Question Type 7: Sums Using Letters

Eleven-Plus Preparation Specialists

This question type involves replacing letters with numbers (or vice versa). As such, your reasoning ability is what you’ll be relying on here – not your vocabulary.

What does this question type involve?

In this question type, you’ll be asked to perform simple sums, using a series of numbers that are provided to you. However, the numbers have been represented by letters. You are told which numbers are which letters, and must then refer back to that ‘code’ as you work through the sum.

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Example questions

A = 2, B = 4, C = 6, D = 8, E = 3

Find the answer to the following sum.

B* C – D * E + B = ?

Answer: B

Here, you will do 4 * 6 (= 24), then subtract 8*3 (= 24). This gives 0. Then, you’d B to get 4. Therefore the answer is 4, which was B.

A Simple 4 Step Approach to Solve Type 7 Questions

These questions should be seen as a chance to get marks without having to worry about not knowing the answer – you can work through them with a clear process and secure marks here.

We advise that you take a four step approach, as follows:

Step 1: Check the Numbers
Step 2: BODMAS
Step 3: Negatives
Step 4: Check the Answer

First of all, you must check the numbers! Remember that the codes can change from one question to the next, so you should check that this is not the case. Ensure that as you fill out the numbers from the letters – in your head or on paper – you do so looking at the information you are given, rather than doing so from what you remember. Using your memory here can lead to mistakes.

Next, the key to getting marks is to use BODMAS. You should be well aware of this anagram, which stands for Brackets, Orders, Divide, Multiply, Add, Subtract. Most of the questions will involve both multiplying/dividing and adding/subtracting, but will not feature brackets – as such using BODMAS (or at least the latter part of the anagram) is important.
Watch out for negatives. You might find negative numbers being used, in which case you must ensure that you have correctly performed the sum, and double check that you’ve found the right letter.

Lastly, check your answer! As above, don’t use your memory to pick the letter, but instead read the letter from the information provided. 

Worked Example

Let’s look at a worked example.

A = 1, B = 3, C = 6, D = 8, E = 10

Find the answer to the following sum.

A * C * E = C * D + C + ?

Here, we begin by checking the numbers and plugging them in. So, we find that we can rewrite this as:

1 * 6 * 10 = 6 * 8 + 6 + ?

Let’s simplify this to 60 = 48 + 6 + ?
→ 60 = 54 + ?

We can therefore see that we need to subtract 54 from 60, giving us 6. This is C. Note that we did 6 * 8, rather than adding 8 + 6. That’s because we followed BODMAS.

So, we know that the answer is 6. We therefore look back at the information provided, and check that 6 is C.

Therefore, we select or write C.

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Top Tricks

The most important thing to consider when attempting this type of question is BODMAS. This is the key. So long as you remember to divide or multiply before you add or subtract, then these questions will be simple.

Common Pitfalls

As above, the most common pitfall is getting BODMAS, or the order of operations to be more precise, in the wrong order. The next most common error is relying on your memory, rather than double-checking letters each time you write them down. Remember, it’s much better to spend 55 seconds on the question and check that you have selected the correct letter, than spend 45 seconds on the question as you use your memory – but therefore right down the wrong letter.


In summary, this question type is straightforward so long as you follow simple mathematical rules, and make sure to correctly translate the letters across into numbers. Stay clear of making any silly mistakes, and also double check your answers.
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