NATA Diagrammatic Reasoning and Aptitude Syllabus

How many odd days are in an ordinary year and a leap year?

An ordinary year (365 days) has 1 odd day; a leap year (366 days) has 2 odd days.

What is the rule for identifying a leap year?

Divisible by 4, but century years must be divisible by 400 (e.g., 2000 is a leap year, 1900 is not).

How many odd days are in 100 years and 400 years?

100 years = 5 odd days; 400 years = 0 odd days (the cycle repeats every 400 years).

What is critical thinking in the context of aptitude tests?

The disciplined evaluation of arguments, evidence, and assumptions to judge validity and draw well-reasoned, unbiased conclusions.

In 'statement and assumption' questions, what is an assumption?

Something taken for granted or presupposed—an unstated premise that must be true for the statement/action to make sense.

In inference questions, what makes a conclusion 'definitely true'?

It must follow logically and necessarily from the given premises alone, with no extra information assumed.

What is the difference between an inference and an assumption?

An inference is a conclusion drawn FROM the given information; an assumption is something presupposed (taken as given) BEFORE/within the statement.

In 'cause and effect' reasoning, how is a cause distinguished from an effect?

The cause is the event/condition that occurs first and produces a result; the effect is the outcome that follows from and depends on the cause.

What is the post hoc fallacy in cause-and-effect reasoning?

Assuming that because event B followed event A, A must have caused B—mistaking sequence for causation.

What is correlation versus causation?

Correlation means two variables move together; causation means one directly produces a change in the other. Correlation does not imply causation.

In course-of-action questions, when is a suggested action considered to 'follow'?

When it is a logical, practical, and proper step that directly addresses the problem stated and produces a reasonable improvement.

What is quantitative comparison in aptitude?

Comparing two quantities to determine whether one is greater, they are equal, or the relationship cannot be determined from the given data.

What are the four standard answer options in a quantitative comparison question?

(A) Quantity A is greater; (B) Quantity B is greater; (C) the two are equal; (D) the relationship cannot be determined.

What is estimation in numerical reasoning and when is it useful?

Approximating values by rounding numbers to find a quick, near-correct answer—useful for eliminating options and saving time when exact calculation is unnecessary.

What is the rule for rounding to estimate a product quickly?

Round each factor to a convenient nearby number, multiply, then adjust mentally; e.g., 49 × 21 ≈ 50 × 20 = 1000.

In decision-making problems with multiple conditions, how do you apply selection criteria?

Check each candidate/option against every condition; the option qualifies only if it satisfies all mandatory conditions (and relevant exceptions).

What is an 'exception condition' in eligibility/decision-making problems?

A special rule that allows a candidate failing one criterion to still qualify (or to be referred to a higher authority) if another stated condition is met.

What is the core goal of an optimization problem?

To maximize or minimize an objective (profit, output, time, cost) subject to given constraints on resources.

In linear programming, what is the objective function?

The linear expression (e.g., Profit = ax + by) that is to be maximized or minimized subject to the constraints.

In linear programming, what is the feasible region?

The set of all points satisfying every constraint—usually a polygon whose vertices are candidate optimal solutions.

Where does the optimal value of a linear objective function occur?

At a vertex (corner point) of the feasible region (by the corner-point/extreme-value theorem).

What is resource allocation in optimization problems?

Distributing limited resources (time, money, materials, labor) among competing activities to achieve the best possible outcome under constraints.

What is opportunity cost in resource-allocation decisions?

The value of the next-best alternative foregone when a particular choice is made.

In a seating/arrangement logic puzzle, what is the first step?

List all entities and constraints, fix the most definite/absolute clue first, then place others relative to it, eliminating impossible positions.

What is a 'blood relation' coding approach in logical reasoning?

Translate each relationship statement into generation levels and gender, often drawing a family tree to track who relates to whom.

In coding-decoding, what is a common letter-shift cipher technique?

Each letter is replaced by another a fixed number of positions ahead/behind in the alphabet (e.g., +1: CAT → DBU).

In direction-sense problems, how do you handle a sequence of turns?

Track net displacement using a coordinate grid (N/S = y-axis, E/W = x-axis), updating facing direction at each turn; use Pythagoras for shortest distance.

What is a Venn diagram used for in reasoning?

To represent logical relationships and overlaps between sets/categories, helping evaluate syllogisms and group membership.

In syllogisms, what does 'Some A are B' allow you to validly conclude?

It guarantees at least one A is B (and hence some B are A); it does NOT establish 'all' or 'no' relationships.

What is the difference between necessary and sufficient conditions?

A necessary condition must hold for an outcome to occur; a sufficient condition, if met, guarantees the outcome. A condition can be one, both, or neither.