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Syllogisms, blood relations, coding-decoding, seating arrangement, puzzles, series, and analytical reasoning.
| Pattern Type | Rule | Example | Next Term |
|---|---|---|---|
| Arithmetic Progression | Constant difference (d) | 2, 5, 8, 11, 14 (d=3) | 17 |
| Geometric Progression | Constant ratio (r) | 3, 9, 27, 81, 243 (r=3) | 729 |
| Squares | n^2 sequence | 1, 4, 9, 16, 25, 36 | 49 |
| Cubes | n^3 sequence | 1, 8, 27, 64, 125 | 216 |
| Square Numbers +1 | n^2 + 1 | 2, 5, 10, 17, 26, 37 | 50 |
| Cube Numbers -1 | n^3 - 1 | 0, 7, 26, 63, 124 | 215 |
| Factorial | n! | 1, 1, 2, 6, 24, 120 | 720 |
| Fibonacci | Sum of previous two | 0, 1, 1, 2, 3, 5, 8, 13 | 21 |
| Triangular Numbers | n(n+1)/2 | 1, 3, 6, 10, 15, 21 | 28 |
| Prime Numbers | Divisible by 1 and itself only | 2, 3, 5, 7, 11, 13 | 17 |
| Alternating Series | Two interleaved patterns | 2, 10, 4, 12, 6, 14 (odd: 2,4,6 even: 10,12,14) | 8, 16 |
| Difference of Differences | Second-order constant | 1, 2, 4, 7, 11 (diffs: 1,2,3,4) | 16 |
| Product Series | Each term = product of previous terms | 2, 3, 6, 18, 108 | 1944 |
| Sum of Digits | Sum of digits forms next term | 7, 7, 14, 5, 19, 10 | 1 |
| Power of 2 | 2^n | 2, 4, 8, 16, 32, 64 | 128 |
─── Alphabet Positions ───
A=1 B=2 C=3 D=4 E=5 F=6 G=7 H=8 I=9 J=10
K=11 L=12 M=13 N=14 O=15 P=16 Q=17 R=18 S=19 T=20
U=21 V=22 W=23 X=24 Y=25 Z=26
─── Vowels & Consonants ───
Vowels: A(1), E(5), I(9), O(15), U(21)
Consonants: B(2), C(3), D(4), F(6), G(7), H(8), J(10), K(11)...
─── Opposite Letters (Sum = 27) ───
A-Z(1-26), B-Y(2-25), C-X(3-24), D-W(4-23), E-V(5-22)
F-U(6-21), G-T(7-20), H-S(8-19), I-R(9-18), J-Q(10-17)
K-P(11-16), L-O(12-15), M-N(13-14)
─── Common Letter Patterns ───
Skip 1 (forward): A C E G I K M O Q S U W Y
Skip 2 (forward): A D G J M P S V Y
Skip 1 (reverse): Z X V T R P N L J H F D B
Skip 2 (reverse): Z W T Q N K H E B
Vowels only: A E I O U
Consonants only: B C D F G H J K L M N P Q R S T V W X Y Z
─── Letter-to-Number Examples ───
Pattern: A, C, F, J, O, ?
Differences: +2, +3, +4, +5, +6 → O(15)+6 = 21 = U
Pattern: Z, X, U, Q, M, ?
Differences: -2, -3, -4, -5, -6 → M(13)-6 = 7 = G
Pattern: AB, CD, EF, GH, ?
Next: IJ (pairs of consecutive letters)
Pattern: AZ, BY, CX, DW, ?
