Four Friends at a Restaurant — Preference Intersection

Preference Intersection questions are among the most approachable in this unit — the challenge isn't complex logical reasoning but systematic, methodical elimination. Your job is to find the one option that passes through every person's acceptance filter simultaneously, which becomes trivial once you stop trying to track everyone in your head at once.

These questions appear in the easy-to-medium band of OC TS and are near-certain marks for students who use a grid. The trap for unprepared students is trying to reason about all four people simultaneously — they miss one person's constraint and pick a cuisine that two of them actually can't eat.

The examiner wants to confirm that you can build a systematic compatibility check — listing each person's valid options — and then find the single choice that gets a tick from every person. Speed is not the challenge; discipline and completeness are.

Four or five people each have preferences or restrictions (e.g. "only likes X and Y", "will eat anything except Z"). A list of options is given. You must find the single option that every person agrees on. Exactly one option always satisfies all constraints simultaneously.