Logical Reasoning

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Logical Reasoning — Key Facts for CUET Syllogisms: All A are B, All B are C → Conclusion: All A are C. Check validity — never assume real-world truth Blood Relations: Father → Son/Daughter, Mother → Son/Daughter, Uncle → Aunt’s husband, Aunt → Uncle’s wife Direction and Distance: Turn left/right by 90° (quarter turn), 45° (if stated), 180° (reverse); always face initial direction Coding-Decoding: Shift each letter by a fixed number (Caesar cipher); position-based codes (A=1, Z=26) Number Series: Find pattern (difference, ratio, squares, alternating) ⚡ Exam tip: In syllogisms, check if conclusion follows necessarily from premises; don’t use real-world knowledge — go by logical form only

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Logical Reasoning — CUET General Test Study Guide

Logical reasoning in CUET tests your ability to think systematically, identify patterns, and draw valid conclusions from given information. The section is designed to assess analytical thinking rather than learned knowledge.

Syllogisms and Logical Deduction:

A syllogism consists of two premises and a conclusion. To evaluate validity:

1. Identify the subject (S) and predicate (P) of the conclusion
2. Check the middle term distribution
3. Apply rules: If both premises are negative → no conclusion; If one premise is negative → conclusion must be negative; If both premises are affirmative → conclusion must be affirmative; Term distributed in conclusion must be distributed in premise

Common Syllogism Patterns:

• All A are B (A ⊂ B), All B are C (B ⊂ C) → All A are C (A ⊂ C). VALID
• Some A are B (A ∩ B ≠ ∅) → Some B are A. VALID (conversion)
• No A is B → No B is A. VALID (obversion)
• Some A are not B → Does NOT mean Some B are not A. NOT necessarily valid.

Example: All roses are flowers. All flowers are beautiful. Conclusion: All roses are beautiful. This is VALID by the chain rule (transitivity).

Blood Relations:

• Father of X → Male parent
• Mother of X → Female parent
• Brother of X → Male sibling (same parents)
• Sister of X → Female sibling (same parents)
• Uncle → Mother’s brother OR father’s brother (maternal/paternal uncle)
• Aunt → Mother’s sister OR father’s sister (maternal/paternal aunt)
• Cousin → Uncle/Aunt’s child
• Niece → Brother/Sister’s daughter
• Nephew → Brother/Sister’s son
• Grandfather → Father’s father OR Mother’s father
• In-laws → Spouse’s family

Direction and Distance:

• Always track starting direction (usually North)
• Right turn = 90° clockwise; Left turn = 90° anticlockwise
• After each turn, note the new facing direction
• If A is 5 km North of B, then B is 5 km South of A
• Diagonal movement: consider component North-South and East-West separately

Coding-Decoding:

• Letter shift: If CODE = 3-15-4-5, each letter shifted by +3 → FRGH; to decode, shift back
• Alphabet positions: A=1, B=2, … Z=26. Reverse: Z=1, Y=2
• Word coding: “RAJ” coded as “ijk” — R→i (R=18, 18+?=26→?=8→i), A→j (1+?=26? 0→j?), J→k
• Position-based: First letter in alphabetical order becomes last, etc.

Number Series:

• Arithmetic: 3, 7, 11, 15 → pattern +4
• Geometric: 2, 6, 18, 54 → pattern ×3
• Square/Cube: 1, 4, 9, 16 → n²
• Fibonacci-like: 1, 1, 2, 3, 5, 8 → sum of previous two
• Alternating: 2, 4, 3, 5, 4 → two interleaved series (+2, -1)

Example: If PALE is coded as 2134 and LEAP is coded as 4312, how is PLEA coded? P→2, L→1, E→3, A→4 (from first equation: P=2, A=1, L=3, E=4 — but LEAP = 4312 means L=4, E=3; A=1; P=2). From PALE = 2134: P=2, A=1, L=3, E=4. From LEAP = 4312: L=4, E=3, A=1, P=2. The codes are not consistent — use positions in word: PALE = 2-1-3-4, LEAP = 4-3-1-2. So PLEA = 2-3-1-4 → “PCAS”.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Logical Reasoning — Comprehensive CUET General Test Notes

Advanced Logical Reasoning:

Venn Diagrams for Syllogisms: Draw three circles representing the three terms (A, B, C). Shade, cross-hatch, or mark X to represent the premises. Check whether the conclusion is necessarily true. Types of relations:

• All A are B → A circle completely inside B
• Some A are B → A and B circles overlap (X in overlap)
• No A is B → A and B circles don’t overlap
• Some A are not B → X in A circle but outside B circle

Statement and Conclusions (More Complex): Given statements followed by conclusions. Determine which conclusions logically follow.

• Statement: All teachers are students. Some students are boys.
• Conclusion 1: Some teachers are boys — DOES NOT FOLLOW (overlap uncertain)
• Conclusion 2: Some students are teachers — FOLLOWS (conversion of “All teachers are students”)
• Conclusion 3: All boys are teachers — DOES NOT FOLLOW (boys could include non-teacher students)

Seating Arrangements:

• Linear: People sitting in a row; determine positions from clues
• Circular: People around a table; key is whether the arrangement is facing inward (toward centre) or outward (back toward centre)
• Clues like “A is sitting between B and C” and “D is second to the left of A” can be solved systematically

Puzzle Types:

• Ordering: Rank people by height, marks, etc. from clues
• Classification: Put items into groups from clues
• Comparison puzzles: Compare multiple attributes across people

Analogy and Odd One Out:

• Analogy: Find the relationship between pair and apply to new pair
  • “Pen : Writer :: Sword : Warrior” (tool : user relationship)
  • “Caterpillar : Butterfly :: Tadpole : Frog” (immature : mature)
• Odd One Out: Find item that doesn’t share the common property
  • 3, 5, 7, 9 → 9 is odd (not prime); or 9 is the only composite
  • Apple, Mango, Carrot, Orange → Carrot is odd (vegetable, others are fruits)

Dice and Cubes:

• Opposite faces of a standard die: 1–6, 2–5, 3–4 (sum = 7)
• If 1 is visible on top and 2 is visible on front, 5 is on right (if dice oriented standardly)
• Open dice problems: Draw the net; check consistency of adjacent faces

Clock Problems:

• Hour hand moves 0.5° per minute; Minute hand moves 6° per minute
• At 3:00, hour hand at 90°, minute hand at 0°
• Angle between hands = |30H - 5.5M| degrees; if > 180°, subtract from 360°
• Mirror images: Time in mirror = 11:60 - given time (e.g., 3:15 → 8:45)

Calendar Problems:

• Odd days: Days beyond complete weeks. 400-year cycle has 146097 days (exactly 20871 weeks). Odd days = remainder when divided by 7.
• Day of week: Calculate odd days and use reference (1 Jan 2000 was Saturday)

CUET Exam Patterns (2022–2024):

• Syllogisms (2–3 questions per test) and blood relations are most frequent
• Coding-decoding and number series appear every year
• Seating arrangements (linear and circular) are common
• Analogy questions are moderate difficulty
• Dice and cube problems occasionally appear
• Common mistakes: making assumptions beyond what’s given; confusing “some” with “all”; not checking both possible directions in distance problems

⚡ Key insight: In logical reasoning, the answer must be certain — not probable or plausible. If a conclusion could be false (even if it seems true in the real world), it’s not logically valid. Use Venn diagrams for syllogisms — they eliminate ambiguity. For seating arrangements, start with definite positions and build incrementally. For coding-decoding, identify the pattern first (letter shift vs position swap), then solve.

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