LESSON 13.6 — Analytical Reasoning
A. Standard Map
| Topic | Typical stem | Attack method | GATE AR frequency |
|---|---|---|---|
| Number / letter series | “What is the next term?” | Identify rule type; check differences, ratios, alternating streams | Medium |
| Coding–decoding | “If HIDE = … then HIGH = ?” | Decode rule from two examples; verify; apply | Medium — 2025 Q7 |
| Blood relations | “How is X related to Y?” | Draw family tree; assign gender only when stated | Medium |
| Direction sense | “How far is she from start?” | Coordinate grid; cumulative displacement | Medium — 2021 Q6 |
| Syllogisms | “Which conclusions follow?” | Draw Venn diagram for each statement; test conclusion | High — 2022 Q9 |
| Venn diagrams | “How many are in only A?” | Inclusion-exclusion formula; fill regions inside-out | High — 2023 Q6 |
| Seating / ordering | “How many arrangements?” | Linear: complementary counting; ordering: build a chain | Medium — 2021 Q5, 2022 Q4 |
GATE AR reality: Syllogism and quantifier-based logic appear most consistently. Coding-decoding appeared in 2025 with a prime-number rule. Seating and direction problems appear once every two years. Series questions are embedded in verbal and numerical items. Every topic here can be solved to guaranteed correctness with a method — guessing is not needed.
B. Mechanism in Words
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Name the type the moment you read the problem. Each type has exactly one method. Misidentifying coding-decoding as a series problem produces a guaranteed wrong answer. Read the stem carefully: “next term” = series; “code for X given Y” = coding; “how is X related to Y” = blood relations.
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Draw before computing. For blood relations, draw a tree. For direction sense, draw a coordinate grid. For syllogisms, draw a Venn diagram. For seating, draw seats and label. Skipping the diagram causes errors that are invisible until you check the answer.
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For syllogisms and Venn diagrams: test each conclusion independently. Draw the Venn regions as permitted by the premises, then ask: “Is this conclusion true in every possible valid diagram?” If there is any diagram where the conclusion fails, the conclusion is invalid.
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For coding-decoding: derive the rule from both given examples before applying it. One example is never sufficient — a rule that fits one pair often breaks on the second. Always verify with both.
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For direction sense: fix a coordinate origin and update position after each move. Do not rely on compass-rose mental rotation. North = +y; South = −y; East = +x; West = −x. Left turn changes direction counterclockwise; right turn clockwise.
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For ordering and seating: use the complementary counting principle when a constraint bans one arrangement. Total arrangements − banned arrangements = valid arrangements. This is faster than listing valid cases directly.
C. Core Concept Explanations
C1. Number and Letter Series — Arithmetic, Geometric, Alternating, Square/Cube
How to find the rule:
1. Compute first differences (term₂ − term₁, term₃ − term₂, …).
2. If differences are constant → AP (arithmetic progression).
3. If differences form an AP → second-order AP (differences of differences are constant).
4. If ratios are constant → GP (geometric progression).
5. If the series has two interleaved patterns → alternating (split odd-position and even-position terms and analyse separately).
Letter series: Letters have position values (A=1, B=2, …, Z=26). Apply the same arithmetic or geometric rules to positions. Skip (or not) the direction of alphabetical movement.
Key patterns to recognise instantly:
| Pattern | Clue | Example |
|---|---|---|
| AP | Constant first difference | 3, 7, 11, 15 (d = +4) |
| GP | Constant ratio | 2, 6, 18, 54 (r = 3) |
| Square | Differences are odd integers | 1, 4, 9, 16, 25 (differences: 3, 5, 7, 9) |
| Cube | Differences are 3n²−3n+1 | 1, 8, 27, 64 (differences: 7, 19, 37) |
| Fibonacci | Each = sum of previous two | 1, 1, 2, 3, 5, 8, 13 |
| Alternating | Odd positions follow one rule, even another | 2, 10, 4, 20, 8, 40 |
Common trap: Assuming a geometric series when the first two terms happen to share a ratio that does not continue. Always verify the rule with at least three consecutive pairs.
C2. Coding–Decoding — Letter Shift, Position, Word-Level
GATE coding-decoding questions provide two coded examples and ask for the code of a third word. The rule must be derived from both examples — a rule that fits only one is insufficient.
Common coding rules:
– Position shift: each letter shifts by a fixed number of places (Caesar cipher). Rule: code(L) = L ± k (with wraparound).