First letter: A,B,C,D → E; Second: Z,Y,X,W → V → EV| Example Series | Pattern Explanation | Missing Term |
|---|---|---|
| 2A, 4B, 6C, 8D, ? | Numbers: +2 (even); Letters: A,B,C,D (next E) | 10E |
| A1, B2, D3, G4, ? | Letters: +1,+2,+3,+4 (A→B→D→G→K); Numbers: +1 | K5 |
| Z1, Y2, W3, T4, ? | Letters: -1,-2,-3,-4; Numbers: +1 | P5 |
| AB2, CD4, EF6, GH8, ? | Letter pairs + 2x, 2x+2, 2x+4, 2x+6... | IJ10 |
| B2, D4, G7, K11, ? | Letters: +2,+3,+4,+5; Numbers: +2,+3,+4,+5 | P16 |
| Type | Relationship | Example | Answer Pattern |
|---|---|---|---|
| Synonym | Same or similar meaning | Happy : Joyful = Sad : ? | Sorrowful (same meaning) |
| Antonym | Opposite meaning | Hot : Cold = Light : ? | Dark (opposite meaning) |
| Part-Whole | Part to whole or whole to part | Wheel : Car = Page : ? | Book (part-whole) |
| Cause-Effect | One causes the other | Rain : Flood = Fire : ? | Burn/Ashes (cause-effect) |
| Tool-Worker | Tool used by worker | Surgeon : Scalpel = Author : ? | Pen (tool-worker) |
| Worker-Workplace | Person works at place | Doctor : Hospital = Teacher : ? | School (worker-workplace) |
| Product-Producer | Made by | Novel : Author = Painting : ? | Painter (product-producer) |
| Object-Function | Object and its purpose | Knife : Cut = Pen : ? | Write (object-function) |
| Degree | Intensity or level | Warm : Hot = Cold : ? | Freezing (degree/intensity) |
| Classification | Type-subtype or category-member | Dog : Animal = Rose : ? | Flower (classification) |
| Action-Object | Action performed on object | Read : Book = Eat : ? | Food (action-object) |
| Symbolic | Symbol represents something | Black : Mourning = White : ? | Peace/Purity (symbolic) |
| Pair | Relationship | Complete: 16 : 4 :: 25 : ? |
|---|---|---|
| 4 : 16 | 4^2 = 16 (square relationship) | 16 : 4 :: 25 : 5 (5^2 = 25, so answer = 5) |
| 2 : 8 | 2^3 = 8 (cube relationship) | 16 : 4 :: 25 : 5 (answer = 5, as 5^2=25) |
| 6 : 30 | 6 x 5 = 30 (multiplication) | 12 : 60 :: 8 : 40 (each x 5) |
| 12 : 3 | 12 / 4 = 3 (division) | 20 : 5 :: 16 : 4 (each / 4) |
| 15 : 45 | 15 x 3 = 45 (proportion) | 10 : 30 :: 7 : 21 (each x 3) |
| 9 : 81 | 9^2 = 81 (square) | 7 : 49 :: 11 : 121 (each squared) |
| 2 : 4 : 8 | 2^1, 2^2, 2^3 (powers) | 3 : 9 : 27 :: 4 : 16 : 64 (powers of 3, then 4) |
| Relation | Definition | Key Tip |
|---|---|---|
| Father / Mother | Direct parent | Always one generation above |
| Son / Daughter | Direct child | Always one generation below |
| Brother / Sister | Same parents | Same generation |
| Grandfather / Grandmother | Parent's parent | Two generations above |
| Grandson / Granddaughter | Child's child | Two generations below |
| Uncle | Father's or Mother's brother | Same generation as parents |
| Aunt | Father's or Mother's sister | Same generation as parents |
| Cousin | Uncle's or Aunt's child | Same generation as you |
| Nephew | Brother's or Sister's son | One generation below |
| Niece | Brother's or Sister's daughter | One generation below |
| Father-in-law | Spouse's father | Same generation as your parent |
| Mother-in-law | Spouse's mother | Same generation as your parent |
| Brother-in-law | Spouse's brother or sister's husband | Same generation |
| Sister-in-law | Spouse's sister or brother's wife | Same generation |
| Maternal Uncle (Mama) | Mother's brother | On mother's side |
| Paternal Uncle (Chacha) | Father's brother | On father's side |
| Maternal Aunt (Mausi) | Mother's sister | On mother's side |
| Paternal Aunt (Bua) | Father's sister | On father's side |
─── Method 1: Family Tree Diagram ───
Notation:
Male: (+) or Rectangle
Female: (-) or Circle
Couple: Horizontal line connecting them
Parent-Child: Vertical line going down
Siblings: Horizontal line with ---
Rules for Tree:
1. Start with the person who is definitely known
2. Draw generation by generation (top to bottom)
3. Use + for male, - for female
4. Always read the question carefully — "only son" vs "only child"
─── Method 2: Self-Referencing ───
Place yourself at center and work outward:
Above you: Parents, Grandparents, Uncles/Aunts
Same level: Siblings, Cousins, Spouse
Below you: Children, Nephews/Nieces, Grandchildren
─── Key Tricky Phrases ───
"Only son of grandfather" = Father (if grandfather has only ONE son)
"Only child of X" = X has no siblings (but may or may not be married)
"Son of my father's only son" = My son
(My father's only son = me; my son = son of me)
"My father's brother's only child" = My cousin (if that uncle has only 1 child)
"Pointing to a man, she said..." = The man is NOT the speaker herself
─── Example Problem ───
"A is B's sister. C is B's mother. D is C's father. E is D's mother.
