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Venn Diagram Worksheet

Logical reasoning lesson 22: Venn diagrams · Set 367 · 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 48 children, 26 sing Hindi songs, 32 sing English songs and 12 sing both. How many sing only English songs?
  2. 2.In a group of 31 children, 15 sing Hindi songs, 22 sing English songs and 11 sing both. How many sing at least one of the two?
  3. 3.In a group of 29 children, 10 like mangoes, 9 like bananas and 3 like both. How many like only bananas?
  4. 4.In a group of 35 children, 18 enjoy drawing, 12 enjoy dancing and 7 enjoy both. How many enjoy neither of the two?
  5. 5.In a group of 52 children, 25 like mangoes, 19 like bananas and 5 like both. How many like exactly one of the two?
  6. 6.In a group of 31 children, 13 enjoy drawing, 21 enjoy dancing and 10 enjoy both. How many enjoy at least one of the two?
  7. 7.In a group of 26 children, 12 play cricket, 13 play football and 3 play both. How many play only football?
  8. 8.In a group of 37 children, 24 sing Hindi songs, 11 sing English songs and 5 sing both. How many sing at least one of the two?
  9. 9.In a group of 39 children, 16 play chess, 20 play carrom and 7 play both. How many play at least one of the two?
  10. 10.In a group of 23 children, 9 sing Hindi songs, 18 sing English songs and 5 sing both. How many sing exactly one of the two?
  11. 11.In a group of 39 children, 26 sing Hindi songs, 19 sing English songs and 7 sing both. How many sing only Hindi songs?
  12. 12.In a group of 52 children, 26 play cricket, 26 play football and 9 play both. How many play at least one of the two?
  13. 13.In a group of 43 children, 18 play cricket, 23 play football and 3 play both. How many play only football?
  14. 14.In a group of 29 children, 20 sing Hindi songs, 14 sing English songs and 8 sing both. How many sing at least one of the two?
  15. 15.In a group of 48 children, 22 play chess, 16 play carrom and 4 play both. How many play neither of the two?
  16. 16.In a group of 18 children, 12 enjoy drawing, 9 enjoy dancing and 4 enjoy both. How many enjoy only drawing?
  17. 17.In a group of 51 children, 31 sing Hindi songs, 31 sing English songs and 12 sing both. How many sing only English songs?
  18. 18.In a group of 36 children, 12 sing Hindi songs, 27 sing English songs and 7 sing both. How many sing only Hindi songs?
  19. 19.In a group of 35 children, 15 enjoy drawing, 21 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  20. 20.In a group of 32 children, 13 enjoy drawing, 17 enjoy dancing and 3 enjoy both. How many enjoy only dancing?
  21. 21.In a group of 34 children, 22 play cricket, 16 play football and 9 play both. How many play exactly one of the two?
  22. 22.In a group of 42 children, 20 play cricket, 20 play football and 11 play both. How many play only cricket?
  23. 23.In a group of 36 grown-ups, 13 drink tea, 22 drink coffee and 5 drink both. How many drink exactly one of the two?
  24. 24.In a group of 41 children, 10 enjoy drawing, 21 enjoy dancing and 4 enjoy both. How many enjoy at least one of the two?
  25. 25.In a group of 16 children, 12 play cricket, 5 play football and 2 play both. How many play only cricket?
  26. 26.In a group of 21 children, 14 play cricket, 12 play football and 7 play both. How many play at least one of the two?
  27. 27.In a group of 39 children, 27 like mangoes, 19 like bananas and 10 like both. How many like only mangoes?
  28. 28.In a group of 43 children, 29 sing Hindi songs, 15 sing English songs and 11 sing both. How many sing only English songs?
  29. 29.In a group of 43 children, 19 like mangoes, 14 like bananas and 2 like both. How many like neither of the two?
  30. 30.In a group of 40 children, 19 play cricket, 11 play football and 5 play both. How many play only cricket?
  31. 31.In a group of 54 children, 24 sing Hindi songs, 29 sing English songs and 9 sing both. How many sing at least one of the two?
  32. 32.In a group of 32 children, 18 like mangoes, 21 like bananas and 11 like both. How many like at least one of the two?
  33. 33.In a group of 35 children, 18 like mangoes, 15 like bananas and 2 like both. How many like at least one of the two?
  34. 34.In a group of 23 children, 11 play cricket, 8 play football and 5 play both. How many play only football?
  35. 35.In a group of 43 children, 27 enjoy drawing, 15 enjoy dancing and 11 enjoy both. How many enjoy exactly one of the two?
  36. 36.In a group of 47 children, 24 play chess, 24 play carrom and 5 play both. How many play only chess?
  37. 37.In a group of 38 children, 13 play cricket, 27 play football and 7 play both. How many play only cricket?
  38. 38.In a group of 22 children, 13 like mangoes, 12 like bananas and 8 like both. How many like neither of the two?
  39. 39.In a group of 53 children, 24 play cricket, 24 play football and 9 play both. How many play exactly one of the two?
  40. 40.In a group of 34 children, 16 sing Hindi songs, 8 sing English songs and 2 sing both. How many sing only English songs?

Answer key

  1. 20
  2. 26
  3. 6
  4. 12
  5. 34
  6. 24
  7. 10
  8. 30
  9. 29
  10. 17
  11. 19
  12. 43
  13. 20
  14. 26
  15. 14
  16. 8
  17. 19
  18. 5
  19. 18
  20. 14
  21. 20
  22. 9
  23. 25
  24. 27
  25. 10
  26. 19
  27. 17
  28. 4
  29. 12
  30. 14
  31. 44
  32. 28
  33. 31
  34. 3
  35. 20
  36. 19
  37. 6
  38. 5
  39. 30
  40. 6

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