CAT (Common Admission Test) Logical Reasoning (DILR) Syllabus

In a quant-based LR set involving averages, how does adding/removing a value change the average?

New average = (sum ± changed value) / (new count). To keep average constant, an added value must equal the current average; values above the average pull it up, below pull it down.

What does a two-set Venn diagram region "A only" represent, and how is it computed?

"A only" = elements in A but not in B = n(A) − n(A∩B). It is the part of circle A that does not overlap circle B.

State the two-set inclusion-exclusion formula for the union of sets A and B.

n(A∪B) = n(A) + n(B) − n(A∩B).

State the three-set inclusion-exclusion formula for n(A∪B∪C).

n(A∪B∪C) = n(A)+n(B)+n(C) − n(A∩B) − n(B∩C) − n(C∩A) + n(A∩B∩C).

In a three-set Venn problem, how do you express "exactly two of the three sets"?

Exactly-two = [n(A∩B)+n(B∩C)+n(C∩A)] − 3·n(A∩B∩C). Each pairwise intersection includes the all-three region, so subtract it three times to leave only the exactly-two regions.

In Venn problems, how do you find "exactly one set" given the pairwise and triple intersections?

Exactly-one = n(A∪B∪C) − (exactly-two) − (all-three). Equivalently compute each single region as n(A) minus its overlaps, then sum the three single-only regions.

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

"All A are C" follows validly. (Universal affirmative chains through the shared middle term B.)

In syllogisms, does any definite conclusion follow from "Some A are B" and "Some B are C"? Why or why not?

No definite conclusion follows. Two particular ("some") premises cannot guarantee a relationship between A and C — the overlapping B members of each may be different, so neither "some A are C" nor any negative is certain.

In syllogisms, what is the rule about the number of negative premises required to draw a negative conclusion?

At least one premise must be negative to validly draw a negative conclusion, and two negative premises yield no valid conclusion. Also, if a premise is negative the conclusion must be negative.

What does the syllogism complementary-pair rule ("either-or" possibility) state?

When neither "Some A are B" nor "No A are B" individually follows, but together they exhaust all cases, the pair "Either some A are B or no A are B" follows as a valid either/or conclusion.

In syllogisms, what valid immediate conversion can you make from "Some A are B"?

"Some B are A" (conversion of a particular affirmative is valid). Also "No A are B" converts to "No B are A." But "All A are B" converts only to "Some B are A," not "All B are A."

In binary-logic / truth-teller puzzles, what are the two categories of people and how do they respond?

Truth-tellers always make true statements; liars always make false statements. (Some variants add 'alternators' who alternate true/false.) Solve by assuming a person's type and checking for contradictions.

What is the standard technique to solve a truth-teller and liar puzzle?

Assume one person is a truth-teller (or liar), trace the implications of all statements, and check consistency. If a contradiction arises, the assumption is wrong; the consistent assignment is the solution.

In binary-logic puzzles, if a person says "I am a liar," what does this reveal about classic two-type (truth-teller/liar) worlds?

It's a paradox impossible for either pure type — a truth-teller wouldn't call themselves a liar, and a liar wouldn't truthfully admit it. So in strict two-type worlds no one can truthfully or falsely say exactly that, signaling an alternator or a trick statement.

In Data Sufficiency questions, what is the standard answer scheme for the five options?

(A) Statement 1 alone sufficient, 2 not; (B) Statement 2 alone sufficient, 1 not; (C) both together sufficient, neither alone; (D) each alone sufficient; (E) both together still insufficient.

In Data Sufficiency, what is the cardinal rule about how you must evaluate the two statements?

Evaluate each statement independently first (never carry information from one to the other), and only combine them if neither alone is sufficient. Determine sufficiency, not the actual answer value.

In Data Sufficiency, what counts as a statement being "sufficient" for a value question?

It is sufficient if it pins the answer to one unique value. If it allows two or more possible values, it is insufficient — even one counterexample makes a statement insufficient.

In Data Sufficiency for a yes/no question, when is a statement sufficient?

When it gives a definite, consistent answer — always "yes" or always "no." A statement that yields "sometimes yes, sometimes no" is insufficient; note that a consistent "no" is still sufficient.

In coding-decoding (letter-shift) problems, how do you decode a word encoded by shifting each letter forward by a fixed number k?

Shift each letter backward by k positions in the alphabet (wrapping around Z→A). First deduce k by comparing one known plaintext/ciphertext pair, then apply the reverse shift to all letters.

In coding-decoding, what is "reverse/opposite letter" coding (mirror coding) and the quick mapping for it?

Each letter maps to its opposite from the other end (A↔Z, B↔Y, C↔X, ...). Quick rule: position-from-start + position-from-end = 27, so the code of the letter at position p is the letter at position (27 − p).

In symbol/substitution coding, what is the systematic approach to crack the code?

Compare pairs of coded words sharing common words/letters; the symbol appearing in both messages corresponds to the common element. Eliminate matched symbols, then deduce remaining ones by position.

In an Input-Output (machine) reasoning problem, what defines the "output" of each step?

The machine applies a fixed rule (e.g., arrange certain words alphabetically or numbers in increasing/decreasing order, one element shifted per step) to the previous step's result; each line is one step's output until no further rearrangement is possible (final step).

In Input-Output problems, how do you find the rule when given the input and a few step outputs?

Compare consecutive steps to see which one element moved and where (front/back) and in what order (ascending/descending, alphabetical, by value). Identify the pattern of which element is selected each step and its destination.

In Input-Output problems, why can you often NOT reconstruct the input from a later step?

Because the rearrangement loses original ordering information — multiple inputs can lead to the same intermediate step. The process is forward-deterministic but not reversible, so input cannot be uniquely recovered from output.

What is the key difference between a "comparison-based" arrangement clue (taller/older) and a fixed-position clue?

A comparison clue (e.g., "A is taller than B") gives only relative order, not exact positions, and may leave gaps; a fixed-position clue (e.g., "A is 3rd") locks an absolute slot. Build a relative chain first, then anchor it with fixed clues.

In ranking problems, how do you interpret "A is third from the top and fifth from the bottom"? What is the total number of people?

Total = (position from top) + (position from bottom) − 1 = 3 + 5 − 1 = 7. The subtraction avoids double-counting A.

In a double-line (two parallel rows facing each other) arrangement, what spatial relationship links a person in row 1 to a person in row 2?

Each person in row 1 faces exactly one person in row 2 (and vice versa). Note the rows face opposite directions, so left/right are mirrored between the two rows; a person's 'opposite' is the one directly across.

In blood-relation logic, how do you decode a chain like "A is the mother of B, who is the father of C"? What is A to C?

B is male (father of C) and B is A's child (A is B's mother), so A is C's grandmother (paternal grandmother). Resolve chains step-by-step, tracking gender and generation.

In a Quant-based LR set using ratios, how do you convert a ratio like 3:4:5 into actual counts given a total of 60?

Sum the ratio parts (3+4+5 = 12), find one part = 60/12 = 5, then multiply: 15, 20, 25. The total must be divisible by the sum of parts for integer counts.

What general 3-step problem-solving order should you apply to almost any LR/DILR set?

1) Read all conditions and identify the structure (linear, circular, grid, selection, etc.) and the variables; 2) Plug in definite clues to build a base diagram/table; 3) Use conditional and negative clues to eliminate cases until a unique consistent arrangement remains.