NTS NAT-IE Analytical Reasoning Syllabus

In a matching grid, what can you conclude once a row has only one open cell remaining?

That single remaining cell must be the correct match for that row; mark it O and then mark X across the rest of its column.

In assignment puzzles, why must each confirmed match (O) be followed by Xs in its row and column?

Because each item matches exactly one item in the other category, so a confirmed pairing makes all other pairings in that same row and column impossible.

Define a 'logical deduction' in analytical reasoning.

A conclusion that necessarily follows from given premises/statements by valid reasoning, true in every case the premises hold, with no extra assumption.

What is a syllogism?

A logical argument with two premises and a conclusion, e.g., 'All A are B; all B are C; therefore all A are C.'

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

All A are C (valid by transitivity of universal affirmatives).

From 'Some A are B' and 'All B are C', what can be concluded?

Some A are C. (At least the A's that are B are also C.)

Why does 'All A are B' NOT allow you to conclude 'All B are A'?

Because the relationship is one-directional; B may include members that are not A. The converse of a universal statement is not automatically true.

Define an 'assumption' as tested in analytical reasoning.

An unstated premise that must be true for an argument's conclusion to hold; it is taken for granted and bridges the gap between evidence and conclusion.

What is the 'negation test' for identifying a necessary assumption?

Negate the candidate assumption; if the argument falls apart or the conclusion no longer holds, it is a necessary assumption. If the argument survives, it is not.

Define a 'conclusion' in the context of statement-conclusion questions.

A judgement or inference that logically and definitely follows from the given statement(s), without requiring outside information.

In statement-conclusion problems, when is a conclusion 'valid' versus 'invalid'?

Valid if it must be true given the statements alone; invalid if it requires extra assumptions, is merely possible, or contradicts the statements.

Define a 'cause and effect' relationship in analytical reasoning.

A link where one event (the cause) directly produces or brings about another event (the effect); the cause precedes and is responsible for the effect.

In cause-and-effect questions, what is the common trap of 'correlation versus causation'?

Two events occurring together or in sequence do not prove one caused the other; they may share a common cause or be coincidental.

How do you decide which of two related statements is the cause and which is the effect?

The cause occurs first in time and is the explanatory/independent event; the effect occurs after and is the result. The effect cannot precede its cause.

In cause-effect statement pairs, what does 'both statements are effects of a common cause' mean?

Neither statement causes the other; instead a third unstated factor produces both, so they are parallel effects rather than cause and effect of each other.

What does it mean to 'strengthen' an argument?

To add information that makes the conclusion more likely or better supported, e.g., by confirming an assumption or ruling out alternative explanations.

What does it mean to 'weaken' an argument?

To add information that makes the conclusion less likely, e.g., by attacking an assumption, providing a counterexample, or offering an alternative cause.

What is the single most effective way to weaken a causal argument (A causes B)?

Present an alternative cause for B, or show B occurs without A, or that A occurs without B, breaking the proposed causal link.

Why does an answer choice that is 'out of scope' neither strengthen nor weaken an argument?

Because it does not bear on the argument's premises, assumption, or conclusion; irrelevant information leaves the argument's strength unchanged.

In strengthen/weaken questions, what is the role of identifying the assumption first?

Most strengtheners support the assumption and most weakeners attack it; pinpointing the assumption tells you exactly what to confirm or undermine.

What is the standard form of an 'if-then' (conditional) statement and its parts?

'If P, then Q.' P is the antecedent (sufficient condition); Q is the consequent (necessary condition).

In 'If P then Q', what does P being a 'sufficient' condition mean?

P guarantees Q: whenever P is true, Q must be true. P is enough to ensure Q.

In 'If P then Q', what does Q being a 'necessary' condition mean?

Q is required for P: P cannot be true unless Q is true. Without Q, P is impossible.

Given 'If P then Q', what is the valid inference called 'modus ponens'?

If P is true, then Q is true. (Affirm the antecedent to conclude the consequent.)

Given 'If P then Q', what is the valid inference called 'modus tollens'?

If Q is false (not Q), then P is false (not P). (Deny the consequent to deny the antecedent.)

Why are 'affirming the consequent' (Q therefore P) and 'denying the antecedent' (not P therefore not Q) invalid?

Because 'If P then Q' does not say Q only comes from P; Q can be true for other reasons and P can be false while Q is still true. Both are formal fallacies.

In logic, what does the inclusive 'OR' (P or Q) mean, and when is it false?

Inclusive OR is true when at least one of P, Q is true (possibly both); it is false only when both P and Q are false.

What does 'AND' (P and Q) require for the whole statement to be true?

Both P and Q must be true simultaneously; if either is false, 'P and Q' is false.

How is 'P unless Q' translated into if-then form?

'P unless Q' means 'If not Q, then P' (equivalently 'P or Q'). Unless introduces the condition under which P need not hold.

State the contrapositive of 'If P then Q', and what is true about its truth value?

The contrapositive is 'If not Q, then not P.' It is logically equivalent to the original and always has the same truth value.

What are the converse and inverse of 'If P then Q', and are they equivalent to the original?

Converse: 'If Q then P.' Inverse: 'If not P then not Q.' Neither is equivalent to the original, but the converse and inverse are equivalent to each other.

State De Morgan's Laws for negating AND/OR statements.

not(P and Q) = (not P) or (not Q); not(P or Q) = (not P) and (not Q). Negation flips AND to OR and negates each part.

How do you negate the statement 'All X are Y'?

Its negation is 'Some X are not Y' (at least one X is not Y). The negation of a universal is a particular.

How do you negate 'Some X are Y'?

Its negation is 'No X are Y' (equivalently 'All X are not Y').

When reading a data table, what should you check first before answering questions?

Read the title, row and column headers, and the units of measurement to know exactly what each value represents.

In a table/chart problem, how do you compute percentage change between two values?

Percentage change = [(New value - Old value) / Old value] x 100.

What does a pie chart represent, and how do you convert a sector to a value?

A pie chart shows parts of a whole as percentages/angles of 360 degrees. Value of a sector = (sector's percentage / 100) x total, or (sector angle / 360) x total.

In a bar chart versus a line graph, what is each best suited to show?

Bar charts compare discrete categories/quantities; line graphs show trends or change over a continuous variable such as time.

When comparing two quantities in a chart, what is the difference between 'ratio' and 'percentage of'?

Ratio expresses A to B as A:B (or A/B). 'A as a percentage of B' = (A / B) x 100, expressing A relative to B as a percent.