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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 228 · 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, 23 play cricket, 18 play football and 8 play both. How many play exactly one of the two?
  2. 2.In a group of 32 children, 12 sing Hindi songs, 16 sing English songs and 6 sing both. How many sing neither of the two?
  3. 3.In a group of 43 grown-ups, 24 drink tea, 14 drink coffee and 10 drink both. How many drink neither of the two?
  4. 4.In a group of 28 children, 14 play cricket, 16 play football and 9 play both. How many play only cricket?
  5. 5.In a group of 29 children, 14 like mangoes, 16 like bananas and 11 like both. How many like exactly one of the two?
  6. 6.In a group of 14 children, 6 enjoy drawing, 6 enjoy dancing and 2 enjoy both. How many enjoy only dancing?
  7. 7.In a group of 45 children, 22 play cricket, 29 play football and 11 play both. How many play neither of the two?
  8. 8.In a group of 48 grown-ups, 28 drink tea, 18 drink coffee and 10 drink both. How many drink exactly one of the two?
  9. 9.In a group of 33 children, 5 play cricket, 20 play football and 2 play both. How many play neither of the two?
  10. 10.In a group of 40 children, 16 like mangoes, 15 like bananas and 2 like both. How many like only bananas?
  11. 11.In a group of 38 children, 15 play cricket, 19 play football and 11 play both. How many play at least one of the two?
  12. 12.In a group of 40 children, 27 enjoy drawing, 21 enjoy dancing and 10 enjoy both. How many enjoy only dancing?
  13. 13.In a group of 29 children, 19 sing Hindi songs, 10 sing English songs and 4 sing both. How many sing only Hindi songs?
  14. 14.In a group of 40 children, 10 sing Hindi songs, 22 sing English songs and 3 sing both. How many sing only English songs?
  15. 15.In a group of 45 children, 13 play cricket, 24 play football and 4 play both. How many play only football?
  16. 16.In a group of 30 children, 21 like mangoes, 9 like bananas and 6 like both. How many like only bananas?
  17. 17.In a group of 39 children, 19 like mangoes, 28 like bananas and 9 like both. How many like only bananas?
  18. 18.In a group of 36 children, 11 play cricket, 19 play football and 5 play both. How many play only cricket?
  19. 19.In a group of 16 children, 10 play cricket, 8 play football and 5 play both. How many play exactly one of the two?
  20. 20.In a group of 39 children, 16 sing Hindi songs, 16 sing English songs and 6 sing both. How many sing at least one of the two?
  21. 21.In a group of 30 children, 15 play chess, 16 play carrom and 11 play both. How many play exactly one of the two?
  22. 22.In a group of 40 children, 15 enjoy drawing, 29 enjoy dancing and 12 enjoy both. How many enjoy neither of the two?
  23. 23.In a group of 32 children, 19 like mangoes, 14 like bananas and 10 like both. How many like only mangoes?
  24. 24.In a group of 31 children, 7 sing Hindi songs, 21 sing English songs and 2 sing both. How many sing at least one of the two?
  25. 25.In a group of 16 children, 11 like mangoes, 9 like bananas and 6 like both. How many like exactly one of the two?
  26. 26.In a group of 53 children, 28 play cricket, 21 play football and 10 play both. How many play exactly one of the two?
  27. 27.In a group of 40 children, 16 play cricket, 14 play football and 4 play both. How many play only football?
  28. 28.In a group of 36 children, 23 sing Hindi songs, 17 sing English songs and 11 sing both. How many sing at least one of the two?
  29. 29.In a group of 45 children, 10 enjoy drawing, 27 enjoy dancing and 7 enjoy both. How many enjoy at least one of the two?
  30. 30.In a group of 27 children, 13 sing Hindi songs, 16 sing English songs and 3 sing both. How many sing only Hindi songs?
  31. 31.In a group of 40 children, 25 play cricket, 20 play football and 8 play both. How many play neither of the two?
  32. 32.In a group of 31 grown-ups, 12 drink tea, 24 drink coffee and 6 drink both. How many drink at least one of the two?
  33. 33.In a group of 42 children, 26 play cricket, 23 play football and 8 play both. How many play only cricket?
  34. 34.In a group of 30 children, 17 like mangoes, 17 like bananas and 8 like both. How many like only mangoes?
  35. 35.In a group of 45 children, 21 play chess, 23 play carrom and 8 play both. How many play at least one of the two?
  36. 36.In a group of 29 children, 14 enjoy drawing, 15 enjoy dancing and 4 enjoy both. How many enjoy neither of the two?
  37. 37.In a group of 34 grown-ups, 23 drink tea, 17 drink coffee and 11 drink both. How many drink only tea?
  38. 38.In a group of 24 children, 11 like mangoes, 14 like bananas and 8 like both. How many like exactly one of the two?
  39. 39.In a group of 34 children, 13 play cricket, 19 play football and 10 play both. How many play only cricket?
  40. 40.In a group of 36 children, 6 enjoy drawing, 19 enjoy dancing and 3 enjoy both. How many enjoy exactly one of the two?

Answer key

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

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