Unit 12 · Multi-Step Conditional Reasoning
School Survey — Venn Diagram Deduction
Lesson 1 of 30
Camp-activity survey questions look wordy, but they are really set puzzles: chain the “everyone who…” rules, then count who can land in each circle.
Nested preference / overlap items appear in the easy band of Selective TS — strong marks when you sketch overlapping groups instead of guessing from the options.
The examiner checks whether you can translate “all A are B”, “no A and C together”, and “more only-X than only-Y” into a consistent Venn picture and infer which activity has the largest audience.
A survey lists several activities and rules about who likes what together or apart. You choose which activity was most popular (or which scenario is forced).
Best approach: Draw one circle per activity. Stack the chains (Harving → Glinting → Kelrish). Mark forbidden overlaps (Mortay ∩ Glinting = ∅). The biggest circle — usually the one everything else feeds into — is the answer.
Question
A school surveyed all its students about which of four traditional camp activities they enjoyed: Glinting, Harving, Kelrish, and Mortay. The survey found the following:
- Everyone who liked Glinting also liked Kelrish.
- Everyone who liked Harving also liked Glinting.
- No one liked both Mortay and Glinting.
- Some students liked both Kelrish and Mortay.
- There were more students who only liked Kelrish than students who only liked Mortay.
Which activity was most popular?
Select an answer to see the explanation.
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