Identify these questions

Maximum and minimum questions are interesting questions that require you to work through information, usually about attributes, to determine a minimum or maximum number of items.

To identify them, look for keywords like “maximum number of…” or “minimum number of…”.

They often look like this:

Lee has a certain number of cacti (cacti is the plural form of cactus). There are an equal number of those with flowers and those with spikes. Of the four barrel cacti, each has either flowers or spikes. Both columnar cacti have spikes. Two barrel cacti have flowers. There are four cacti with spikes and four cacti with flowers.

What is the minimum possible number of cacti on Lee’s balcony?

A: 5 B: 6 C: 7 D: 8 E: 9 or more

The strategy to answer these questions

To answer these questions:

1. Scan through to find the requirement – is it maximum or minimum? If it’s a minimum number, always see how you can try to bring the number down (usually this is by adding multiple attributes to one item). If it’s a maximum number, always see how you can bring the number up as higher numbers are preferred (usually this is by adding or associating one attribute per item).
2. Actively work through the information provided and classify the attributes in an organised way e.g. a table. Take note of words like “only”, “or” and in the absence of further information, see if it’s safe to assume multiple attributes per item.
3. Tick the right boxes based on your reading of information and your reasoning and cross out information so that you’re keeping track of what you’ve processed.
4. From the question, identify the correct co-ordinate 'tick' or number of co-ordinate 'ticks' and find your answer.

Table Set Up Example

Example Question/s

Watch video for explanation of the following question/s:

Lee has a certain number of cacti (cacti is the plural form of cactus). There are an equal number of those with flowers and those with spikes. Of the four barrel cacti, each has either flowers or spikes. Both columnar cacti have spikes. Two barrel cacti have flowers. There are four cacti with spikes and four cacti with flowers.

What is the minimum possible number of cacti on Lee’s balcony?

A: 5 B: 6 C: 7 D: 8 E: 9 or more

I need to assemble a team of lawyers. There are four lawyers who practice finance law and five who practice criminal law. One of the female lawyers only practices in criminal law.

As this is a money laundering case, I need one more lawyer who specialises in criminal law over the number of finance lawyers. What is the minimum possible number of lawyers do I need on my team?

A: 5 B: 6 C: 7 D: 8 E: 9 or more

There are a number of guests in a limousine. There are five guests wearing rings and six guests wearing necklaces. Both guests wearing blue are wearing necklaces only and another wearing red is wearing a ring only. There are the same number of guests wearing red, yellow and blue. One guest wears green.

What is the minimum of guests in the limousine?

A: 5 B: 6 C: 7 D: 8 E: 9 or more

I have a lolly jar with a certain number of lollies inside. There are six lollies that have sprinkles on them and four who have only sugar dusting or sprinkles. There are an equal number of green lollies as there are to purple lollies. Three green lollies have sugar dusting and three purple lollies have sugar dusting too. There are two green lollies with just sugar dusting.

What is the minimum possible number of lollies in my lolly jar?

A: 5 B: 6 C: 7 D: 8 E: 9 or more

Key Rules to remember

• Lower numbers are preferred when ‘minimum’ is required – therefore, see if multiple attributes can be associated with 1 item.
  
• Larger numbers are preferred when ‘maximum’ is required – therefore, see if only one attribute can be associated with 1 item.
  
• Pay attention to words like “only”, “or”, “and” and any absence of constraints to determine how you can allocate attributes.
• Organise your work in a table and keep track of information you process to avoid costly mistakes like duplication and time used in rework.

Practice time!

Now, it's your turn to practice.

Click on the button below and start your practice questions. We recommend doing untimed mode first, and then, when you're ready, do timed mode.

Every question has two solutions videos after you complete the question. The first is a quick 60 second video that shows you how our expert answers the question quickly. The second video is a more in-depth 5-steps or less explainer video that shows you the steps to take to answer the question. It's really important that you review the second video because that's where you'll learn additional tips and tricks.

Once you're done with the practice questions, move on to the next checkpoint.

Now, let's get started on your practice questions.

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