3.6 Number-Based Verbal Reasoning

Number-Based Verbal Reasoning

The official Kent Test familiarisation booklet is explicit about what numbers are doing in the reasoning booklet: "If you find numbers in a verbal reasoning question they aren't there to test your mathematics, they are being used as symbols, and you are asked to find out the relationship between them so that — for example — you can predict what the next one will be."

That single sentence sets the strategy. The arithmetic will be small. The difficulty is in spotting the relationship, not in computing it. A child who finds themselves doing long multiplication has misread the rule.

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Number Sequences: Work the Gaps

The reliable opening move is always the same. Write the differences underneath the sequence.

4, 9, 14, 19, ? Gaps: +5, +5, +5 → constant, so the answer is 19 + 5 = 24.

If the gaps are not constant, take the gaps of the gaps.

2, 3, 5, 8, 12, ? Gaps: +1, +2, +3, +4 → second differences are constant at +1, so the next gap is +5 and the answer is 17.

The sequence families to recognise on sight

The interleaved family causes the most trouble because the gaps look chaotic. The tell is a sequence that jumps up and down: split it into odd-numbered and even-numbered positions and test each separately.

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Number-in-Brackets Items

A number sits inside brackets between two others, and the same hidden rule links all three. Two worked examples are given; you apply the rule to a third.

8 [22] 3 5 [16] 3 9 [ ? ] 4

Work through a fixed test order and stop at the first rule that survives both examples:

Sum doubled is the same as (first × 2) + (second × 2). Apply it: (9 × 2) + (4 × 2) = 26.

The discipline that matters is checking the second example. Several rules will fit any single example — product minus 2 also gives 22 from 8 and 3 — and a rule confirmed on one example only is a guess dressed up as an answer. Run the fixed order (sum, difference, product, sum doubled, product minus one term, difference doubled) and you will rarely need more than four tries.

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Where Numbers Meet Letters

Letter codes and alphabet-position ciphers are covered in full in section 3.3. What matters here is the join between the two systems: an item that asks you to do arithmetic on letters and hand back the answer as a letter.

Give the answer to this sum as a letter: F + H − D Using alphabet positions, $6 + 8 - 4 = 10$, and the tenth letter is J.

Two rules keep these safe:

• Check whether the question supplies its own values. If a question states "A = 2, B = 4, C = 6, D = 8", the standard alphabet positions no longer apply and the answer letter must be read back through the question's own scale. Underline the definition before you start.
• Watch for answers outside the alphabet. If an operation produces a number above 26 or below 1, the intended rule is usually to wrap around — 26 + 2 becomes B — but only if the question says so. If it does not, you have applied the wrong operation.

Algebraic Letter Values

A short step further: letters carry numeric values and an expression must be evaluated, sometimes with the answer returned as a letter.

If a = 3, b = 5, c = 6, d = 2, find the value of (a × c) ÷ (b − d). $(3 \times 6) \div (5 - 2) = 18 \div 3 = \mathbf{6}$, which is c.

Note how small the numbers stay throughout. That is the familiarisation booklet's point restated: the paper is testing whether you can find and apply a relationship, not whether you can calculate.

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Two Structures That Look Like Sequences But Are Not

Number analogies. Written as 4 is to 12 as 7 is to ?, these ask for a relationship applied twice rather than a run continued. Test multiplication before addition: $4 \times 3 = 12$, so $7 \times 3 = \mathbf{21}$. Addition would give 15, and both will be offered.

Odd one out with numbers. A set such as 16, 25, 36, 42, 49 is not a sequence at all — it is a classification. Four are square numbers and 42 is not. The signals are a set given in no obvious order, and no gap to fill. Ask "what do four of these share?" rather than "what comes next?".

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The Verification Habit

For every number-based item, the final action is the same: substitute the answer back into the original pattern and check it holds. In a sequence, confirm the gap between your answer and the previous term matches the rule. In a brackets item, confirm the rule works on both given examples and on your answer. This costs a few seconds and catches the single most common failure in this question type, which is a rule that fits the first example and nothing else.