 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  24. 24.In a group of 40 children, 25 play chess, 12 play carrom and 8 play both. How many play only carrom?
  25. 25.In a group of 44 children, 26 play cricket, 13 play football and 6 play both. How many play only football?
  26. 26.In a group of 35 children, 18 sing Hindi songs, 20 sing English songs and 5 sing both. How many sing only English songs?
  27. 27.In a group of 40 children, 12 like mangoes, 21 like bananas and 8 like both. How many like neither of the two?
  28. 28.In a group of 34 grown-ups, 19 drink tea, 16 drink coffee and 8 drink both. How many drink only tea?
  29. 29.In a group of 22 grown-ups, 13 drink tea, 13 drink coffee and 7 drink both. How many drink at least one of the two?
  30. 30.In a group of 43 children, 20 like mangoes, 11 like bananas and 2 like both. How many like neither of the two?
  31. 31.In a group of 26 children, 12 like mangoes, 11 like bananas and 8 like both. How many like only bananas?
  32. 32.In a group of 53 children, 29 play chess, 21 play carrom and 12 play both. How many play neither of the two?
  33. 33.In a group of 38 children, 9 enjoy drawing, 24 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  34. 34.In a group of 22 grown-ups, 10 drink tea, 15 drink coffee and 7 drink both. How many drink neither of the two?
  35. 35.In a group of 41 children, 18 enjoy drawing, 26 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  36. 36.In a group of 47 children, 26 play cricket, 31 play football and 12 play both. How many play neither of the two?
  37. 37.In a group of 36 children, 17 sing Hindi songs, 18 sing English songs and 12 sing both. How many sing at least one of the two?
  38. 38.In a group of 28 children, 17 play chess, 19 play carrom and 9 play both. How many play only chess?
  39. 39.In a group of 35 children, 12 play cricket, 17 play football and 7 play both. How many play at least one of the two?
  40. 40.In a group of 45 children, 22 play cricket, 23 play football and 9 play both. How many play at least one of the two?

Answer key

  1. 34
  2. 8
  3. 45
  4. 5
  5. 12
  6. 7
  7. 38
  8. 38
  9. 16
  10. 36
  11. 21
  12. 18
  13. 35
  14. 25
  15. 5
  16. 1
  17. 13
  18. 25
  19. 23
  20. 17
  21. 19
  22. 7
  23. 14
  24. 4
  25. 7
  26. 15
  27. 15
  28. 11
  29. 19
  30. 14
  31. 3
  32. 15
  33. 25
  34. 4
  35. 32
  36. 2
  37. 23
  38. 8
  39. 22
  40. 36

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