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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 502 · 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 35 children, 8 play chess, 21 play carrom and 3 play both. How many play neither of the two?
  2. 2.In a group of 41 children, 24 play chess, 17 play carrom and 12 play both. How many play only carrom?
  3. 3.In a group of 35 children, 13 enjoy drawing, 18 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  4. 4.In a group of 28 children, 21 sing Hindi songs, 6 sing English songs and 3 sing both. How many sing only English songs?
  5. 5.In a group of 37 children, 22 play cricket, 16 play football and 4 play both. How many play only football?
  6. 6.In a group of 45 children, 22 enjoy drawing, 15 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  7. 7.In a group of 37 children, 10 play chess, 25 play carrom and 6 play both. How many play at least one of the two?
  8. 8.In a group of 38 children, 19 sing Hindi songs, 25 sing English songs and 11 sing both. How many sing only English songs?
  9. 9.In a group of 24 children, 15 play cricket, 15 play football and 9 play both. How many play only cricket?
  10. 10.In a group of 48 children, 25 sing Hindi songs, 17 sing English songs and 5 sing both. How many sing exactly one of the two?
  11. 11.In a group of 38 children, 12 play cricket, 18 play football and 6 play both. How many play neither of the two?
  12. 12.In a group of 38 children, 19 sing Hindi songs, 13 sing English songs and 8 sing both. How many sing only English songs?
  13. 13.In a group of 40 children, 18 enjoy drawing, 26 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  14. 14.In a group of 27 children, 21 like mangoes, 13 like bananas and 9 like both. How many like neither of the two?
  15. 15.In a group of 47 children, 26 play chess, 27 play carrom and 10 play both. How many play at least one of the two?
  16. 16.In a group of 31 grown-ups, 15 drink tea, 26 drink coffee and 12 drink both. How many drink only coffee?
  17. 17.In a group of 35 children, 15 enjoy drawing, 22 enjoy dancing and 8 enjoy both. How many enjoy only drawing?
  18. 18.In a group of 45 children, 29 sing Hindi songs, 15 sing English songs and 9 sing both. How many sing at least one of the two?
  19. 19.In a group of 20 children, 13 play cricket, 11 play football and 8 play both. How many play only football?
  20. 20.In a group of 47 children, 24 play cricket, 27 play football and 8 play both. How many play exactly one of the two?
  21. 21.In a group of 35 children, 18 enjoy drawing, 26 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  22. 22.In a group of 54 children, 29 like mangoes, 23 like bananas and 9 like both. How many like neither of the two?
  23. 23.In a group of 51 children, 24 play cricket, 23 play football and 4 play both. How many play only cricket?
  24. 24.In a group of 25 grown-ups, 11 drink tea, 16 drink coffee and 6 drink both. How many drink exactly one of the two?
  25. 25.In a group of 36 children, 26 sing Hindi songs, 12 sing English songs and 8 sing both. How many sing only Hindi songs?
  26. 26.In a group of 58 children, 25 enjoy drawing, 27 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  27. 27.In a group of 33 grown-ups, 15 drink tea, 13 drink coffee and 8 drink both. How many drink neither of the two?
  28. 28.In a group of 38 children, 27 play chess, 14 play carrom and 7 play both. How many play exactly one of the two?
  29. 29.In a group of 43 children, 16 sing Hindi songs, 24 sing English songs and 8 sing both. How many sing only English songs?
  30. 30.In a group of 37 children, 17 like mangoes, 12 like bananas and 7 like both. How many like at least one of the two?
  31. 31.In a group of 27 children, 9 enjoy drawing, 12 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  32. 32.In a group of 44 children, 27 play chess, 19 play carrom and 7 play both. How many play neither of the two?
  33. 33.In a group of 34 grown-ups, 23 drink tea, 16 drink coffee and 8 drink both. How many drink only tea?
  34. 34.In a group of 53 children, 19 play cricket, 32 play football and 12 play both. How many play only cricket?
  35. 35.In a group of 47 children, 18 sing Hindi songs, 19 sing English songs and 5 sing both. How many sing only Hindi songs?
  36. 36.In a group of 45 children, 12 sing Hindi songs, 23 sing English songs and 3 sing both. How many sing exactly one of the two?
  37. 37.In a group of 33 children, 14 like mangoes, 24 like bananas and 6 like both. How many like exactly one of the two?
  38. 38.In a group of 23 children, 15 enjoy drawing, 17 enjoy dancing and 11 enjoy both. How many enjoy neither of the two?
  39. 39.In a group of 36 children, 14 sing Hindi songs, 11 sing English songs and 2 sing both. How many sing only English songs?
  40. 40.In a group of 43 children, 25 like mangoes, 25 like bananas and 9 like both. How many like neither of the two?

Answer key

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

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