CMAT Logical Reasoning Syllabus

Which conversion is valid for 'No A is B', and which is invalid for 'All A are B'?

'No A is B' converts validly to 'No B is A' (E converts to E). 'All A are B' cannot convert to 'All B are A' (A only converts to the particular 'Some B are A').

What is the 'possibility' rule used to evaluate syllogism conclusions like 'Some A are not B is a possibility'?

A possibility conclusion is true if the given statements do not rule it out (the scenario can be drawn without contradiction). If the statements force the situation a different way, the possibility is false.

In a syllogism, what does the Venn diagram method involve and why is it preferred?

Draw circles representing each term and overlap them per the statements, then test each conclusion against all valid diagrams. It is preferred because a conclusion holds only if it is true for every possible diagram.

What distinguishes a 'strong' argument from a 'weak' argument in argument-evaluation questions?

A strong argument is both relevant to the question and directly addresses it with substantial, logical reasoning. A weak argument is irrelevant, trivial, of minor importance, ambiguous, or based on a false assumption.

In a Cause and Effect question, how do you identify which statement is the cause and which is the effect?

The cause is the earlier, independent event that produces the other; the effect is the later event resulting from it. Test: removing the cause should remove the effect, and the cause precedes the effect in time.

What is a common trap when judging cause and effect between two correlated events?

Assuming correlation equals causation, or that two events have a direct cause-effect link when both may instead be independent effects of a common third cause.

What is the difference between an 'inference' and an 'assumption' when drawn from a passage?

An inference is a conclusion logically extracted FROM the stated facts (comes after the statement); an assumption is something taken for granted that underlies the statement (comes before it).

In logical deduction, what is a valid inference required to be?

It must be necessarily true given the premises - it cannot go beyond the information, must not contradict the facts, and should be the most directly supported conclusion, not merely probable.

In number series, what arithmetic patterns should you check first?

Constant difference (arithmetic), constant ratio (geometric), differences forming their own series, squares/cubes, prime numbers, and alternate-term patterns.

In the series 2, 6, 12, 20, 30, ..., what is the pattern and the next term?

Differences increase by 2 each time (4, 6, 8, 10), i.e. terms are n(n+1): 1x2, 2x3, 3x4... The next difference is 12, so the next term is 30 + 12 = 42.

In an alphabet series, what numeric positions do A, M, N, and Z hold, and what is the reverse-position trick?

A=1, M=13, N=14, Z=26. Reverse (EJOTY/opposite) position of any letter = 27 - its forward position (e.g. C is 3rd from start and 24th from end since 27-3=24).

What is the EJOTY mnemonic used for in alphabet problems?

E, J, O, T, Y mark positions 5, 10, 15, 20, 25 respectively, allowing quick location of any letter's number by counting from the nearest of these milestones.

In letter-shift coding (e.g. CAT becomes ECV), how do you decode it?

Find the constant shift in alphabetical positions between original and code letters (here +2), then reverse the shift (subtract 2) on the code to recover the original word.

What are the main types of Coding-Decoding patterns tested?

Letter-shifting (forward/backward), letter-to-number coding, substitution (word-for-word), symbol coding, and conditional/matrix coding where rules depend on position or symbols.

How do you solve a 'substitution' coding question such as 'sky is called sea, sea is called river... what do birds fly in?'

Replace each real word with its given substitute and answer using the substitute term - birds fly in the 'sky', and sky is called 'sea', so the answer is 'sea'.

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

Analogy: identify the relationship in a given pair and apply the same relationship to complete a second pair. Classification: find the common property among items and select the one that does not share it.

List common relationship types used in verbal analogies.

Cause-effect, part-whole, worker-tool, synonym, antonym, object-function, category-member, and degree/intensity relationships.

In symbol-based operations where +, -, x, ÷ are interchanged, what rule governs the order of evaluation?

First substitute the symbols with their reassigned operations, then apply BODMAS/PEMDAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) to compute the result.

In 'mathematical inequality' coding (e.g. @ means greater than or equal to), how do you combine two relations like A @ B and B > C?

Translate symbols to inequality signs, align them into a single chain (A >= B > C), then derive the definite relation between the end terms (A > C). A conclusion is true only if a single unbroken inequality direction connects the terms.

In visual/non-verbal reasoning series, what transformations should you look for between figures?

Rotation (clockwise/anti-clockwise by a fixed angle), reflection, addition/removal of elements, change in shading, increase in number of sides, and movement of an element along a path.

In a clock, how many degrees does the hour hand and the minute hand each move per minute?

The minute hand moves 6 degrees per minute (360/60); the hour hand moves 0.5 degrees per minute (360/12/60). The minute hand gains 5.5 degrees per minute on the hour hand.

What is the formula for the angle between the hour and minute hands at H hours and M minutes?

Angle = |30H - 5.5M| degrees. If the result exceeds 180, subtract from 360 to get the smaller angle.

How many times in 12 hours do the hands of a clock coincide and how often are they at right angles?

The hands coincide 11 times in 12 hours (22 times a day). They form a right angle (90 degrees) 22 times in 12 hours (44 times a day).

What is the odd-days concept and how is the day of the week found in calendar problems?

Odd days = remainder when the total number of days is divided by 7. Counting odd days from a known reference date and mapping the remainder (0=same weekday, 1=next day, etc.) gives the required day.

State the leap-year rule and the odd days contributed by ordinary versus leap years.

A year is a leap year if divisible by 4, except centuries which must be divisible by 400. An ordinary year (365 days) has 1 odd day; a leap year (366 days) has 2 odd days.

When a cube of side n units is painted on all faces and cut into unit cubes, how many small cubes have exactly 3, 2, 1, and 0 painted faces?

3 faces (corners) = 8; 2 faces (edges) = 12(n-2); 1 face (face centres) = 6(n-2) squared; 0 faces (interior) = (n-2) cubed.

On a standard die, what is the rule about opposite faces, and which numbers are opposite?

Opposite faces of a standard die sum to 7: 1 opposite 6, 2 opposite 5, 3 opposite 4. Faces that appear together in different views are therefore adjacent, never opposite.

Given two views of a dice with one common face, how do you find the face opposite a target face?

If a face appears in both views (common face), rotate; the faces NOT adjacent to the target in any view are its opposite. By elimination, the face never seen adjacent to the target is opposite it.

In Input-Output (machine logic) problems, what is the goal and how do you find the rule?

A machine rearranges words/numbers in a fixed step-by-step pattern each step. Compare consecutive steps to deduce the operation (e.g. arrange words alphabetically, numbers ascending, shift one element per step), then apply that rule to reach any later step.

In Input-Output problems, why can you usually not work backwards from the final output to the input?

Because the rearrangement loses information about original positions (it is not always reversible), so questions ask for forward steps; you must determine the logic from the given input rather than reconstruct the input from the output.