UCAT Venn Diagrams: how to solve them
While every student should be acquainted with venn diagrams, UCAT students need to be best friends with them. As diagrams that denote the relationship between two, three or more groups (or 'sets'), they are an extremely common Decision Making question type. As luck would have it, there's only so many ways venn diagram questions can be asked - and there's a structured approach to answering every single one of them!
What is a Venn diagram question?
Venn diagram questions typically describe two or more groups with counts of members included in some, none, or all of them. You'll then be asked to find the number of members within a specific region (or regions).
The good thing about venn diagram questions is that it is the most formulaic question type in the Decision Making subtest. Once you've identified the specific region the question is asking for, plug in the correct formula (or combination of formulas) and you'll be able to find your answer.
Exactly one: In one set or the other but not both. The two only-regions added, with the overlap deliberately left out.
Running example: 200 students; 120 take Biology, 90 take Chemistry, 50 take both.
There are variations to how venn diagram questions are delivered: in most cases, you'll be using venn diagrams as a component of your working rather than it being asked directly. The core skill is identifying a question actually actually requires a venn diagram so you can approach it correctly.
The most common mistake we see with students is not failing to understand which formula to use - it's using the correct formula but for the wrong region! Make a habit of double-checking what the question is actually asking.
Employee Commuter Benefits Survey
A company surveyed its 200 employees about two commuter benefits: a cycle-to-work scheme and a discounted train pass. 120 use the cycle scheme, 85 have the train pass, and 50 have both.
How many employees use exactly one of the two benefits?
Common mistakes
Trap guides are being published. Links open as each goes live.
A reliable method
How to practice
There's an easy battle and a hard battle to every venn diagram question.
The easy battle is learning the formulas.
The hard battle is reading the question properly.
MedPath's adaptive bank provides plenty of practice questions that allows every student to get comfortable with venn diagram structures and steers your practice towards the traps you keep getting wrong.
Practise Venn diagrams adaptively.
MedPath drills Venn questions region by region, with a worked interactive solution for each, and steers practice toward the regions you keep getting wrong.
Common questions
Do I need to know set theory notation?+
No. UCAT Venn questions are written in plain language (“both”, “neither”, “only”, “at least one”), not symbols, and the only rule you need is inclusion-exclusion: add the sets, subtract the overlap. A basic on-screen calculator is available in Decision Making, though the numbers are kept clean enough to do in your head.
How are they scored?+
As part of Decision Making’s 300–900 scaled score. They are single-best-answer, so unlike the multi-statement Decision Making types there is no partial credit: you need the exact region count to earn the mark.
What’s the most common mistake?+
Solving for the wrong region. Most often it is reporting the union (everyone in at least one set) when the question asked for “exactly one” or “neither”, or forgetting to take the overlap out of a single set. The arithmetic is rarely the problem; reading the target region is.