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Logical Venn Diagrams Practice Questions with Detailed Solutions – Level 2

Medium-level Venn diagram reasoning: two-set and three-set counting, exactly one and neither cases, overlap limits, and matching classes like Kerala, India and Asia.

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Questions, answer key and solutions.

Questions
50
Duration
50 min
Marks
50

Negative marking

Attempts
100
Access
Free
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About this test

Logical Venn Diagram Level 2 Practice Quiz: Set Counting and Class Relations

This is the Level 2 set of logical Venn diagram practice questions on Aptitude360. It mixes numerical two-set and three-set counting problems with diagram-matching questions on how classes relate. Every question comes with a worked solution explaining the region-by-region method.

Topics covered in this Venn diagram Level 2 set

  • Two-set problems that find how many like both, only one or neither of two things
  • Three-set problems on sports, subjects, languages and skills using all seven regions
  • Percentage-based surveys converted to actual numbers of people
  • Minimum and maximum possible overlap of two or three groups
  • Counting cases described as exactly one, at most one and only one
  • Choosing the diagram for classes such as Kerala, India and Asia or Pens, Pencils and Stationery
  • Number-based classes such as even numbers, prime numbers and multiples

Key set formulas for Venn diagram questions

  • Union of two sets: \( n(A\cup B)=n(A)+n(B)-n(A\cap B) \)
  • Neither of the two: \( n(U)-n(A\cup B) \)
  • Exactly one of two: \( n(A)+n(B)-2\,n(A\cap B) \)
  • Union of three sets: \( n(A\cup B\cup C)=\sum n(A)-\sum n(A\cap B)+n(A\cap B\cap C) \)
  • Least overlap of two: \( n(A\cap B)\ge n(A)+n(B)-n(U) \)
  • Greatest overlap of two: \( n(A\cap B)\le \min\{n(A),n(B)\} \)

Revision tips for logical Venn diagram problems

  • Fill a three-set diagram from the centre outwards: the common region first, then the pairs, then the only regions.
  • Subtract the neither group from the total before applying the union formula.
  • In class-relation questions, ask whether one class lies wholly inside another, overlaps it or shares nothing with it.
  • Watch the wording carefully: both includes those who like all three, while exactly two does not.

Who should practise this Level 2 Venn set

Students who already know basic Venn diagrams and want medium-level practice for aptitude and reasoning sections of competitive exams.

FAQs about Logical Venn Diagrams Practice Questions with Detailed Solutions – Level 2

What are logical Venn diagrams in reasoning?
Logical Venn diagrams use circles to show how groups or classes relate to each other. A circle can lie inside another, overlap it or stay completely separate, depending on whether the classes are subsets, partly common or unrelated.
Which subject do logical Venn diagrams come under?
They are part of logical reasoning, and the counting problems also use set theory from mathematics. Competitive aptitude tests usually place them in the reasoning section.
How do you solve three-set Venn diagram questions?
Start with the region common to all three sets, then find the regions common to exactly two sets, and finally the regions belonging to only one set. Add every region to check that the total matches the given number.
How do you find the number of people in neither set?
First find the union using the inclusion-exclusion rule. Then subtract the union from the total number of people in the group.

Test structure

How the paper is split, and how long each part runs. A section you have finished cannot be returned to.

SectionQuestionsTime
Logical Venn Diagrams Level 25050 min

Marking & rules

Total marks
50 across 50 questions.
Negative marking
A wrong answer costs marks. Leaving a question unanswered costs nothing.
Attempts
100 in total. An attempt is spent the moment you begin one.

What you get when you submit

The analysis is ready the moment you submit the paper.

Score and accuracy

Marks, percentage, right, wrong and skipped, and the time you took.

Section by section

The same figures for each section, so a weak one cannot hide in an average.

The full answer key

Every question with your answer, the right one, the working, and the video where there is one.

Where you stand

Your score against the spread of everyone else who has sat this test.

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