– Position-based formula: code(L) = f(position of L), e.g., 2n − 1, 2n + 1, 27 − n.
– Reverse alphabet: A↔Z, B↔Y, C↔X, …; formally, code(L) = 27 − position(L).
– Prime mapping: code(L) = the Nth prime, where N = alphabetical position of L. Tested in GATE AR 2025 Q7 (HIDE → 19-23-7-11; H=8 → 8th prime = 19, I=9 → 9th prime = 23, D=4 → 4th prime = 7, E=5 → 5th prime = 11).
– Word-level coding: whole words are replaced by other words based on a semantic or functional relationship.
Derivation method:
1. List each letter of the first coded example with its position and code.
2. Compute the transformation (difference, ratio, prime index, etc.) for each letter.
3. Verify that the same rule applies to every letter in the second coded example.
4. Apply the confirmed rule to the target word.
Letter series vs coding: Series questions ask “what comes next in a sequence?” Coding questions give you two mappings and ask you to apply the rule to a new input. Do not mix the two methods.
C3. Blood Relations — Diagram Method
Blood relation questions describe family connections in words and ask how two named persons are related. The most reliable method is to draw a family tree as you read.
Diagram conventions:
– Box or name at the top → ancestor; lower → descendant.
– Horizontal line = married/coupled; vertical line = parent-child.
– Gender is assigned only when explicitly stated. “My parent’s sibling” is not necessarily an uncle; do not assume.
Key relation chains to memorise:
| Statement | Resolved relation |
|---|---|
| Son of my mother = | Brother (if different person) or self |
| Mother of my father = | Paternal grandmother |
| Father of my mother = | Maternal grandfather |
| Only daughter of my mother’s father = | My mother (if she is the only daughter) |
| Sibling of my parent = | Aunt or uncle (gender uncertain unless stated) |
| Child of my sibling = | Nephew or niece |
GATE trap: “Pointing to a photo, X says he is the son of my grandfather’s only son.” The only son of grandfather = X’s father (if the only son is X’s father). Son of X’s father = X himself or X’s brother. Since X is pointing to a photo of someone else, the person is X’s brother.
Gender trap: Do not assume the gender of a person unless it is stated. If the problem says “parent’s sibling,” that sibling could be male or female. Mark gender as unknown (use “?” in the diagram) until the text provides clarity.
C4. Direction Sense — Cumulative Displacement
Coordinate method (mandatory for GATE):
– Fix start point at origin (0, 0).
– North = positive y; South = negative y; East = positive x; West = negative x.
– Update coordinates after each move.
– Final position = (x, y); distance from start = √(x² + y²).
Turning rules:
– Facing North: left turn → West; right turn → East.
– Facing East: left turn → North; right turn → South.
– Facing South: left turn → East; right turn → West.
– Facing West: left turn → South; right turn → North.
GATE AR 2021 Q6 pattern: Directions NE and NW given explicitly; NE means equal East and North components; NW means equal North and West components. Resolve each NE/NW step into x and y components before updating coordinates.
Straight-line distance vs path length: The question nearly always asks for straight-line distance from the starting point — use Pythagoras. Path length (total km walked) is the sum of all individual steps.
Common Pythagorean pairs for GATE: (3,4,5), (5,12,13), (8,15,17), (6,8,10), (9,12,15). Recognise these to avoid irrational answers in well-set questions.
C5. Syllogisms — Venn Method; Valid vs Invalid Conclusions
A syllogism gives two or more categorical statements and asks which conclusions necessarily follow.
Statement types and Venn representations:
| Statement | Diagram rule |
|---|---|
| All A are B | Circle A is entirely inside circle B |
| No A is B | Circles A and B are completely separate (no overlap) |
| Some A are B | Circles A and B overlap (intersection is non-empty) |
| Some A are not B | Part of circle A lies outside circle B |
Valid inference chains (must memorise):
| Premises | Valid conclusion |
|---|---|
| All A are B + All B are C | All A are C |
| All A are B + No B is C | No A is C |
| All A are B + Some B are C | No guaranteed conclusion about A and C |
| Some A are B + All B are C | Some A are C |
| Some A are B + No B is C | Some A are not C |
| No A is B + All C are B | No C is A |
GATE AR 2022 Q9 (actual): All teachers are professors + No professor is a male → No teacher is a male (valid chain: T⊂P, P∩M=∅ → T∩M=∅). Some males are engineers + No professor is male → No guaranteed conclusion about engineers and professors (the “some” creates a gap). Only Conclusion III (No male is a teacher) was valid.
