Venn Diagram formats – part 2

Expect to see several questions with numbers in the diagram and complex statements as the answer choices.

Among Venn Diagram questions, this format is the most common. You are likely to see at least two such questions on Test Day. You may even see three or four in this format.

If a Venn diagram with numbers has complex answers, you will notice that:

• Some (if not all) answer choices are lengthy textual statements.
• You must do more than a simple sum to check some (or all) of the answers.

These answers are complex because you need more time and effort to see if each one is correct.

You will generally feel the need to slow down when you see complex answers. However, you can train yourself to use some strategies and techniques to save time.

It may help to think of long textual statements in Venn Diagram answers as roughly similar to five-part statements in Inference questions.

The correct answer will match the diagram. This means that the information in the diagram will support the correct answer. With logic or maths, the diagram will help you to prove that the correct answer is correct.

Incorrect answers will not match the diagram. They may contradict it or simply misalign with the information provided. You do not necessarily have to do all the working to disprove each incorrect answer.

As soon as you spot a Venn Diagram answer is wrong – eliminate it, briskly and ruthlessly. Do no more work than is necessary to see that the answer is wrong.

You can check textual answers in a Venn Diagram question in any order.

This means you can skip the longest answer as you will not need to check it.

• If one of the other three answers is correct, you will click it and move on to the next question. No need to check the remaining answers.
• If the other three answers are clearly wrong, click the longest answer without checking it. By process of elimination, you know it is correct.

To save time, start with the shortest, simplest answer. Either it will be correct, or it will be the quickest to eliminate. Continue with the next shortest, simplest answer.

Or you may prefer to check the answers in order from A to D, skipping the longest one.

Long answers in Venn Diagram questions will tend to focus on specific subgroups that are formed by combining or excluding shapes in the diagram.

As a result, the answers can get extremely wordy and therefore tough to untangle.

As always, try to turn words into shapes as it will be much quicker to analyse shapes to see which ones are included or excluded from certain overlapping portions.

Many long answers in Venn Diagram questions are about ‘in’ versus ‘not in’.

The answer will claim that a specific subgroup is inside one or more other shapes, or that it is not inside one or more other shapes.

It will help to think in shapes and turn the answer’s claim into a series of ‘in’ and ‘not in’ relationships that you can compare directly to the diagram to see if it matches.

Venn Diagram answers including all, some and none are usually simple to compare to the diagram.

An ‘all’ answer must include every single one. If any are outside of the specific subgroup in the answer, the answer is wrong.

A ‘none’ answer must not include even one. If any are inside the specific subgroup in the answer, the answer is wrong.

A ‘some’ answer includes part but not all. If all or none are inside the specific subgroup in the answer, the answer is wrong.

Notice that these words empower you to eliminate quickly without any calculations.

Be prepared to go to the calculator when working with long answers in Venn Diagram questions.

You may have to add up the specific subgroup, or the total in one or more shapes.

You may also have to do other maths using partial or entire amounts in a specific subgroup or one or more shapes.

Most commonly, the maths will involve a percentage, ratio or percentage change. Make sure you are comparing the right groups or subgroups in your maths. Think about whether you need the numbers that are inside or outside (or ‘in’ or ‘not in’) certain shapes.

Many textual answers in Venn Diagram questions will make comparative claims.

These claims are numerical, but you may be able to verify them without precise maths.

Some answers will claim that one group is greater or smaller than another, or that groups are equal.

Other answers may compare a group to a benchmark fraction or percentage.

Train yourself to take a moment before you go to the calculator and see if you can eyeball or do a quick visual comparison to eliminate such answers.

You might be able to compare the groups and see that they are obviously unequal, or that the relative sizes are far out of proportion with the claim in the answer.

When you see a Venn Diagram question with long textual answers, don’t stress.

Look for shorter, simpler answers that you can quickly check and prove or eliminate.

Some answers will require a quick visual comparison to see that they are incorrect.

Some answers will force you to do elaborate maths, but check these answers last. If there is more than one such answer, attack the simplest one first.

As always, you need to check three answers at most. If the first three answers you check are definitely wrong, you know the remaining answer must be correct.