Venn diagram questions look busy, but each number sits in its own small region. Read the diagram one region at a time and the answer is simple.
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Q1. In a club, there are 58 members. Among them, 25 members drink tea, 23 members drink coffee and only 7 members drink both tea and coffee. What is the ratio of the number of members who drink tea or coffee but not both, to the number of members who drink neither tea nor coffee? [CAPF (ACs) 2026]
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Answer: D
Tea-only is 25-7=18, coffee-only is 23-7=16, so ‘one but not both’ totals 34. The union is 25+23-7=41, so ‘neither’ is 58-41=17. The ratio 34:17 simplifies to 2:1.
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Q2.
The Venn diagram below shows how many people like English, Hindi, and Sanskrit.
Study the diagram carefully.
How many people like all three of English, Hindi, and Sanskrit?
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Answer: D
The Venn diagram shows how many people like English, Hindi, and Sanskrit. Only English: 21. Only Hindi: 15. Only Sanskrit: 10. English and Hindi only: 8. Hindi and Sanskrit only: 4. English and Sanskrit only: 6. All three: 2. This is the number in the centre region, where all three circles overlap. So the answer is 2.
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Q3.
The Venn diagram below shows how many people like Chess, Carrom, and Badminton.
Study the diagram carefully.
How many people like only Badminton?
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Answer: C
The Venn diagram shows how many people like Chess, Carrom, and Badminton. Only Chess: 14. Only Carrom: 12. Only Badminton: 16. Chess and Carrom only: 6. Carrom and Badminton only: 5. Chess and Badminton only: 7. All three: 3. This question asks for one region’s number directly, with no other region added. So the answer is 16.
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Q4.
The Venn diagram below shows how many people like Newspaper A, Newspaper B, and Newspaper C.
Study the diagram carefully.
How many people in total like at least one of Newspaper A, Newspaper B, or Newspaper C?
Show answer and explanation
Answer: B
The Venn diagram shows how many people like Newspaper A, Newspaper B, and Newspaper C. Only Newspaper A: 25. Only Newspaper B: 20. Only Newspaper C: 16. Newspaper A and Newspaper B only: 10. Newspaper B and Newspaper C only: 8. Newspaper A and Newspaper C only: 6. All three: 5. Add up every region in the diagram, since each region is a different group of people. So the answer is 90.
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Q5.
The Venn diagram below shows how many people like Tea, Coffee, and Milk.
Study the diagram carefully.
How many people like Milk but not Tea?
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Answer: A
The Venn diagram shows how many people like Tea, Coffee, and Milk. Only Tea: 18. Only Coffee: 14. Only Milk: 12. Tea and Coffee only: 9. Coffee and Milk only: 7. Tea and Milk only: 6. All three: 5. Add the only-one region to the one overlap region that excludes the other subject. So the answer is 19.
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Q6.
The Venn diagram below shows how many people like Physics, Chemistry, and Biology.
Study the diagram carefully.
How many people like both Physics and Biology (whether or not they also like the third)?
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Answer: D
The Venn diagram shows how many people like Physics, Chemistry, and Biology. Only Physics: 15. Only Chemistry: 19. Only Biology: 11. Physics and Chemistry only: 7. Chemistry and Biology only: 8. Physics and Biology only: 4. All three: 3. Add the two-way overlap region for this pair to the centre region. So the answer is 7.
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Q7.
The Venn diagram below shows how many people like Cricket, Football, and Hockey.
Study the diagram carefully.
How many people like Hockey (whether or not they like the other two)?
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Answer: C
The Venn diagram shows how many people like Cricket, Football, and Hockey. Only Cricket: 22. Only Football: 17. Only Hockey: 13. Cricket and Football only: 9. Football and Hockey only: 6. Cricket and Hockey only: 5. All three: 4. Add that subject’s own region to every overlap region touching it. So the answer is 28.
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Q8.
The Venn diagram below shows how many people like Painting, Dancing, and Singing.
Study the diagram carefully.
How many people like exactly one of the three: Painting, Dancing, Singing?
Show answer and explanation
Answer: B
The Venn diagram shows how many people like Painting, Dancing, and Singing. Only Painting: 17. Only Dancing: 13. Only Singing: 19. Painting and Dancing only: 6. Dancing and Singing only: 9. Painting and Singing only: 5. All three: 4. Add the three only-one regions, and leave out every overlap region. So the answer is 49.
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Q9.
The Venn diagram below shows how many people like English, Hindi, and Sanskrit.
Study the diagram carefully.
How many people like at least two of the three: English, Hindi, Sanskrit?
Show answer and explanation
Answer: A
The Venn diagram shows how many people like English, Hindi, and Sanskrit. Only English: 21. Only Hindi: 15. Only Sanskrit: 10. English and Hindi only: 8. Hindi and Sanskrit only: 4. English and Sanskrit only: 6. All three: 2. Add the three two-way overlap regions plus the centre region. So the answer is 20.
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Q10.
The Venn diagram below shows how many people like Chess, Carrom, and Badminton.
Study the diagram carefully.
How many people like exactly two of the three subjects: Chess, Carrom, Badminton?
Show answer and explanation
Answer: D
The Venn diagram shows how many people like Chess, Carrom, and Badminton. Only Chess: 14. Only Carrom: 12. Only Badminton: 16. Chess and Carrom only: 6. Carrom and Badminton only: 5. Chess and Badminton only: 7. All three: 3. Add the three two-way overlap regions, but leave out the centre region. So the answer is 18.
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Q11.
The Venn diagram below shows how many people like Newspaper A, Newspaper B, and Newspaper C.
Study the diagram carefully.
How many people like all three of Newspaper A, Newspaper B, and Newspaper C?