Test for validity: Draw the Venn diagram that satisfies all premises. If the conclusion is true in every possible such diagram → valid. If any valid diagram makes it false → invalid. If and only if the conclusion must be true in all cases.
Quantifier precision (GATE AR 2023 Q6): “Almost all of X’s friends are hardworking” → “Some of X’s friends are hardworking” is a valid inference. “All of X’s friends are hardworking” is NOT — “almost all” ≠ “all.”
C6. Venn Diagrams — 2-Set and 3-Set
2-set inclusion-exclusion:
|A ∪ B| = |A| + |B| − |A ∩ B|
Rearranging: |A ∩ B| = |A| + |B| − |A ∪ B|
Only A (in A but not B) = |A| − |A ∩ B|
3-set inclusion-exclusion:
|A ∪ B ∪ C| = |A| + |B| + |C| − |A∩B| − |B∩C| − |A∩C| + |A∩B∩C|
Region-filling strategy (inside-out):
1. Fill the innermost region first: only all three = |A∩B∩C|.
2. Fill two-set intersections (excluding the triple): |A∩B only| = |A∩B| − |A∩B∩C|.
3. Fill single-set regions: |A only| = |A| − |A∩B| − |A∩C| + |A∩B∩C|.
4. Verify: sum of all regions = |A ∪ B ∪ C|.
“At least one” = |A ∪ B ∪ C|. “None” = Total − |A ∪ B ∪ C|.
At most one = only-A + only-B + only-C + none.
Complement interpretation: “How many are NOT in A?” = Total − |A|. This uses the total of the entire population, not |A ∪ B|.
C7. Seating / Ordering — Linear, Circular
Linear seating — total arrangements:
n distinct persons in n seats: n! arrangements.
With one person fixed at one seat: (n−1)!.
With one person excluded from one seat: n! − (n−1)! (complementary counting).
GATE AR 2021 Q5 (actual): 4 persons, R cannot sit at position 2.
Valid = 4! − 3! = 24 − 6 = 18 (complementary: subtract all arrangements where R is at seat 2).
Ordering / ranking problems (GATE AR 2022 Q4 pattern): Build a chain from comparative clues.
– “A is harder than B” → B < A in the ordering.
– Combine all clues into a single ordered chain; identify the extremes.
– If two items are not compared, their relative order is undetermined — do not infer it.
Circular seating (awareness):
– n persons in a circle: (n−1)! distinct arrangements (one position is fixed to remove rotational equivalence).
– For arrangements with a reflective symmetry constraint (necklace problems): (n−1)! / 2.
– GATE GA typically presents linear seating, not circular. Circular is mentioned as awareness only.
Consecutive / non-consecutive constraints:
– “A and B must sit together”: treat A+B as a single unit → (n−1)! × 2! arrangements.
– “A and B must NOT sit together”: total − together = n! − (n−1)! × 2!.
D. Worked Examples and Practice Sets
Series Pattern Taxonomy Table
| Series type | Rule | Example | Next term | Detection clue |
|---|---|---|---|---|
| Arithmetic (AP) | Constant difference d | 5, 9, 13, 17 | 21 (d=4) | First differences constant |
| Geometric (GP) | Constant ratio r | 3, 6, 12, 24 | 48 (r=2) | First ratios constant |
| Square | Terms are n² | 1, 4, 9, 16 | 25 | First differences are odd (3,5,7,9) |
| Cube | Terms are n³ | 1, 8, 27, 64 | 125 | Second differences are 6n |
| Second-order AP | Differences form AP | 1, 2, 4, 7, 11 | 16 (diffs: 1,2,3,4,5) | Second differences are constant |
| Alternating | Two interleaved APs or GPs | 2, 10, 4, 20, 8, 40 | 16 (odd: ×2; even: ×2) | Odd-position terms follow one rule, even another |
| Fibonacci | Each = sum of previous two | 1, 1, 2, 3, 5, 8 | 13 | Each term = tₙ₋₁ + tₙ₋₂ |
| Multiply-add | Each = previous × k + c | 3, 7, 15, 31, 63 | 127 (×2+1) | Ratio approaches k; differences also double |
Diagnostic checklist: Compute first differences → constant? (AP) → No. Compute first ratios → constant? (GP) → No. Are terms perfect squares or cubes? (Square/Cube) → No. Compute differences of differences → constant? (Second-order AP) → No. Try splitting into odd/even positions. (Alternating) → If still unsure, check Fibonacci.
