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Logical Venn Diagrams Practice Questions with Detailed Solutions – Level 3

Harder logical Venn diagram practice on three-set counts, least and greatest overlaps and percentage surveys, plus matching nested, overlapping and disjoint classes to the right diagram.

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Questions, answer key and solutions.

Questions
50
Duration
60 min
Marks
50

Negative marking

Attempts
100
Access
Free
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Normal practice, or a Simulated test

Both use the same questions. Normal practice is untimed and needs no account: choose an option and the answer and solution appear at once. The Simulated test is the real computer-based format, with one 60-minute clock, a question palette and full screen, and your score, the key and the solutions arrive when you submit.

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Every question on one page, loading as you scroll. Choose an option and see straight away whether it was right.

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  • Solutions in place. The explanation, and the video where one has been added, sit under the question.
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Real exam conditions

Simulated

Timed CBT

The computer-based test format: one clock, a question palette, and a score the moment you submit.

  • A clock that does not pause. 60 minutes from the moment you begin, and the paper is submitted for you when it reaches zero.
  • Question palette. Answered, not answered and marked for review, section by section, as the real interface has it.
  • Full screen, proctored. The test takes over the screen; leaving it three times submits the paper.
  • Answers hidden until you submit. The key, the explanations and your score all arrive together at the end.

About this test

Logical Venn Diagrams Level 3: Set Overlaps and Class Relationships

This Level 3 set tests two-set and three-set counting, the least and greatest possible overlaps, percentage surveys and matching groups of classes to the right circle diagram. It is free practice on Aptitude360 for the Logical Reasoning syllabus, and every question has a detailed written solution.

Topics covered in this Level 3 Venn diagram set

  • Two-set problems with a neither group, including only-one and exactly-one counts
  • Three-set problems using pairwise and triple overlaps to find exactly-two and none counts
  • Least and greatest possible overlap of two or three sets, and the gap between them
  • Percentage surveys where a known overlap gives the total population
  • Class relationships among numbers, elements, gases and everyday categories
  • Matching nested, overlapping or disjoint circle arrangements to the correct classes

Key set formulas for Venn diagram counting

  • Union of two sets: \( n(A\cup B)=n(A)+n(B)-n(A\cap B) \)
  • Only A, out of three sets: \( n(A)-n(A\cap B)-n(A\cap C)+n(A\cap B\cap C) \)
  • In neither set, where \( n(U) \) is the total: \( n(U)-n(A\cup B) \)
  • Least overlap of two sets: \( \max\{0,\ n(A)+n(B)-n(U)\} \)
  • Greatest overlap of two sets: \( \min\{n(A),\ n(B)\} \)
  • Least triple overlap: \( \max\{0,\ n(A)+n(B)+n(C)-2n(U)\} \)

Class relationship ideas to revise

  • One class lying wholly inside another, such as an element inside its group
  • Two classes that partly overlap inside a larger class
  • Classes with nothing in common, drawn as separate circles
  • How the stated universe, such as positive integers only, changes the answer

Revision tips for harder Venn diagram questions

  • Fill the region common to all sets first, then work outward to the single-set regions
  • Convert every percentage to one base before using a given count to find the total
  • For extreme overlaps, test the smaller set fully inside the larger and the sets spread as far apart as the total allows

Who this Level 3 set suits

Logical reasoning learners who are comfortable with basic Venn diagrams and now want tougher two-set and three-set practice.

FAQs about Logical Venn Diagrams Practice Questions with Detailed Solutions – Level 3

What are logical Venn diagrams in reasoning?
Logical Venn diagrams use circles to show how classes relate. A circle inside another shows one class contained in the other, overlapping circles show common members, and separate circles show classes with nothing in common.
Logical Venn diagrams come under which subject?
They are part of logical reasoning. The counting questions also draw on set theory from mathematics.
How do you solve three-set Venn diagram questions?
Start with the region common to all three sets and subtract it from each pairwise overlap to get the exactly-two regions. For each set, subtract its two exactly-two regions and the all-three region from the set total to get its only-one region, then use the overall total to find how many belong to none.
How do you find the minimum overlap of two sets?
Add the sizes of the two sets and subtract the total number of elements. If the result is below zero, the minimum overlap is zero, and the maximum overlap is always the size of the smaller set.

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 35060 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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