11+ Picking a Figure illustration | Pick a card
Pick a figure, but not just any figure.

VR - Picking a Figure to Fulfil Criteria

This article was formerly a part of Following Instructions with Figures and Picking a Figure to Fulfil Criteria. For the sake of clarity, that has now been split into two more specific articles. To read the information which used to be included, see Following Instructions with Figures.

Picking a Figure to Fulfil Criteria is a variation on the words-and-maths questions in the Eleven Plus Verbal Reasoning exam. These kinds of questions tend not to occur very often; the standard NFER test in Kent, for instance, does not include them.

However, some individual schools using the Verbal Reasoning paper like to employ these variations, so we shall explore them here.

Picking a Figure to Fulfil Criteria is basically a test of a candidate’s knowledge of mathematical terms.

How Are These Kind Of Questions Posed In The Exam?

Candidates are shown several numbers and asked a question about them. As long as a child knows what different mathematical terms mean (there should only be terms that bright ten-year-olds are familiar with) then these questions should be relatively easy. If they do not understand the terms we shall see in this lesson, then now is the time to teach them!

Let’s look at Picking a Figure to Fulfil Criteria questions in action.

Example Question One


Which of the following is not a factor of 24?

2 6 4 48 12

‘Factor’ means a number which fits exactly into another. Therefore 2, 4, 6 and 12 all fit into 24 whereas 48 does not. It’s there as a red herring because 24 is a factor of 48.

Similar questions could use the term 'multiple'. A multiple is like the opposite of a factor - it's a figure that can be made by multiplying a given figure. For example, 30 and 50 are both multiples of 10.

Example Question Two


Which of the following is not a multiple of 6?

84 60 96 112 120

This needs you to be able to do some division. In order to know whether a figure is a multiple of a smaller number, you need to find out whether it fits perfectly into the larger number without a remainder.

Only 60 falls into the regular times tables for the number six; the rest are higher numbers and will stretch those who are not great at maths. This makes me wonder why you often get these questions in a Verbal Reasoning paper, but we have to work with what we're given!

The other numbers all divide by six exactly with the exception of 112.

Example Question Three


Which of the following is a prime number?

4 9 11 14 18

Prime numbers appear less often in the exam, but they are there occasionally. Prime numbers are ones which can only be divided by two numbers (one and themselves) without leaving a remainder. They will only appear in the 1 times table and their own times table, but in no others.

Looking at the options given in the question:

4 is in the 2 times table
9 is in the 3 times table
14 is in the 2 and the 7 times tables
18 is in the 2, 3, 6 and 9 times tables

The answer must be 11, as it only appears in the 1 and 11 times table.

Technique Tip

Any even number (with the exception of 2) cannot be a prime number as it will appear in the 2 times table. Make sure your child knows this as it can save valuable time in the exam. Also, the number 1 is not a prime number as it can only be divided by one number (itself), not two.

Some brighter children might want to memorise the prime numbers (this is not easy to do!). If you think it is something your child can manage, then here is a list of all the prime numbers between 1 and 100:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.

Example Question Four


Which of the following is a square number?

12 14 16 18 20

Just like prime numbers, square numbers are occasionally (though rarely) included in the exam. Square numbers are the result of multiplying a number by itself.

Looking at the options given in the question, you may have spotted that 16 is a square number as it is the result of 4 x 4.

The best way to quickly spot square numbers is to memorise them – at least the smaller ones. Otherwise you’ll have to go through each option the slow way, which I’ll show you later. For now, here are the first twelve square numbers:

1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 = 49
8 x 8 = 64
9 x 9 = 81
10 x 10 = 100
11 x 11 = 121
12 x 12 = 144

Most 10-year-olds should know these, so long as they know their times tables. Those who do not will have to tackle each number in turn. Looking at the possible answers:

12 is higher than 3 x 3 but lower than 4 x 4, so cannot be a square number.
14 is higher than 3 x 3 but lower than 4 x 4, so cannot be a square number.
16 is higher than 3 x 3 but equal to 4 x 4 so must be the correct answer.

As you can see, this is a long and slow process, so memorising the square numbers will help your child a great deal.

Sample Tests

As I said at the start of this lesson, these kinds of questions rarely appear on the Verbal Reasoning paper. Nevertheless, they are good to practise with as they help to ingrain mathematical terms in a child’s head.

The best way to practise is by revising with some maths questions. You’ll find plenty of these on the Education Quizzes site, in the Eleven Plus maths section. You can follow this link straight to them: 11-Plus Maths Quizzes.

We also have four quizzes in the Picking A Figure To Fulfil Criteria format. As always, you will find these in the Eleven Plus Verbal Reasoning section, or you can follow these links:

Pick a Figure 1

Pick a Figure 2

Pick a Figure 3

Pick a Figure 4

Go through these with your child to see how well they do. You will be able to spot if there are any terms they are not familiar with, and you can help clear this up. It will also test their ability to read questions carefully – often the single word ‘not’ can be missed by careless candidates, meaning they choose the wrong answer. Practise should help them to learn concentration. Good luck!

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