How is A related to D?"
Solution:
D's father → E (D's mother)
D's child → C (B's mother, B's sister is A)
So A is D's grandchild (specifically, granddaughter if A is female)
Answer: A is the granddaughter of D| Statement | Question | Answer |
|---|---|---|
| "Introducing a man, a woman said: He is the only son of my mother's mother" | How is the man related to the woman? | Maternal Uncle (mother's brother) |
| "Pointing to a photograph, a man says: She is the daughter of my grandfather's only son" | How is the girl related to the man? | Sister (grandfather's only son = father; his daughter = sister) |
| "A is the son of B. C is B's sister. C has a son D and a daughter E." | How is A related to D? | Cousin (both are children of siblings B and C) |
| "Rahul says: This girl is the wife of the grandson of my mother." | How is Rahul related to the girl? | Father-in-law (grandson of mother = Rahul's son; wife of son = daughter-in-law; but Rahul is father-in-law of the girl) |
| Direction | Degrees (from North) | Turn from N (clockwise) |
|---|---|---|
| North (N) | 0 or 360 | 0 degrees |
| North-East (NE) | 45 | 45 degrees clockwise |
| East (E) | 90 | 90 degrees clockwise |
| South-East (SE) | 135 | 135 degrees clockwise |
| South (S) | 180 | 180 degrees clockwise |
| South-West (SW) | 225 | 225 degrees clockwise |
| West (W) | 270 | 270 degrees clockwise |
| North-West (NW) | 315 | 315 degrees clockwise |
─── Basic Turns ───
Right Turn = 90 degrees clockwise
Left Turn = 90 degrees anti-clockwise
About Turn = 180 degrees (reverses direction)
Right-angle turn = Right turn or Left turn
Multiple Right Turns:
1 Right = 90 degrees
2 Right = 180 degrees (reverses direction)
3 Right = 270 degrees (same as 1 Left)
4 Right = 360 degrees (back to original direction)
Multiple Left Turns:
1 Left = 270 degrees (same as 1 Right in reverse)
2 Left = 180 degrees (reverses direction)
3 Left = 90 degrees (same as 1 Right)
4 Left = 360 degrees (back to original direction)
─── Finding Final Direction ───
Start facing North:
Turn Right → East
Turn Right → South
Turn Right → West
Turn Left → South → East → North
─── Shadow Direction ───
Morning (sunrise): Shadow falls to the WEST
Noon (sun overhead): No shadow or directly below
Evening (sunset): Shadow falls to the EAST
If a man faces a shadow in the morning:
His shadow is to his West → he faces East
If a man faces a shadow in the evening:
His shadow is to his East → he faces West
─── Finding Shortest Distance ───
After movement, find:
Net North-South displacement = total North distance - total South distance
Net East-West displacement = total East distance - total West distance
Shortest distance = sqrt((Net N-S)^2 + (Net E-W)^2)
Use Pythagoras theorem if movements are perpendicular.
Example:
Walk 4 km North, turn Right (now East), walk 3 km East
Net displacement: 4 km North, 3 km East
Shortest distance from start = sqrt(16 + 9) = sqrt(25) = 5 km
─── Example: Complex Movement ───
Starting at origin, facing North:
Walk 10 m South, turn Left (now East), walk 5 m, turn Left (now North),
walk 10 m, turn Right (now East), walk 3 m.
