NTS NAT-IA Analytical Reasoning Syllabus

For the conditional 'If P then Q,' state its contrapositive and its logical status.

The contrapositive is 'If not Q then not P,' and it IS logically equivalent to the original statement.

Which valid argument form lets you conclude Q from 'If P then Q' and P?

Modus ponens (affirming the antecedent): given 'If P then Q' and P is true, conclude Q.

Which valid argument form lets you conclude 'not P' from 'If P then Q' and 'not Q'?

Modus tollens (denying the consequent): given 'If P then Q' and Q is false, conclude P is false.

Name the two classic logical fallacies associated with conditional statements.

Affirming the consequent (from 'If P then Q' and Q, wrongly concluding P) and denying the antecedent (from 'If P then Q' and not-P, wrongly concluding not-Q).

In reasoning, what is the difference between cause and effect?

The cause is the event/condition that produces a result; the effect is the result/outcome produced by the cause. The cause precedes the effect in time.

In cause-and-effect questions, what is the key error of 'correlation implies causation'?

The mistaken assumption that because two events occur together or in sequence, one must cause the other; they may be coincidental or share a common cause.

What is a 'common cause' (confounding) explanation in cause-effect reasoning?

A situation where two correlated events are both produced by a third underlying factor, so neither directly causes the other.

In cause-effect analysis, what does 'reverse causation' mean?

When the assumed effect is actually the cause and the assumed cause is actually the effect (the direction of causation is backwards).

Define a 'necessary condition.'

A condition that MUST be present for an outcome to occur; without it the outcome cannot happen, but its presence alone does not guarantee the outcome. (Q is necessary for P: 'If P then Q.')

Define a 'sufficient condition.'

A condition whose presence GUARANTEES the outcome; if it holds, the outcome must occur, but the outcome could also arise other ways. (P is sufficient for Q: 'If P then Q.')

In 'If P then Q,' which is the sufficient condition and which is the necessary condition?

P is the sufficient condition (it guarantees Q); Q is the necessary condition (it must hold for P to hold).

What does it mean for a condition to be 'necessary and sufficient'?

The condition holds if and only if the outcome holds (P ⇔ Q): P guarantees Q and Q guarantees P; they always occur together.

How do you express 'P only if Q' as a conditional?

'P only if Q' translates to 'If P then Q' (Q is necessary for P).

In blood-relation problems, what relations are referred to as 'maternal' versus 'paternal'?

Maternal relations come through the mother's side (e.g., maternal uncle = mother's brother); paternal relations come through the father's side (e.g., paternal uncle = father's brother).

In blood relations, who is your father's brother, and who is your mother's brother?

Father's brother is your paternal uncle; mother's brother is your maternal uncle.

In blood relations, define a 'first cousin.'

The child of your uncle or aunt (i.e., a child of your parent's sibling).

In a blood-relation chain, who are your 'in-laws' such as brother-in-law and sister-in-law?

Brother-in-law = your spouse's brother or your sister's husband; sister-in-law = your spouse's sister or your brother's wife.

What is the recommended technique to solve blood-relation puzzles quickly?

Draw a family tree/diagram using symbols (e.g., + for male, - for female, horizontal lines for spouses/siblings, vertical lines for parent-child) and decode the relation step by step.

In blood relations, who is described by 'the only daughter of my grandfather' if the speaker is male?

The speaker's father's only sister would be his aunt; but 'only daughter of my grandfather' typically means the speaker's mother or aunt depending on which grandfather—generally the father's mother is excluded; it refers to the daughter (the speaker's aunt or mother).

What is a 'comparison and ranking' problem?

A problem that orders items by a single comparative attribute (height, weight, age, marks, etc.) using clues like 'greater than,' 'less than,' or 'equal to' to build a ranked sequence.

In ranking, if 'A > B' and 'B > C,' what can you conclude, and what property is this?

You conclude A > C. This is the transitive property of inequalities/ordering.

In a ranking problem, what does 'A is not the tallest' combined with 'A is taller than B and C' tell you?

A holds a middle-to-high position: someone is taller than A, while A is above B and C—so A is neither at the very top nor at the bottom.

In comparison problems, how do you handle a clue with mixed attributes like 'A is older but shorter than B'?

Treat each attribute as a separate ranking; build one order for age and a different order for height, since the two rankings are independent.

In direction-sense problems, what are the four cardinal and four ordinal (intercardinal) directions?

Cardinal: North, South, East, West. Ordinal: North-East, North-West, South-East, South-West (between the cardinals).

Standing facing North, what direction is to your right, left, and back?

Right is East, left is West, and back (behind) is South.

In direction sense, which formula gives the shortest (straight-line) distance between start and end after perpendicular movements?

The Pythagorean theorem: shortest distance = √(a² + b²), where a and b are the net displacements along the two perpendicular axes.

In a direction-sense problem, after a series of turns, how do you find net displacement North-South and East-West?

Add all northward movements and subtract southward (net vertical), and add all eastward and subtract westward (net horizontal); the two nets give the resultant position.

In direction sense, what does a clockwise 90-degree turn do to a person originally facing North?

A 90-degree clockwise turn makes them face East (North→East→South→West for successive clockwise 90-degree turns).

What does 'interpreting given conditions' require a student to do in analytical reasoning?

To translate the verbal clues precisely into logical/diagrammatic form—distinguishing strict vs. inclusive wording (e.g., 'at least,' 'exactly,' 'no more than')—without adding unstated assumptions.

When interpreting conditions, what is the difference between 'at least one,' 'exactly one,' and 'at most one'?

'At least one' = one or more; 'exactly one' = precisely one (no more, no fewer); 'at most one' = zero or one.

What is the purpose of an 'evaluating statement adequacy' (data sufficiency) question?

To decide whether the information given in one or more statements is SUFFICIENT to answer the question—not to compute the actual answer, only to judge sufficiency.

In a two-statement data-sufficiency question, what are the standard five answer options?

(A) Statement 1 alone is sufficient but not 2; (B) Statement 2 alone is sufficient but not 1; (C) Both together are sufficient but neither alone; (D) Each alone is sufficient; (E) Both together are still not sufficient.

In evaluating statement adequacy, what common mistake involves combining statements too early?

Evaluating each statement independently first is required; combining them prematurely can make you wrongly judge one statement sufficient/insufficient. Test each alone before testing together.