Worked Example 1 — Syllogism with Venn Method
Given:
Statement 1: All painters are artists.
Statement 2: All artists are creative people.
Statement 3: Some creative people are not scientists.
Conclusions:
I. All painters are creative people.
II. Some creative people are painters.
III. Some scientists are not artists.
Step 1 — Draw the Venn diagram:
From S1: Painters ⊂ Artists (painter circle entirely inside artist circle).
From S2: Artists ⊂ Creative (artist circle entirely inside creative circle).
Combined: Painters ⊂ Artists ⊂ Creative — a nested three-circle structure.
From S3: Part of Creative lies outside Scientists — the creative-scientist overlap is non-exhaustive.
Step 2 — Test each conclusion:
Conclusion I — “All painters are creative people”:
Painters ⊂ Artists ⊂ Creative → Painters ⊂ Creative by transitivity. This holds in every valid diagram. VALID ✓
Conclusion II — “Some creative people are painters”:
Since all painters are creative (Conclusion I, proven valid), and the set of painters is non-empty, some creative people are painters. VALID ✓
Conclusion III — “Some scientists are not artists”:
S3 says some creative are not scientists, but this does not tell us the converse (some scientists are not creative, or some scientists are not artists). The Venn diagram is compatible with a diagram where all scientists are artists — S3 doesn’t rule this out. INVALID ✗
Answer: Conclusions I and II are valid; Conclusion III is not.
Worked Example 2 — 3-Set Venn Calculation
Given: In a group of 100 people surveyed about beverage preferences:
60 like Coffee (C), 50 like Tea (T), 40 like Juice (J).
30 like both Coffee and Tea, 20 like both Tea and Juice, 15 like both Coffee and Juice. 10 like all three.
Find: (a) How many like only Coffee? (b) How many like at least one? (c) How many like none?
Step 1 — Fill regions inside-out:
– Only all three: 10
– Only C and T (not J): 30 − 10 = 20
– Only T and J (not C): 20 − 10 = 10
– Only C and J (not T): 15 − 10 = 5
– Only C: 60 − 20 − 5 − 10 = 25
– Only T: 50 − 20 − 10 − 10 = 10
– Only J: 40 − 10 − 5 − 10 = 15
Step 2 — At least one (|C ∪ T ∪ J|):
Using inclusion-exclusion:
= 60 + 50 + 40 − 30 − 20 − 15 + 10 = 95
Verify: 25 + 10 + 15 + 20 + 10 + 5 + 10 = 95 ✓
Step 3 — None:
= 100 − 95 = 5
Answers: (a) Only Coffee = 25; (b) At least one = 95; (c) None = 5.
E. Common Confusions
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“Some A are B” does not imply “Some B are A” is provable from syllogism premises alone. It is true in real logic, but GATE syllogism questions require conclusions to follow from the given statements, not from general logical equivalences. “Some B are A” is in fact always convertible from “Some A are B” — but check whether the question permits this conversion.
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“All A are B” does NOT mean “All B are A.” Students frequently reverse the direction of the universal statement. “All cats are animals” does not imply “All animals are cats.” The set relationship is A ⊂ B, not A = B.
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Blood relations: gender assumed without being stated. “My father’s sibling” is not necessarily “my uncle” — the sibling could be female (making her an aunt). Mark gender as unknown unless the text uses a gendered term.
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Direction: “turned left” vs “turned to face left.” Turning left from North gives West, not East. Always update the facing direction at each turn before the next movement.
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Series: the first two terms are insufficient to fix a rule. Three terms determine an AP or GP. Two terms are compatible with infinitely many rules. Always use at least three terms to confirm before selecting the next term.
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Venn: “only C and T” ≠ |C∩T|. The intersection |C∩T| includes those who like all three. “Only C and T” excludes those who also like J. Compute: |C∩T only| = |C∩T| − |C∩T∩J|. This subtraction is the most common 3-set Venn error.
