Venn Diagram formats – part 3

Some Venn Diagram questions will have Venn diagrams as answer choices, almost always with numbers in the diagrams.

You must select the diagram that best represents the information in the stimulus, in the form of rules describing the correct diagram.

Note, however, that you cannot create the correct diagram from the information provided. Instead, you must eliminate incorrect diagrams that violate the rules.

The first step when the answers are Venn diagrams is to check the key.

There are three possibilities:

• The key includes shapes with labels telling you which shape corresponds to each group or category in the answers.
• The key is given in textual information, often as the last sentence after the rules. Again, each shape will correspond to a group or category in each answer.
• There is no key, so any shape could represent any group or category. This means that a shape could represent different groups in different answers.

Take a moment to orient yourself to the order of the shapes in the answer choices.

Approach the order in a consistent way: normally left to right, or clockwise – whatever you prefer.

Notice whether the key gives the shapes in a different order than the answer choices. This can make it easy to err when working quickly.

You must compare each rule to the diagrams, one rule at a time.

Eliminate any answers with diagrams that violate the rule.

If a diagram follows the rule, retain the answer as you will need to check it against the remaining rules.

This way, you can limit your work. You will have fewer answers to compare to the remaining rules once you have eliminated a diagram or two.

You may check the rules against the Venn diagrams in the answer choices in any order. Do not assume that the first rule provided must be checked first.

In these questions:

• Start with the simplest rule – the one that you can compare most quickly to each of the four diagrams.
• Compare the rule to each diagram individually. Eliminate answers that violate the rule; retain answers that follow the rule.
• Continue with the next simplest rule with any remaining answers.
• Leave the most complex rule for last. Ideally, at this point you will have only two remaining answers, so you will have less work with the hardest rule.

You must eliminate quickly and accurately when the answers are Venn diagrams.

As always, think in shapes as you compare each rule to the diagrams.

Consider whether you need the groups that overlap entirely, partially or not at all.

Be ready to discard answers when any aspect of the diagram violates a rule.

If there is no key, take a moment to work out which shape corresponds to each group.

However, without a key, it is possible that different shapes will represent different groups in the diagrams.

Focus on the relationships between groups to eliminate incorrect diagrams. It may come down to which parts of shapes must or must not contain numbers, or potentially an invalid overlap based on other parts of the same shape.

Without a key, the logic is far more challenging. Look for subtle reasons to eliminate diagrams that are impossible, based on the rules.

When the answers are Venn diagrams and there is no key, ask yourself:

• Which groups must not overlap?
• Which groups are entirely inside another?
• Which groups overlap partially?
• If two groups overlap partially, what happens in the other parts of those groups?

You may see one or more questions without Venn diagrams in the stimulus or the answer choices.

In these questions, the UCAT assumes you will draw a diagram in order to solve the question.

Sometimes, it could help to make a diagram in your notebook to work through the information provided.

Other times, you can answer these questions using algebra. In this sense, they are more like word problems you may have seen in maths exams.

In a question with no Venn diagram, you may find three main groups.

The UCAT assumes you will draw a diagram in your notebook to break out the numbers according to these three groups.

Such a diagram – as shown in the official UCAT explanations – will include three circles arranged so that all three overlap, along with each possible pair of overlaps.

If there are three main groups in a question with no Venn diagram:

• Take a moment to clarify the three groups in your mind.
• Check the goal – what aspect of the diagram must you solve for? This could be one entire group, or any component of the diagram – such as one of the overlaps.
• Decide whether to make a rough diagram in your notebook, or whether to solve algebraically.

Sometimes, the information is relatively simple, so you can just add or subtract as needed to work out the unknown components that you need to find the goal.

Whether you decide to solve algebraically or draw a diagram of the three groups, it will help to be clear about the possible subgroups.

There are seven subgroups of those that are part of at least one group:

• Group 1 only
• Group 2 only
• Group 3 only
• Group 1 and Group 2 but not Group 3
• Group 1 and Group 3 but not Group 2
• Group 2 and Group 3 but not Group 1
• All three groups

You might also have an eighth subgroup – those that are in none of the groups. However, this is quite uncommon in official UCAT practice questions in this format.

If there are three main groups in a question with no Venn diagram, take care to distinguish:

• Any people or things that are in one group.
• People or things that are only in one group.

Note that the former include the entire group, which contains all of the overlaps along with those who are only in the group. The latter is a subgroup that excludes the overlaps.

Some questions without Venn diagrams are simply about two groups.

You can solve these questions using the formula: Group 1 + Group 2 – Both + Neither

Notice that you must subtract Both to avoid anyone or anything from being counted twice, as these people or things are in Group 1 and also in Group 2.

When a question without Venn diagrams is about two groups, you can always solve algebraically.

Identify the goal from the question stem, then think about how to set up and solve for this unknown value.

You may choose to use the formula Group 1 + Group 2 – Both + Neither, or you may spot a different approach.

You may need to define one or more groups in terms of a variable. As long as you have only one variable, you can then solve your equation for the unknown.

You may come across a question with no Venn diagrams that does not fit neatly and obviously into the other formats described.

In other words:

• You can’t use the three circles approach to draw a diagram in the notebook because it does not have three clear groups.
• You can’t use the Group 1 + Group 2 – Both + Neither formula because it does not break down simply into two clear groups.

The only approach is to turn words into algebra. Start with a focus on the unknown value, then try to use the information provided to make an equation.

If there are two unknowns, you may need to solve with two equations. Thankfully, official Venn Diagram questions requiring more intense algebra like this are rare.