Venn diagram questions in UCAT Decision Making are much easier when you fill the diagram in the right order.
The biggest mistake students make is starting with the largest totals. That can lead to double counting.
A safer method is to begin with the most specific information.
If you know how many people are in the overlap between two groups, place that number first.
Then work out the parts that belong to only one group.
Finally, calculate how many are outside the circles if the total population is given.
For example, imagine 60 students play football, 40 play tennis and 20 play both.
The 20 belongs in the overlap.
That means 40 play football only, because 60 includes the 20 who also play tennis.
It also means 20 play tennis only.
If there are 100 students in total, 20 are in neither group.
This order keeps the arithmetic clean.
Three-circle Venn diagrams are more complex, but the principle is the same. Start with the centre where all three overlap, then work outward.
Always check whether a number includes the overlap or refers to an “only” region. The wording matters.
Another good habit is to label the circles clearly before doing anything else. A diagram becomes confusing very quickly if you forget which group is which.
Venn questions reward organisation more than advanced maths. Keep the structure tidy, start with the most specific region and check your totals.
That usually turns a messy-looking problem into a straightforward one.
