Pariksha SaathiReasoning
Venn Diagram: Practice Questions with Answers
19 practice questions on Venn Diagram, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.
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Q.1
In a survey of 100 people, 60 read Newspaper A, 40 read Newspaper B, and 25 read both. How many read only Newspaper A? How many read only Newspaper B?
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Answer: Only A = 35, Only B = 15
Solution:
- Only A = A − Both = 60 − 25 = 35.
- Only B = B − Both = 40 − 25 = 15.
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Q.2
In a group of 70 students, 40 play Chess, 35 play Carrom, and 10 play neither game. How many play both Chess and Carrom?
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Answer: 15
Solution:
- At least one = Total − Neither = 70 − 10 = 60.
- Both = Chess + Carrom − At least one = 40 + 35 − 60 = 15.
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Q.3
In a group of 50 people, 20 speak Hindi, 25 speak English, and 10 speak both languages. How many speak neither Hindi nor English?
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Answer: 15
Solution:
- At least one = 20 + 25 − 10 = 35.
- Neither = 50 − 35 = 15.
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Q.4
In a class of 100 students, 50 play Cricket, 40 play Football, 30 play Hockey. 15 play both Cricket and Football, 12 play both Football and Hockey, 10 play both Cricket and Hockey, and 5 play all three games. How many students play at least one of the three games?
Show answer
Answer: 88
Solution:
- Apply the three-set formula: 50 + 40 + 30 − 15 − 12 − 10 + 5.
- = 120 − 37 + 5 = 88.
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Q.5
In a class of 60 students, 35 like Mathematics, 30 like Science, and 15 like both subjects. How many students like at least one of the two subjects? How many like neither?
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Answer: At least one = 50, Neither = 10
Solution:
- At least one = Mathematics + Science − Both = 35 + 30 − 15 = 50.
- Neither = Total − At least one = 60 − 50 = 10.
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Q.6
Using the same class of 100 students (Cricket/Football/Hockey data above), how many play Cricket only (and neither of the other two games)?
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Answer: 30
Solution:
- Only Cricket = Cricket − (Cricket∩Football) − (Cricket∩Hockey) + (all three).
- = 50 − 15 − 10 + 5 = 30.
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Q.7
In a class of 50 students, 28 like Painting, 22 like Dancing, and 10 like both. How many like at least one activity? How many like neither?
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Q.8
Using the same 150-person Cricket/Football/Tennis data above, how many like exactly two of the three sports (not all three)?
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Q.9
In a group of 150 people, 70 like Cricket, 60 like Football, 50 like Tennis. 20 like both Cricket and Football, 15 like both Football and Tennis, 18 like both Cricket and Tennis, and 8 like all three sports. How many like at least one of the three sports?
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Q.10
In a survey of 80 people, 45 drink Tea, 35 drink Coffee, and 15 drink both. How many drink only Tea? How many drink only Coffee?
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Q.11
In a group of 60 people, 25 like Tea only, 20 like Coffee only, and 8 like both. How many like neither?
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Q.12
In a survey of 110 people, 52 can do Juggling, 44 can do Magic tricks, 38 can do Mime. 17 can do both Juggling and Magic tricks, 13 can do both Magic tricks and Mime, 16 can do both Juggling and Mime, and 6 can do all three. How many can do only Juggling?
- A 25
- B 52
- C 19
- D 31
Show answer
Correct answer: (A) 25
Only Juggling = Juggling - (Juggling&Magic tricks) - (Juggling&Mime) + All three = 52-17-16+6 = 25.
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Q.13
In a group of 130 people, 60 speak Hindi, 55 speak Tamil, 50 speak Bengali. 20 speak both Hindi and Tamil, 18 speak both Tamil and Bengali, 16 speak both Hindi and Bengali, and 8 speak all three languages. How many speak exactly two of the three languages?
- A 30
- B 54
- C 46
- D 38
Show answer
Correct answer: (A) 30
Exactly two = (Hindi&Tamil - All) + (Tamil&Bengali - All) + (Hindi&Bengali - All) = (20-8)+(18-8)+(16-8) = 30.
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Q.14
In a class of 60 students, 25 play Chess, 30 play Carrom, and 20 play neither. How many play exactly one of the two games?
- A 25
- B 40
- C 15
- D 35
Show answer
Correct answer: (A) 25
At least one = 60 − 20 = 40. Both = 25 + 30 − 40 = 15. Exactly one = (at least one) − (both) = 40 − 15 = 25.
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Q.15
In a group of 80 people, 50 like tea, 40 like coffee, and 15 like neither. How many like both tea and coffee?
- A 25
- B 15
- C 30
- D 20
Show answer
Correct answer: (A) 25
At least one = 80 − 15 = 65. Both = (tea) + (coffee) − (at least one) = 50 + 40 − 65 = 25.
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Q.16
In a class of 70 students, 45 like Hindi, 38 like English, and 20 like both. How many students like only Hindi?
- A 25
- B 45
- C 20
- D 18
Show answer
Correct answer: (A) 25
Only Hindi = (students who like Hindi) − (students who like both) = 45 − 20 = 25.
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Q.17
In a survey of 200 people, 90 use Product B, and 30 use both Product A and Product B. If 150 people use at least one of the two products, how many use Product A?
- A 90
- B 60
- C 120
- D 150
Show answer
Correct answer: (A) 90
At least one = A + B − both, so 150 = A + 90 − 30, giving A = 150 − 90 + 30 = 90.
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Q.18
In a group of 120 people, 60 speak Tamil, 55 speak Telugu, and 50 speak Kannada. 25 speak both Tamil and Telugu, 20 speak both Telugu and Kannada, 18 speak both Tamil and Kannada, and 10 speak all three languages. How many speak exactly two of the three languages?
- A 33
- B 63
- C 43
- D 53
Show answer
Correct answer: (A) 33
Exactly two = (Tamil∩Telugu − all three) + (Telugu∩Kannada − all three) + (Tamil∩Kannada − all three) = (25−10) + (20−10) + (18−10) = 15+10+8 = 33.
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Q.19
In a group of 150 sports fans, 60 like Cricket, 50 like Football, and 40 like Hockey. 18 like both Cricket and Football, 12 like both Football and Hockey, 10 like both Cricket and Hockey, and 5 like all three sports. How many like only Cricket?
- A 37
- B 60
- C 42
- D 33
Show answer
Correct answer: (A) 37
Only Cricket = Cricket − (Cricket∩Football) − (Cricket∩Hockey) + (all three) = 60 − 18 − 10 + 5 = 37.
How these questions were made
Written by Mahesh Srivastava, Founder of Pariksha Saathi. Published: 2026-10-03.
Authored by an AI assistant (Claude) - not reviewed by a subject-matter expert.