CAT Data Interpretation and Logical Reasoning Syllabus

What is the difference between people facing the centre versus facing outward in circular arrangements?

Facing centre: left = clockwise, right = anticlockwise. Facing outward: left = anticlockwise, right = clockwise. The left/right interpretation flips between the two cases.

In seating arrangement puzzles, what are 'definite' versus 'possible' clues, and which should you use first?

Definite clues fix an exact position or relationship; possible clues allow multiple placements. Always apply definite clues first to anchor the arrangement, then use possible clues to eliminate cases.

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

Your father's brother is your uncle (paternal), so his son is your cousin (cousin brother).

In blood relations, what relation is your 'mother's brother' to you?

Your mother's brother is your maternal uncle.

What technique uses + and - or symbols to solve coded blood relation problems?

The symbol/notation method: assign symbols for gender (e.g., + male, - female) and draw a family tree/generation diagram from the coded relationships to deduce the final relation.

In blood relations, what relation is your 'sister's husband' to you?

Your sister's husband is your brother-in-law.

What is a syllogism in logical reasoning?

A syllogism is a form of deductive reasoning with two given premises (statements) from which a logically necessary conclusion must be drawn.

What are the four standard types of categorical statements used in syllogisms?

A (universal affirmative: All A are B), E (universal negative: No A is B), I (particular affirmative: Some A are B), and O (particular negative: Some A are not B).

In syllogisms, what is the rule about conclusions when both premises are particular (Some)?

If both premises are particular (Some/Some not), no definite conclusion can be drawn from them alone.

In syllogisms, what is the rule about conclusions when both premises are negative?

If both premises are negative, no valid conclusion can be drawn.

What does the 'Some A are B' statement imply for the converse?

'Some A are B' implies 'Some B are A' (the I-type statement is convertible/symmetric).

What does 'All A are B' allow you to conclude by conversion?

'All A are B' only allows the conclusion 'Some B are A' (not 'All B are A'), since the converse of a universal affirmative is particular.

What is a 'possibility' conclusion in syllogisms and when is it always true?

A possibility conclusion states something 'may be' true. A possibility is valid if no premise definitely contradicts it; e.g., from 'All A are B', 'Some B are not A is a possibility' holds.

What is a logical/number sequence (series) problem?

A problem giving a sequence of numbers, letters, or figures following a hidden rule, where you must identify the pattern to find the missing or next term.

What are the common patterns to check in a number series?

Constant difference (arithmetic), constant ratio (geometric), squares/cubes, prime numbers, alternating series, and differences-of-differences (second-order patterns).

In a series, how do you detect a geometric (multiplicative) pattern?

Divide each term by its previous term; if the ratio is constant, the series is geometric and the next term is the last term multiplied by that common ratio.

What is the general approach to solving a logical puzzle (e.g., matrix/grid puzzle)?

Build a grid mapping each entity to each attribute, then mark confirmed yes/no cells from the clues, eliminating impossibilities until each entity has a unique consistent assignment.

In a floor-based puzzle, how is the lowest floor typically numbered and counted?

The ground/lowest floor is usually numbered 1 and the topmost is the highest number; 'above' means a higher floor number and 'below' means a lower floor number.

What is a key strategy for tackling puzzle-based LR sets efficiently in CAT?

Scan all sets, pick those with the most definite (fixed) clues and fewest variables, and start solving from the most constrained clue to reduce branching.

In number-based problems, what is the divisibility rule for 3?

A number is divisible by 3 if the sum of its digits is divisible by 3.

What is the divisibility rule for 11?

A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is 0 or a multiple of 11.

What is the relationship between HCF and LCM of two numbers?

HCF x LCM = product of the two numbers. So LCM = (a x b) / HCF for two numbers a and b.

In algebra-based problems, what is the quadratic formula for ax^2 + bx + c = 0?

x = (-b ± sqrt(b^2 - 4ac)) / (2a), where b^2 - 4ac is the discriminant.

For a quadratic ax^2 + bx + c = 0, what are the sum and product of the roots?

Sum of roots = -b/a; Product of roots = c/a.

What does the discriminant (b^2 - 4ac) tell you about the roots of a quadratic?

If > 0: two distinct real roots; if = 0: two equal real roots; if < 0: two complex (non-real) roots.

In geometry-based problems, what is the Pythagorean theorem?

In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: c^2 = a^2 + b^2.

What is the formula for the area of a triangle given base and height, and given three sides?

Area = (1/2) x base x height. With three sides, use Heron's formula: Area = sqrt(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2.

In arithmetic-based problems, what is the formula relating speed, distance, and time?

Speed = Distance / Time; equivalently Distance = Speed x Time and Time = Distance / Speed.

What is the simple interest formula in arithmetic problems?

Simple Interest = (Principal x Rate x Time) / 100, where rate is per annum and time is in years.

What is the compound interest amount formula for annual compounding?

Amount = Principal x (1 + Rate/100)^Time; Compound Interest = Amount - Principal.

In logical-reasoning-based problems, what distinguishes deductive reasoning from inductive reasoning?

Deductive reasoning derives a guaranteed conclusion from general premises (general to specific); inductive reasoning infers a probable generalization from specific observations (specific to general).