NTS NAT-ICS Analytical Reasoning Syllabus

What is a circular arrangement problem?

A puzzle where entities are seated around a closed loop (e.g., a round table), so positions are relative and there is no fixed first or last seat.

For n distinct people around a circular table, how many distinct seating arrangements are there?

(n − 1)! arrangements, because rotations of the same circle are considered identical.

For n people in a circle where clockwise and counterclockwise arrangements are treated as the same (e.g., a bracelet), how many distinct arrangements exist?

(n − 1)!/2 arrangements.

In circular arrangements, why is 'left' and 'right' direction critical when people face the center versus face outward?

When seated facing the center, a person's left/right is opposite to an observer's; if they face outward, left/right flip again. Misreading facing direction reverses every neighbor relationship.

How do you handle the constraint 'A sits opposite B' at a round table of n people?

It only works when n is even; A and B occupy seats exactly n/2 apart, fixing their relative positions across the table.

What is a ranking/sequencing problem in analytical reasoning?

A puzzle ordering entities along a single comparative scale (tallest to shortest, oldest to youngest, fastest to slowest) based on relational clues.

How do you interpret 'A is taller than B but shorter than C' in a ranking puzzle?

The partial order is C > A > B, meaning C is tallest of the three and B shortest, with A in between.

In sequencing, what is the difference between a 'strict' order and clues that only give relative position?

A strict order fixes exact ranks (A is 1st), while relative clues (A is above B) only constrain pairwise positions, often leaving several valid total orders.

What does 'transitivity' mean when chaining ranking clues?

If A > B and B > C, then A > C; comparisons carry through a chain to establish order between non-adjacent items.

What is a committee/team formation (selection/grouping) problem?

A puzzle where you choose a subset of available candidates to form a group, subject to rules about who can or cannot serve together and group size.

What does a 'minimum and maximum group size' rule require you to track in selection problems?

The count of selected members must always stay within the stated bounds, so each inclusion/exclusion must be checked against how many slots remain.

In team formation, how do you handle 'A and B must serve together'?

They form a linked pair: if one is selected the other must be too, and if one is excluded the other must be excluded—diagram as A ↔ B.

In team formation, how do you handle 'A and B cannot serve together'?

At most one of them is on the team (A → ~B and B → ~A); they are mutually exclusive but both may be left off.

What is a conditional selection rule, and give its general form?

A rule stating that selecting one entity forces or forbids another; general form 'If X is selected then Y is selected' (X → Y) or 'If X then not Y' (X → ~Y).

From the conditional selection rule 'If P is chosen then Q is chosen', what must be true if Q is rejected?

P must also be rejected (contrapositive: ~Q → ~P).

How do biconditional selection rules ('A is selected if and only if B is selected') behave?

A and B are always together: either both are in or both are out; A → B and B → A both hold.

What is a matching/pairing problem in analytical reasoning?

A puzzle that assigns members of one set to members of another (e.g., people to cars, students to subjects), often as a one-to-one correspondence.

What is the difference between a one-to-one and a one-to-many matching problem?

In one-to-one, each element of one set pairs with exactly one unique element of the other; in one-to-many, a single element (e.g., one teacher) may be matched to several elements (e.g., multiple students).

What tool is most effective for solving matching/pairing puzzles with multiple attributes?

A grid (matrix) with rows and columns for each attribute set, marking confirmed matches with a tick and impossible matches with a cross to eliminate options.

What is a syllogism?

A form of deductive argument with two premises and a conclusion, where the conclusion is drawn from the relationship between terms in the premises.

In a syllogism, what are the three terms called?

The major term (predicate of the conclusion), the minor term (subject of the conclusion), and the middle term (appears in both premises but not the conclusion).

What are the four standard categorical (syllogism) statement types A, E, I, and O?

A = universal affirmative (All S are P); E = universal negative (No S are P); I = particular affirmative (Some S are P); O = particular negative (Some S are not P).

What valid conclusion follows from 'All A are B' and 'All B are C'?

All A are C.

What can be concluded from 'All A are B' and 'No B are C'?

No A are C.

Why does 'Some A are B' combined with 'Some B are C' yield no definite conclusion?

Two particular ('some') premises share no guaranteed overlap of the same members, so no valid categorical conclusion can be drawn—the middle term is undistributed.

In syllogism solving, what is the 'possibility' or 'either-or' conclusion case?

When neither of two complementary conclusions follows definitely but together they exhaust the options, the pair is accepted as an 'either...or' valid conclusion.

What is a 'statements and conclusions' question?

A reasoning item giving one or more statements assumed true, where you must decide which proposed conclusion(s) logically and necessarily follow from them.

What is the golden rule for answering 'statements and conclusions' items?

Treat the given statements as completely true even if they contradict real-world facts, and accept only conclusions that necessarily follow from them—no outside knowledge.

What is a 'statements and assumptions' question, and how is an assumption defined?

It gives a statement and asks which unstated ideas it takes for granted; an assumption is something necessarily presupposed for the statement to hold, not merely consistent with it.

What is the standard test to check whether a proposed assumption is valid in a 'statements and assumptions' item?

The negation test: negate the assumption; if the statement falls apart or becomes illogical, the assumption is necessary (implicit); if the statement still stands, it is not a required assumption.