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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 168 · 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 41 children, 12 like mangoes, 26 like bananas and 6 like both. How many like exactly one of the two?
  2. 2.In a group of 33 children, 11 sing Hindi songs, 24 sing English songs and 5 sing both. How many sing only English songs?
  3. 3.In a group of 28 children, 21 play cricket, 17 play football and 12 play both. How many play at least one of the two?
  4. 4.In a group of 28 children, 17 enjoy drawing, 12 enjoy dancing and 9 enjoy both. How many enjoy only drawing?
  5. 5.In a group of 27 children, 13 enjoy drawing, 15 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  6. 6.In a group of 35 children, 20 play chess, 19 play carrom and 9 play both. How many play only chess?
  7. 7.In a group of 48 grown-ups, 21 drink tea, 25 drink coffee and 10 drink both. How many drink only coffee?
  8. 8.In a group of 46 children, 32 play cricket, 15 play football and 12 play both. How many play only football?
  9. 9.In a group of 47 children, 17 like mangoes, 26 like bananas and 9 like both. How many like only bananas?
  10. 10.In a group of 40 children, 19 sing Hindi songs, 20 sing English songs and 7 sing both. How many sing at least one of the two?
  11. 11.In a group of 25 grown-ups, 17 drink tea, 17 drink coffee and 11 drink both. How many drink only tea?
  12. 12.In a group of 29 grown-ups, 11 drink tea, 9 drink coffee and 5 drink both. How many drink exactly one of the two?
  13. 13.In a group of 43 grown-ups, 19 drink tea, 27 drink coffee and 7 drink both. How many drink only tea?
  14. 14.In a group of 38 children, 10 play cricket, 21 play football and 7 play both. How many play neither of the two?
  15. 15.In a group of 25 children, 17 like mangoes, 14 like bananas and 10 like both. How many like exactly one of the two?
  16. 16.In a group of 32 children, 24 enjoy drawing, 10 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  17. 17.In a group of 38 children, 22 like mangoes, 5 like bananas and 2 like both. How many like only bananas?
  18. 18.In a group of 33 children, 9 like mangoes, 12 like bananas and 3 like both. How many like exactly one of the two?
  19. 19.In a group of 20 children, 9 sing Hindi songs, 11 sing English songs and 3 sing both. How many sing exactly one of the two?
  20. 20.In a group of 46 children, 20 like mangoes, 20 like bananas and 5 like both. How many like only mangoes?
  21. 21.In a group of 38 children, 23 like mangoes, 17 like bananas and 11 like both. How many like only bananas?
  22. 22.In a group of 46 children, 23 enjoy drawing, 28 enjoy dancing and 11 enjoy both. How many enjoy only dancing?
  23. 23.In a group of 39 children, 24 like mangoes, 10 like bananas and 6 like both. How many like only bananas?
  24. 24.In a group of 43 children, 14 play cricket, 29 play football and 11 play both. How many play exactly one of the two?
  25. 25.In a group of 34 children, 18 sing Hindi songs, 6 sing English songs and 2 sing both. How many sing only Hindi songs?
  26. 26.In a group of 28 children, 12 play chess, 20 play carrom and 7 play both. How many play neither of the two?
  27. 27.In a group of 35 children, 15 like mangoes, 14 like bananas and 6 like both. How many like neither of the two?
  28. 28.In a group of 54 grown-ups, 32 drink tea, 24 drink coffee and 12 drink both. How many drink neither of the two?
  29. 29.In a group of 40 children, 13 like mangoes, 24 like bananas and 5 like both. How many like neither of the two?
  30. 30.In a group of 55 children, 25 like mangoes, 25 like bananas and 6 like both. How many like only mangoes?
  31. 31.In a group of 33 children, 21 play cricket, 16 play football and 5 play both. How many play only cricket?
  32. 32.In a group of 35 children, 14 play cricket, 17 play football and 2 play both. How many play neither of the two?
  33. 33.In a group of 33 children, 8 enjoy drawing, 22 enjoy dancing and 4 enjoy both. How many enjoy exactly one of the two?
  34. 34.In a group of 24 grown-ups, 14 drink tea, 14 drink coffee and 7 drink both. How many drink only tea?
  35. 35.In a group of 28 children, 15 like mangoes, 23 like bananas and 12 like both. How many like at least one of the two?
  36. 36.In a group of 30 children, 23 enjoy drawing, 11 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  37. 37.In a group of 46 children, 20 enjoy drawing, 18 enjoy dancing and 3 enjoy both. How many enjoy only drawing?
  38. 38.In a group of 44 children, 30 enjoy drawing, 23 enjoy dancing and 10 enjoy both. How many enjoy only drawing?
  39. 39.In a group of 36 children, 19 sing Hindi songs, 9 sing English songs and 5 sing both. How many sing only Hindi songs?
  40. 40.In a group of 51 children, 25 enjoy drawing, 24 enjoy dancing and 7 enjoy both. How many enjoy only dancing?

Answer key

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

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