F. Exam Traps
| Trap | Incorrect belief | Correct principle |
|---|---|---|
| Affirming the consequent | From “All A are B” + “X is B,” conclude “X is A” | Invalid inference. B is a superset of A; being in B doesn’t guarantee being in A |
| Invalid conclusion from “Some” + “All” | From “Some A are B” + “All B are C,” conclude “All A are C” | Valid: “Some A are C.” Invalid: “All A are C” — only the subset of A that overlaps B can be extended to C |
| Series jump without rule | A series has an apparent pattern for 3 terms; student extends without checking the 4th term | Always verify the rule holds for all consecutive pairs, not just the first two gaps |
| Two-term rule assumption | 2, 4 → assume GP with r=2; could equally be AP with d=2 | Never select a rule from fewer than three terms; use additional terms to disambiguate |
| Alternating series treated as single AP | 2, 5, 4, 10, 8, 20 seen as “differences vary randomly” | Split into odd and even positions: odd = 2,4,8 (GP r=2); even = 5,10,20 (GP r=2) |
| Blood relation gender assumed | “Father’s parent” assumed to be grandfather | “Father’s parent” is either grandfather (father’s father) or grandmother (father’s mother). Do not assign gender until the text specifies |
| Coding rule derived from one example | One example of HIDE → code fits a certain rule; rule applied directly | Always verify with the second coded example before applying. Rules that fit one word often fail on the second |
| Syllogism: partial chain accepted | From “All A are B” + “Some C are B,” conclude “Some C are A” | Invalid: B is the middle term but it appears as the predicate in both premises (the middle term must be distributed at least once). No valid conclusion |
| Direction: relative left/right vs absolute | Facing South, “turn left” thought to give West | Turn left from South = East (not West). Relative turns depend on current facing direction, not the compass map |
| Venn “at least one” includes “all three” | Student double-counts the triple-overlap | Inclusion-exclusion automatically corrects for this: |
G. Answer-Writing Cues
Syllogism validation template:
“Drawing the Venn diagram: [describe set containment from each statement]. Testing Conclusion [X]: in the valid diagram, [conclusion] holds because [specific containment relationship]. Therefore Conclusion [X] is [valid/invalid].”
Series rule derivation template:
“First differences: [list]. Second differences: [list]. Rule identified as [AP / GP / second-order AP / alternating]. Applying: next term = [previous term] [+/×/other] [value] = [answer].”
Direction sense template:
“Starting at (0,0) facing [direction]. After each move: [(x,y) coordinates and facing direction at each step]. Final position: ([x], [y]). Distance = √([x²] + [y²]) = [answer] km.”
Time-boxing rule:
“Syllogism and Venn: 90 seconds for 2-mark questions — draw diagram first (30 sec), test each conclusion (20 sec each). Series: 45 seconds for 1-mark — list differences, ratios, or split odd/even before choosing.”
H. PYQ Linkage Note
| Skill | GATE AR GA appearance | Pattern |
|---|---|---|
| Syllogism — 3 statements, partial chain | 2022 Q9 (2 marks) | Teachers/Professors/Males. Only Conclusion III valid; I and II failed because “some males are engineers” + “no professor is male” leaves engineers-vs-professors undetermined |
| Quantifier inference — “almost all” vs “all” | 2023 Q6 (2 marks) | “Almost all” → “some” is valid; “all” is not. Classic quantifier-weakening rule |
| Seating — complementary counting | 2021 Q5 (1 mark) | 4 persons, R not at seat 2: 4! − 3! = 18. Complementary method is standard |
| Ordering / ranking chain | 2022 Q4 (1 mark) | 5 languages ranked by difficulty; chain built from comparative clues: S<F<D<J<C |
| Direction sense — coordinate resolution | 2021 Q6 (2 marks) | NE and NW directions resolved into equal x/y components; final position found by tracking coordinates |
| Coding-decoding — prime mapping | 2025 Q7 (2 marks) | HIDE=19-23-7-11; rule: each letter → Nth prime where N = alphabetical position. H(8)→8th prime=19, I(9)→9th prime=23, etc. |
| Number series — geometric split | 2024 Q4 (2 marks) | Mixed infinite series split into two geometric sub-series; not a “next term” series but required recognising GP structure |
| Blood relations | Not confirmed in 2021–2026 GA | Appears in other GATE streams; syllabus-listed; medium-probability for 2027 |
Forecast for 2027: Syllogism is near-certain based on 2022 and 2023 recurrence. Coding-decoding is likely after its 2025 appearance. Direction sense recurs approximately every two years. A series question may appear embedded in a letter analogy or number pattern.
I. Mini-Check — Lesson 13.6
Instructions: Q1 and Q2 are MSQ — select all correct options. Q3, Q4, Q5 are MCQ with one correct answer. No NAT questions.
