College of Policing National Sift / Online Assessment Process Numerical, Verbal and Logical Reasoning Syllabus

What is the difference between a necessary condition and a sufficient condition in deductive reasoning?

A sufficient condition guarantees the outcome (if A then B). A necessary condition is required for the outcome but does not alone guarantee it. 'A is necessary for B' means B cannot occur without A.

What logical flaw is 'affirming the consequent'?

Invalidly arguing: 'If A then B; B is true; therefore A.' The consequent being true does not prove the antecedent, because B could have other causes. Example: 'If it rains the ground is wet; the ground is wet; therefore it rained' — flawed.

What logical flaw is 'denying the antecedent'?

Invalidly arguing: 'If A then B; A is false; therefore B is false.' This is invalid because B may still be true for other reasons.

What is a valid 'modus ponens' argument?

A valid form: 'If A then B; A is true; therefore B is true.' If the premises hold, the conclusion must follow.

What is a valid 'modus tollens' argument?

A valid form: 'If A then B; B is false; therefore A is false.' Denying the consequent validly forces denial of the antecedent.

What is the logical flaw of 'correlation implies causation'?

Assuming that because two things occur together or change together, one must cause the other. The link may be coincidence or due to a third (confounding) factor.

What is a 'straw man' fallacy?

Misrepresenting or oversimplifying someone's argument into a weaker version, then attacking that distorted version rather than the original claim.

What is an 'ad hominem' fallacy?

Attacking the person making an argument (their character or motives) instead of addressing the substance of the argument itself.

What is a 'false dilemma' (false dichotomy)?

Presenting only two options as if they are the only possibilities, when in fact other alternatives exist.

What is 'hasty generalisation'?

Drawing a broad conclusion from a sample that is too small or unrepresentative to support it.

What is 'circular reasoning' (begging the question)?

An argument where the conclusion is assumed within the premises, so the reasoning proves nothing new. Example: 'It is reliable because it is trustworthy.'

How do you identify the next term in an arithmetic sequence?

Find the common difference $d$ by subtracting consecutive terms, then add $d$ to the last term. The $n$th term is $a_n = a_1 + (n-1)d$.

How do you identify the next term in a geometric sequence?

Find the common ratio $r$ by dividing a term by the previous one, then multiply the last term by $r$. The $n$th term is $a_n = a_1 \cdot r^{\,n-1}$.

In the sequence $2, 6, 12, 20, 30, \ldots$, what is the pattern and the next term?

The differences increase by $2$ each time ($4, 6, 8, 10, \ldots$). The next difference is $12$, so the next term is $30 + 12 = 42$. (Equivalently $a_n = n(n+1)$.)

What strategy helps when a number sequence has no obvious single rule?

Examine the differences between terms (first differences), then the differences of those differences (second differences), and check for alternating patterns, multiplication, or two interleaved sequences.

In diagrammatic/spatial reasoning, what transformations should you check between a shape and its options?

Rotation, reflection (mirror image), translation (position shift), and changes in size, shading, number of elements, or orientation of internal features.

How can you distinguish a rotation from a reflection of a figure?

A rotation preserves the 'handedness' (chirality) of the figure — it can be turned to match. A reflection reverses it into a mirror image that cannot be matched by rotation alone in the plane.

What is a reliable method for solving 'odd one out' spatial puzzles?

Identify the property shared by the majority (e.g. number of sides, symmetry, shading rule, rotation direction), then find the single figure that breaks that rule.

In deductive reasoning from rules, how should you treat the word 'all' versus 'some'?

'All' is a universal claim allowing no exceptions; 'some' means at least one (and possibly all). You cannot deduce 'all' from 'some', and a single counterexample disproves an 'all' statement.

What does the logical statement 'No A are B' allow you to deduce?

It is equivalent to 'No B are A' (the relationship is symmetric): the two categories share no members. You cannot deduce anything about members outside A or B.

If 'All A are B' and 'All B are C', what valid conclusion follows?

'All A are C' (transitivity / a valid syllogism). Every member of A is necessarily a member of C.

What time-management technique helps maximise score under strict timed conditions?

Spend a roughly equal, capped amount of time per question; if a question exceeds that, mark it, move on, and return later. Answer easy/high-confidence items first to bank marks before the clock pressures harder ones.

In a timed test of $30$ questions in $20$ minutes, roughly how long can you spend per question on average?

$\frac{20 \text{ min}}{30} = \frac{20 \times 60}{30} = 40$ seconds per question on average. Use this as a pacing benchmark, banking time on easy items.

Why is practising under realistic timing important before the assessment?

It builds speed and accuracy together, calibrates your pacing instinct, reduces anxiety through familiarity, and exposes which question types slow you down so you can improve them before test day.

What evidence-based techniques help manage test anxiety during the assessment?

Controlled slow breathing (e.g. longer exhales), positive self-talk, focusing on one question at a time, reframing arousal as readiness, and good preparation/sleep beforehand to reduce baseline stress.

What are the most common careless errors in numerical reasoning, and how do you avoid them?

Misreading units/scale, decimal-point/place-value slips, using the wrong base for a percentage, and answering a different question than asked. Avoid them by re-reading the question and sense-checking the magnitude of your answer.

How does the elimination strategy improve your odds on multiple-choice questions?

By removing answers that are clearly wrong (impossible magnitude, wrong units, fails a quick check), you narrow the field — improving guess probability from, say, $\frac{1}{5}$ to $\frac{1}{2}$ when two options remain.

What features of an answer option let you eliminate it quickly without full calculation?

Wrong sign or direction of change, an implausible order of magnitude, wrong units, a value outside the possible range, or an answer that contradicts the question's stated constraints.

Why is precision of vocabulary important in critical-reading judgements?

Small wording changes alter meaning: qualifiers like 'all', 'most', 'may', 'always', or 'only' change whether a statement is supported. Misreading one quantifier can flip True/False/Cannot Say or hide a logical flaw.

What is the difference between 'imply' and 'infer' when discussing statements?

To imply is what the speaker or text suggests without stating outright (it comes from the source). To infer is what the reader concludes from the evidence (it comes from the audience). The text implies; the reader infers.

How should you handle a multi-step calculation under time pressure to stay accurate?

Break it into clear ordered steps, write down intermediate values, keep units attached, and do a final magnitude sense-check. Doing it in one rushed mental leap is where careless errors occur.