Final position:
North-South: -10 + 10 = 0 (back to starting latitude)
East-West: 5 + 3 = 8 m East
Final position: 8 m East of starting point
Final direction: East| Problem | Solution Steps | Answer |
|---|---|---|
| A man walks 5 km South, turns right, walks 3 km, turns right, walks 5 km. Where is he? | South 5, East 3, North 5 → Net: East 3, North-South = 0 | 3 km East of start, facing West |
| Ram walks 30m North, turns right 50m, turns right 30m. Distance from start? | North 30, East 50, South 30 → Net: East 50 | 50m from start |
| A faces North, turns 135 clockwise. Which direction? | 135 from North = between East and South = South-East | South-East |
| At 6 AM, you observe your shadow to your left. Facing which direction? | Shadow left in morning (shadow is West) → Left = West → Facing North | North |
| Statement | Venn Diagram | Definite Conclusion |
|---|---|---|
| All A are B | Circle A fully inside Circle B | Some B are A (always true); Some A are B (always true) |
| Some A are B | Circles A and B partially overlap | Some B are A (always true); NO definite conclusion about All |
| No A are B | Circles A and B completely separate | All A are not B; All B are not A; Some A are not B; Some B are not A |
| Some A are not B | Part of A is outside B | Some A are B is NOT necessarily true; Some B are not A is NOT necessarily true |
| Statement 1 | Statement 2 | Definite Conclusion | Cannot Conclude |
|---|---|---|---|
| All A are B | All B are C | All A are C | — |
| All A are B | Some B are C | — | No definite conclusion about A and C |
| All A are B | No B are C | No A is C | — |
| All A are B | Some B are not C | — | Cannot say about A and C definitively |
| Some A are B | All B are C | Some A are C | Cannot say "All A are C" |
| Some A are B | Some B are C | — | No definite conclusion |
| Some A are B | No B are C | Some A are not C | Cannot say "No A are C" |
| Some A are B | Some B are not C | — | No definite conclusion |
| No A are B | All B are C | No A is C | Cannot say about relationship between A and B's other parts |
| No A are B | Some B are C | — | No definite conclusion about A and C |
| No A are B | No B are C | — | No definite conclusion about A and C |
| Some A are not B | All B are C | — | No definite conclusion (A outside B could be inside or outside C) |
| Some A are not B | No B are C | — | A outside B could be inside or outside C |
─── When to Apply "Either-Or" ───
Conditions for Either-Or:
1. Only two conclusions are possible
2. They must be complementary (one negates the other)
3. Both cannot be false simultaneously
4. All other conclusions must have been found false
Valid Complementary Pairs:
"Some A are B" AND "No A are B" → Either-Or
"All A are B" AND "Some A are not B" → Either-Or
NOT Complementary (not Either-Or):
"All A are B" AND "No A are B" → Contradictory (both cannot be true)
"Some A are B" AND "Some A are not B" → NOT complementary
─── Procedure ───
1. Draw Venn diagrams for ALL possible scenarios
2. A conclusion is "follows" ONLY if true in ALL diagrams
3. If no single diagram satisfies all conclusions, and you have
exactly two complementary conclusions left, answer is "Either-Or"
─── Example ───
Statements: All cats are dogs. Some dogs are rats.
Conclusions:
I. Some cats are rats. → Does NOT follow (cats may not overlap with rats)
II. No cat is a rat. → Does NOT follow (cats may overlap with rats)
III. Some dogs are cats. → Follows (reverse of "All cats are dogs")
IV. All dogs are cats. → Does NOT follow
Final Answer: Only III follows.| Type | Method | Example |
|---|---|---|
| Letter Shifting | Each letter shifted by fixed positions | CAT → FCW (+3); DOG → GRJ (+3) |
| Reverse Alphabet | A=Z, B=Y, C=X (A=27-Z) | CAT → XZG; DOG → WLT |
| Position Coding | Letter replaced by its position number | CAT → 3-1-20; DOG → 4-15-7 |
| Reverse Order | Letters reversed | LOVE → EVOL; CAT → TAC |
| Opposite Pair | A↔Z, B↔Y (sum=27) | CAT → XZG (C=3→24=X, A=1→26=Z, T=20→7=G) |
| Word Substitution | Each word replaced by another | Red = Blue, Sky = Sea → "Blue Sea" means "Red Sky" |
| Conditional | Code changes based on condition | If word starts with vowel: reverse; else: shift +2 |
| Number-Letter Mix | Numbers assigned to letters uniquely | A=1, B=2... then apply operations |
─── Problem 1: Letter Shifting ───
If FRIEND = HTKGPF, how is CANDLE coded?
F(+2)→H, R(+2)→T, I(+2)→K, E(+2)→G, N(+2)→P, D(+2)→F
Each letter shifted by +2
CANDLE → C(+2)=E, A(+2)=C, N(+2)=P, D(+2)=F, L(+2)=N, E(+2)=G
Answer: ECPFNG
─── Problem 2: Reverse Order ───
If ROSE is coded as ESOR, how is TULIP coded?
ROSE → reverse → ESOR
TULIP → reverse → PILUT
Answer: PILUT
─── Problem 3: Position Sum ───
If BOOK = 28, PEN = 37, what is PAGE?
BOOK = B(2)+O(15)+O(15)+K(11) = 43...
Wait, BOOK = 2+15+15+11 = 43 ≠ 28
Alternative: Check sum of first and last: B+K = 2+11 = 13, O+O = 15+15 = 30
Or: B(2)x2 + O(15) + K(11) = 4+15+11 = 30...
