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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 282 · 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 36 children, 14 play chess, 17 play carrom and 3 play both. How many play at least one of the two?
  2. 2.In a group of 38 children, 21 sing Hindi songs, 20 sing English songs and 5 sing both. How many sing at least one of the two?
  3. 3.In a group of 24 children, 13 play chess, 11 play carrom and 3 play both. How many play neither of the two?
  4. 4.In a group of 20 grown-ups, 12 drink tea, 7 drink coffee and 2 drink both. How many drink exactly one of the two?
  5. 5.In a group of 36 children, 22 enjoy drawing, 20 enjoy dancing and 10 enjoy both. How many enjoy exactly one of the two?
  6. 6.In a group of 38 children, 14 play cricket, 24 play football and 7 play both. How many play exactly one of the two?
  7. 7.In a group of 46 children, 30 play cricket, 17 play football and 10 play both. How many play only football?
  8. 8.In a group of 42 children, 19 play chess, 21 play carrom and 7 play both. How many play exactly one of the two?
  9. 9.In a group of 35 grown-ups, 21 drink tea, 15 drink coffee and 7 drink both. How many drink neither of the two?
  10. 10.In a group of 28 children, 16 enjoy drawing, 17 enjoy dancing and 7 enjoy both. How many enjoy exactly one of the two?
  11. 11.In a group of 41 children, 20 like mangoes, 21 like bananas and 2 like both. How many like exactly one of the two?
  12. 12.In a group of 20 grown-ups, 10 drink tea, 7 drink coffee and 4 drink both. How many drink only coffee?
  13. 13.In a group of 26 children, 11 enjoy drawing, 16 enjoy dancing and 8 enjoy both. How many enjoy only dancing?
  14. 14.In a group of 29 children, 21 play cricket, 14 play football and 7 play both. How many play only cricket?
  15. 15.In a group of 19 children, 12 like mangoes, 10 like bananas and 6 like both. How many like only mangoes?
  16. 16.In a group of 42 children, 21 play chess, 9 play carrom and 3 play both. How many play exactly one of the two?
  17. 17.In a group of 52 children, 24 like mangoes, 29 like bananas and 9 like both. How many like only bananas?
  18. 18.In a group of 26 children, 12 enjoy drawing, 15 enjoy dancing and 5 enjoy both. How many enjoy only drawing?
  19. 19.In a group of 40 children, 21 sing Hindi songs, 21 sing English songs and 4 sing both. How many sing neither of the two?
  20. 20.In a group of 42 children, 20 like mangoes, 26 like bananas and 10 like both. How many like at least one of the two?
  21. 21.In a group of 35 grown-ups, 20 drink tea, 23 drink coffee and 11 drink both. How many drink only coffee?
  22. 22.In a group of 43 children, 17 like mangoes, 19 like bananas and 2 like both. How many like only mangoes?
  23. 23.In a group of 21 children, 8 enjoy drawing, 14 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  24. 24.In a group of 33 children, 13 sing Hindi songs, 22 sing English songs and 6 sing both. How many sing only Hindi songs?
  25. 25.In a group of 29 children, 12 enjoy drawing, 23 enjoy dancing and 9 enjoy both. How many enjoy only dancing?
  26. 26.In a group of 43 children, 19 like mangoes, 15 like bananas and 4 like both. How many like only mangoes?
  27. 27.In a group of 20 children, 10 enjoy drawing, 13 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  28. 28.In a group of 46 children, 27 like mangoes, 19 like bananas and 12 like both. How many like at least one of the two?
  29. 29.In a group of 45 children, 24 sing Hindi songs, 23 sing English songs and 5 sing both. How many sing only Hindi songs?
  30. 30.In a group of 54 children, 23 play cricket, 23 play football and 7 play both. How many play at least one of the two?
  31. 31.In a group of 50 children, 28 play cricket, 26 play football and 12 play both. How many play exactly one of the two?
  32. 32.In a group of 29 grown-ups, 12 drink tea, 12 drink coffee and 8 drink both. How many drink only tea?
  33. 33.In a group of 42 children, 10 play cricket, 24 play football and 6 play both. How many play exactly one of the two?
  34. 34.In a group of 27 children, 13 play cricket, 13 play football and 6 play both. How many play exactly one of the two?
  35. 35.In a group of 29 children, 16 play cricket, 10 play football and 2 play both. How many play neither of the two?
  36. 36.In a group of 38 children, 13 sing Hindi songs, 21 sing English songs and 4 sing both. How many sing exactly one of the two?
  37. 37.In a group of 34 grown-ups, 13 drink tea, 23 drink coffee and 4 drink both. How many drink at least one of the two?
  38. 38.In a group of 44 children, 16 play cricket, 26 play football and 8 play both. How many play only cricket?
  39. 39.In a group of 46 children, 22 play chess, 17 play carrom and 5 play both. How many play neither of the two?
  40. 40.In a group of 40 children, 18 play cricket, 16 play football and 2 play both. How many play neither of the two?

Answer key

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

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