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Question Type 17: Finish the Sum

Eleven-Plus Preparation Specialists

This is one of the verbal reasoning question types that doesn’t feature any words – instead, it relies entirely on maths. It’s in the section because it’s a reasoning question. However, you will find this in the Maths Section of some 11+ papers, instead of in the Verbal Reasoning section. This question type will be simple for those who are strong in Maths.

What does this question type involve?

You will be given a simple sum and asked to complete it. The missing number is often towards the end of the sum. That’s it – there’s no more complexity than that!

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Example questions

Please complete the following sum.
1+3 = 2+?

Answer: 2
This is a very simple example. We just need to subtract 2 from (3+1), which gives us 4-2 = 2.

Please complete the following sum.

38/2 = 6*4 – ?

Answer: 5
This is a slightly more complex version. You’ll need to calculate that 38/2 = 19, and that 24 * 4 = 24. Then, you’ll need to perform 24 – 19, to get 5.

A 3 Step Approach to Type 17 Questions on Finishing the Sum

Your approach here should be simple, and use algebra as appropriate. We recommend that you focus on the three following core steps:

Step 1: BODMAS
Step 2: Simple Solution
Step 3: Algebra

The first step is absolutely vital, and where a lot of mistakes could be made. You must remember to follow the BODMAS rule of operations. This stands for brackets, order of powers or roots, division, multiplication, addition, subtraction. Commonly, the sums will involve both multiplying/dividing and adding/subtracting in the same part, which means that you must remember the latter half of BODMAS. Brackets and squares are rarely involved, although you should be aware that brackets always come first.

Your next step should be to look for a simple solution. You must remember that you need to work quickly through questions, which means that using algebra for every single one is not the best use of your time. For example, if you are asked:

What is the missing number?
7*2 = 10 + ?

You should be able to quickly realise that the first half of the sum is 14, and that you are therefore looking for a number that gives you 14 when added to 10 – i.e. the answer is 4.

If the question is more complicated, then it might be worth using algebra. However, in general we would advise that you try to solve the puzzle quickly using mental arithmetics.

Worked Example

What is the missing number?

5 * 3 + 2 = 20 – ?

Here, we would focus on BODMAS first. Let’s work through in order (in reality hopefully this would be a quicker process.) First is brackets – so we can move on. Next is order – which means squares and square roots. There are none of these symbols so we can move on again. Next is division and multiplication. We have a multiplication, so let’s tackle that. 5 * 3 is 15. There are no divisions. Next up is addition and subtraction. So, we need to add 2 to 15, to get 17. Looking at the other side, we know that 20 – ? = 17.

You should try to solve this quickly using mental maths. There ought to be no need for algebra. However, just to illustrate what you would write, you’d write:

20-x = 17
Rearrange to 20-17 = x

Therefore x = 3

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Top Tricks

The main thing to focus on in this section is working through the numbers in a logical order. Use BODMAS, and then work through the numbers in a way that makes sense to you and allows you to solve quickly. You should practise doing this type of question in your head as much as possible to get as quick as you can.

Common Pitfalls

We’ve focused on BODMAS already – but we’ll emphasise it again. Always do your divisions and multiplications before you do your additions and subtractions. Failure to follow this simple rule is the reason that many students lose marks in this domain.

Summary

In summary these questions are great for those who don’t read so widely or have a more developed vocabulary, as they feature Maths rather than English. Get the basics right and work through efficiently to pick up the marks. 
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