MAT Intelligence and Critical Reasoning Syllabus

In 'Statements and Arguments', how do you decide whether a given argument is strong or weak?

A strong argument is directly related to the statement, addresses its core, and is logically sound and significant. A weak argument is irrelevant, superficial, ambiguous, based on an individual case, or restates the statement.

What is the key rule for judging arguments: should personal opinions or real-world facts be used?

No—arguments are evaluated only for relevance and logical strength relative to the statement, not by whether you personally agree or by external facts; assume the statement is true.

In the 'Statements and Assumptions' type, what is an assumption?

An assumption is something taken for granted or presupposed—an unstated idea that must be true for the statement to make sense. It is implicit, not directly written.

What is the test to decide whether an assumption is implicit in a statement?

Negate the assumption: if negating it makes the statement absurd or collapses its logic, the assumption is implicit. If the statement still holds after negation, the assumption is not implicit.

In 'Inference' questions, how does an inference differ from a directly stated fact or a conclusion?

An inference is a logically derived fact that must be true based on the given information but is not explicitly stated; a stated fact is written verbatim, while a conclusion is a summarising judgment drawn from the passage.

In 'Statement and Conclusion' problems, when does a conclusion 'follow'?

A conclusion follows only if it can be logically and definitely derived from the given statement(s) alone, without extra assumptions and without contradicting the statement.

What is the difference between an inference and an assumption in critical reasoning?

An assumption comes before/underlies the statement (a precondition taken for granted); an inference comes after (a conclusion drawn from the statement). Assumption = unstated premise; inference = unstated result.

In 'Course of Action' problems, what makes a suggested action a valid course of action?

A valid course of action must directly address the problem in the statement, be practical/feasible, and lead to improvement or solve/reduce the problem—not be extreme, impractical, or irrelevant.

In Course of Action questions, why are extreme actions like 'ban it completely' or 'punish everyone' usually rejected?

Because valid courses of action should be practical, proportionate and constructive; extreme, absolute, or punitive solutions are typically deemed impractical or unreasonable and do not 'follow'.

What is 'logical consistency' in critical reasoning, and what makes a set of statements inconsistent?

Logical consistency means a set of statements can all be true at the same time. Statements are inconsistent (contradictory) if accepting all of them forces a contradiction—no scenario satisfies them simultaneously.

What does it mean for an argument to be 'valid' versus 'sound' in logic?

An argument is valid if the conclusion necessarily follows from the premises (form is correct). It is sound if it is valid AND all its premises are actually true. Validity is about structure; soundness adds truth.

In syllogisms, what are the four standard categorical statement types (A, E, I, O)?

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

What is the 'immediate inference' from 'Some A are B' regarding the converse?

'Some A are B' implies 'Some B are A' (conversion of an I statement is valid). However it does NOT guarantee 'Some A are not B' or 'All A are B'.

In syllogisms, what conclusion follows from 'All A are B' and 'All B are C'?

'All A are C' definitely follows (and therefore 'Some A are C' and 'Some C are A'). 'All C are A' does NOT follow.

In syllogisms, what is the rule about drawing a conclusion from two particular premises (two 'Some' statements)?

No definite conclusion can be drawn from two particular premises; at least one premise must be universal for a valid categorical conclusion to follow.

In syllogisms, what is the rule about drawing a conclusion from two negative premises?

No valid conclusion follows from two negative premises ('No' / 'Some...not'). At least one premise must be affirmative to reach a definite conclusion.

In syllogisms, what is the 'either-or' (complementary pair) case and when does it apply?

When neither of two conclusions individually follows but together they exhaust all possibilities (they form a complementary I–O pair on the same terms, e.g., 'Some A are B' and 'Some A are not B'), then 'either conclusion I or II follows'.

In syllogisms, what does 'Some A are B' allow regarding the possibility 'All A are B' and 'All B are A'?

From 'Some A are B', the possibility cases 'All A are B' and 'All B are A' may both be possibly true (they don't contradict 'Some'), though neither definitely follows.

What is the difference between an analogy and a classification (odd-one-out) question?

An analogy gives a related pair and asks you to complete a second pair using the same relationship (A:B :: C:?); classification gives a group and asks you to find the item that does NOT share the common property.

In analogy problems, what are common relationship types to look for?

Synonym/antonym, part-to-whole, cause-effect, worker-tool, object-function, category-example, degree/intensity, and symbolic (number/letter pattern) relationships.

In a number-analogy like 4:64 :: 5:?, how do you find the answer?

Identify the operation linking the pair: 4³ = 64, so the rule is 'cube'. Apply it: 5³ = 125. So 4:64 :: 5:125.

What is the basic approach to solving an Input-Output (machine arrangement) problem?

Find the rule the machine applies in each step (sorting, shifting, arithmetic, or rearranging words/numbers by some criterion), confirm it across all given steps, then apply it forward or backward to reach the asked step.

In Input-Output problems, why can you usually NOT reverse-engineer the original input from a later step?

Because the rearrangement rules (e.g., 'shift the largest number to the front') are typically not reversible—information about original order is lost—so questions normally ask for forward steps, not the original input.

What general strategy helps solve puzzle problems with multiple variables (e.g., people, days, items)?

Make a grid/table linking each variable, fill in definite (direct) clues first, use elimination for negative clues, then apply conditional clues; track all possibilities until only one consistent solution remains.

In a 'blood relations within a puzzle' or coded-relation problem, what does the symbol approach involve?

Translate each relationship symbol (e.g., '+' = father, '−' = sister) into a small family chart, build the chain person by person, then read off the asked relationship—watching gender carefully.

What is the difference between verbal and non-verbal (visual) reasoning?

Verbal reasoning uses words, statements and language-based logic; non-verbal reasoning uses figures, patterns, shapes and images—testing visual pattern recognition rather than language.

In non-verbal series problems, what transformations should you check between successive figures?

Rotation (clockwise/anticlockwise by a fixed angle), reflection/mirroring, addition or removal of elements, change in shading, movement of an element along a path, and increase/decrease in number of components.

In paper folding and punching (non-verbal) problems, how is the final unfolded pattern determined?

Each punched hole reappears symmetrically across every fold line when unfolded; so a single punch on a paper folded k times produces 2^k holes arranged symmetrically about the fold axes.

In mirror-image vs water-image (non-verbal) problems, what is the difference?

A mirror image reflects left↔right (vertical axis), reversing horizontal orientation; a water image reflects top↔bottom (horizontal axis), inverting the figure vertically. Each is the reflection about the respective axis.

In figure-counting non-verbal problems (e.g., 'how many triangles'), what systematic method avoids missing figures?

Count by size/order: first the smallest individual shapes, then shapes made of two parts, three parts, and so on up to the whole figure, summing all counts—labelling regions to track combinations.