Q1. (MSQ) Based on the following statements, which conclusions are valid? Select all that apply.
Statements:
1. All painters are artists.
2. All artists are creative people.
Conclusions:
(A) All painters are creative people.
(B) Some creative people are painters.
(C) All creative people are artists.
(D) No creative person is a painter.
Answer: (A), (B)
Explanation:
– (A) Painters ⊂ Artists ⊂ Creative (by transitivity of S1 and S2). All painters are creative. Valid ✓
– (B) Since all painters are creative (from A) and painters is a non-empty set, some creative people are (at least) painters. Valid ✓
– (C) “All creative people are artists” reverses S2. S2 says all artists are creative, not that all creative people are artists. Creative is the superset; not every creative person is necessarily an artist. Invalid ✗
– (D) Directly contradicts (B) which is proven valid. If some creative people are painters, then it is false that no creative person is a painter. Invalid ✗
Q2. (MSQ) Which of the following correctly identify the next term in the given series? Select all that apply.
(A) 1, 4, 9, 16, 25 → next term is 36.
(B) 2, 4, 8, 16, 32 → next term is 54.
(C) 3, 5, 9, 17, 33 → next term is 65.
(D) 0, 1, 1, 2, 3, 5, 8 → next term is 13.
Answer: (A), (C), (D)
Explanation:
– (A) Pattern: n² (1²=1, 2²=4, 3²=9, 4²=16, 5²=25). Next: 6²=36 ✓
– (B) Pattern: geometric, r=2 (2,4,8,16,32). Next: 32×2=64, not 54. ✗
– (C) Pattern: each term = 2×(previous) − 1. 3→5: 2×3−1=5. 5→9: 2×5−1=9. 9→17. 17→33. Next: 2×33−1=65 ✓
– (D) Fibonacci: 0,1,1,2,3,5,8. Next: 5+8=13 ✓
Q3. (MCQ) In a certain code, ARCH is written as 26-9-24-19 and PLAN is written as 11-15-26-13. Using the same code, how would DOME be written?
(A) 4-12-14-5
(B) 23-15-14-22
(C) 23-12-14-22
(D) 22-12-14-23
Answer: (C) 23-12-14-22
Explanation:
Derive the rule from ARCH:
A(1)→26: 27−1=26. R(18)→9: 27−18=9. C(3)→24: 27−3=24. H(8)→19: 27−8=19.
Rule: code(letter) = 27 − alphabetical position.
Verify with PLAN: P(16)→11=27−16 ✓; L(12)→15=27−12 ✓; A(1)→26 ✓; N(14)→13=27−14 ✓.
Apply to DOME: D(4)→23, O(15)→12, M(13)→14, E(5)→22. Code = 23-12-14-22.
(A) uses the alphabetical position directly (not the transform). (B) and (D) invert O and E — applying the rule in wrong order.
Q4. (MCQ) Priya starts at point A facing North. She walks 4 km, then turns right and walks 3 km, then turns right again and walks 4 km. How far is she from A, and in which direction?
(A) 5 km, East
(B) 3 km, South
(C) 3 km, East — but facing South
(D) 7 km, South
Answer: (C) 3 km away from A, facing South
Explanation:
Coordinate trace from (0,0):
– Face North, walk 4 km → (0, 4)
– Turn right → now facing East; walk 3 km → (3, 4)
– Turn right → now facing South; walk 4 km → (3, 0)
Facing: South. Position: (3, 0).
Distance from A = √(3² + 0²) = 3 km.
(A) “East” is wrong — she is facing South. (B) 3 km South is directionally wrong — she is 3 km East of A, not South of A. (D) 7 = 4 + 3 — this is the total path length, not the straight-line distance from A.
Q5. (MCQ) Pointing to a photograph, Ananya says: “He is the son of the only daughter of my maternal grandfather.” How is the person in the photograph related to Ananya?
(A) Father
(B) Brother
(C) Nephew
(D) Cousin
Answer: (B) Brother
Explanation:
Step through the chain:
– My maternal grandfather = my mother’s father.
– Only daughter of my maternal grandfather = my mother (she is his only daughter).
– Son of my mother = my brother (since the photo is of someone else, not Ananya herself).
The person in the photograph is Ananya’s brother. (A) Father would require the son to be one generation up. (C) Nephew would require the person to be the son of Ananya’s sibling, not her mother. (D) Cousin requires a different branch of the family tree.