Show answer and explanation
Answer: C
The Venn diagram shows how many people like Newspaper A, Newspaper B, and Newspaper C. Only Newspaper A: 25. Only Newspaper B: 20. Only Newspaper C: 16. Newspaper A and Newspaper B only: 10. Newspaper B and Newspaper C only: 8. Newspaper A and Newspaper C only: 6. All three: 5. This is the number in the centre region, where all three circles overlap. So the answer is 5.
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Q12.
The Venn diagram below shows how many people like Tea, Coffee, and Milk.
Study the diagram carefully.
How many people like only Coffee?
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Answer: B
The Venn diagram shows how many people like Tea, Coffee, and Milk. Only Tea: 18. Only Coffee: 14. Only Milk: 12. Tea and Coffee only: 9. Coffee and Milk only: 7. Tea and Milk only: 6. All three: 5. This question asks for one region’s number directly, with no other region added. So the answer is 14.
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Q13.
The Venn diagram below shows how many people like Physics, Chemistry, and Biology.
Study the diagram carefully.
How many people in total like at least one of Physics, Chemistry, or Biology?
Show answer and explanation
Answer: A
The Venn diagram shows how many people like Physics, Chemistry, and Biology. Only Physics: 15. Only Chemistry: 19. Only Biology: 11. Physics and Chemistry only: 7. Chemistry and Biology only: 8. Physics and Biology only: 4. All three: 3. Add up every region in the diagram, since each region is a different group of people. So the answer is 67.
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Q14.
The Venn diagram below shows how many people like Cricket, Football, and Hockey.
Study the diagram carefully.
How many people like Football but not Hockey?
Show answer and explanation
Answer: D
The Venn diagram shows how many people like Cricket, Football, and Hockey. Only Cricket: 22. Only Football: 17. Only Hockey: 13. Cricket and Football only: 9. Football and Hockey only: 6. Cricket and Hockey only: 5. All three: 4. Add the only-one region to the one overlap region that excludes the other subject. So the answer is 26.
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Q15.
The Venn diagram below shows how many people like Painting, Dancing, and Singing.
Study the diagram carefully.
How many people like both Painting and Dancing (whether or not they also like the third)?
Show answer and explanation
Answer: C
The Venn diagram shows how many people like Painting, Dancing, and Singing. Only Painting: 17. Only Dancing: 13. Only Singing: 19. Painting and Dancing only: 6. Dancing and Singing only: 9. Painting and Singing only: 5. All three: 4. Add the two-way overlap region for this pair to the centre region. So the answer is 10.
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Q16.
The Venn diagram below shows how many people like English, Hindi, and Sanskrit.
Study the diagram carefully.
How many people like English (whether or not they like the other two)?
Show answer and explanation
Answer: B
The Venn diagram shows how many people like English, Hindi, and Sanskrit. Only English: 21. Only Hindi: 15. Only Sanskrit: 10. English and Hindi only: 8. Hindi and Sanskrit only: 4. English and Sanskrit only: 6. All three: 2. Add that subject’s own region to every overlap region touching it. So the answer is 37.
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Q17.
The Venn diagram below shows how many people like Chess, Carrom, and Badminton.
Study the diagram carefully.
How many people like exactly one of the three: Chess, Carrom, Badminton?
Show answer and explanation
Answer: A
The Venn diagram shows how many people like Chess, Carrom, and Badminton. Only Chess: 14. Only Carrom: 12. Only Badminton: 16. Chess and Carrom only: 6. Carrom and Badminton only: 5. Chess and Badminton only: 7. All three: 3. Add the three only-one regions, and leave out every overlap region. So the answer is 42.
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Q18.
The Venn diagram below shows how many people like Newspaper A, Newspaper B, and Newspaper C.
Study the diagram carefully.
How many people like at least two of the three: Newspaper A, Newspaper B, Newspaper C?
Show answer and explanation
Answer: D
The Venn diagram shows how many people like Newspaper A, Newspaper B, and Newspaper C. Only Newspaper A: 25. Only Newspaper B: 20. Only Newspaper C: 16. Newspaper A and Newspaper B only: 10. Newspaper B and Newspaper C only: 8. Newspaper A and Newspaper C only: 6. All three: 5. Add the three two-way overlap regions plus the centre region. So the answer is 29.
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Q19.
The Venn diagram below shows how many people like Tea, Coffee, and Milk.
Study the diagram carefully.
How many people like exactly two of the three subjects: Tea, Coffee, Milk?
Show answer and explanation
Answer: C
The Venn diagram shows how many people like Tea, Coffee, and Milk. Only Tea: 18. Only Coffee: 14. Only Milk: 12. Tea and Coffee only: 9. Coffee and Milk only: 7. Tea and Milk only: 6. All three: 5. Add the three two-way overlap regions, but leave out the centre region. So the answer is 22.
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Q20.
The Venn diagram below shows how many people like Physics, Chemistry, and Biology.
Study the diagram carefully.
How many people like all three of Physics, Chemistry, and Biology?
Show answer and explanation
Answer: B
The Venn diagram shows how many people like Physics, Chemistry, and Biology. Only Physics: 15. Only Chemistry: 19. Only Biology: 11. Physics and Chemistry only: 7. Chemistry and Biology only: 8. Physics and Biology only: 4. All three: 3. This is the number in the centre region, where all three circles overlap. So the answer is 3.
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Q21.
The Venn diagram below shows how many people like Cricket, Football, and Hockey.
Study the diagram carefully.
How many people like only Cricket?
Show answer and explanation
Answer: A
The Venn diagram shows how many people like Cricket, Football, and Hockey. Only Cricket: 22. Only Football: 17. Only Hockey: 13. Cricket and Football only: 9. Football and Hockey only: 6. Cricket and Hockey only: 5. All three: 4. This question asks for one region’s number directly, with no other region added. So the answer is 22.
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