Try: B(2)+O(15)+O(15)+K(11) = 43...
If BOOK = 28: Maybe reverse positions: K(11)+O(15)+O(15)+B(2) → nope = 43
Try position product or different formula:
B(2)+O(15)+O(15)+K(11) = 43 with each letter x 2/3...
Actually: BOOK = 2x2 + 15x? + ... let me recalculate
B(2)x1 + O(15)x1 + O(15)x1 + K(11)x1 = 43
Check PEN = P(16)+E(5)+N(14) = 35 ≠ 37
Maybe it's: Position x 2 for consonants, x 1 for vowels?
BOOK: B(4)+O(15)+O(15)+K(22) = 56... no
Try: Sum of positions - some constant?
Let me use a simpler known example:
If CAT = 24 (C=3, A=1, T=20; sum = 24)... that works with 3+1+20 = 24
If DOG = 26 (D=4, O=15, G=7; sum = 26)... that works too
BOOK: 2+15+15+11 = 43, not 28. Let me try a different problem.
─── Problem 3 (simpler): Reverse Position ───
If APPLE = 85 (A=26, P=11, P=11, L=15, E=22 → using reverse alphabet positions)
Wait: A in reverse = 26 (26-1+1), P = 26-15 = 11, L = 26-11 = 15, E = 26-4 = 22
26+11+11+15+22 = 85 ✓
What is ORANGE using reverse positions?
O = 26-14 = 12, R = 26-17 = 9, A = 26, N = 26-13 = 13, G = 26-6 = 20, E = 22
12+9+26+13+20+22 = 102
Answer: 102| Type | Description | Key Points |
|---|---|---|
| Linear (Row) | People sit in a single straight line | Left and Right depend on facing direction; if facing North: Left = West, Right = East |
| Circular | People sit around a circle | Facing Centre: Left = clockwise, Right = anti-clockwise |
| Square / Rectangular | People sit at corners and/or middle of sides | Combination of linear and circular concepts; 4/8/10 positions typical |
| Double Row | Two rows facing each other | A's Left = B's Right and vice versa; they face each other |
| Polygon | People sit around pentagon, hexagon, etc. | Similar to circular but with fixed positions at vertices |
─── Linear Arrangement Rules ───
Facing North:
Left = West, Right = East
1st position is extreme left, last is extreme right
Facing South:
Left = East, Right = West
1st position is extreme left (viewer's right), last is extreme right
Mixed facing (some North, some South):
When two people face opposite directions:
- Their left and right are OPPOSITE of each other
- "A sits to the left of B" depends on B's facing direction
─── Circular Arrangement Rules ───
Facing Centre:
Left = Clockwise, Right = Anti-clockwise
Facing Outward (Away from Centre):
Left = Anti-clockwise, Right = Clockwise
Mixed (some face centre, some face outward):
- If facing each other: directions are OPPOSITE
- If facing same direction: directions are SAME
- "Adjacent" means next to (immediate neighbor)
- "Second to the left" means leave one person, then count
─── Solving Steps ───
1. Read all clues first before placing anyone
2. Start with DEFINITE clues (exact positions, person at corner/end)
3. Then use RELATIVE clues (sits between, sits next to, second to left of)
4. Draw negative clues too (X is NOT at end, Y is NOT next to Z)
5. Verify final arrangement with ALL given clues
6. Answer questions based on your diagram
─── Common Clue Types ───
"A sits at the extreme left/right" → Definite position
"B is third to the left of C" → Relative position
"D sits between E and F" → Adjacency
"G sits opposite to H" → Circular/Double row
"I is not at either end" → Elimination clue
"J sits second to the right of K" → Relative position
"There are two people between L and M" → Gap clue─── Problem: 5 people sit in a row facing North ───
Clues:
1. A sits at the extreme left end
2. C sits third to the right of A
3. B sits between A and D
4. E sits at the extreme right end
Solution:
Position: 1 2 3 4 5
From clue 1: A is at position 1
1:A 2: 3: 4: 5:
From clue 2: C is 3rd to right of A → position 1+3 = 4
1:A 2: 3: 4:C 5:
From clue 4: E is at extreme right → position 5
1:A 2: 3: 4:C 5:E
From clue 3: B sits between A and D
Remaining positions: 2 and 3
B must be between A(1) and D, so B = 2, D = 3
1:A 2:B 3:D 4:C 5:E
Verify: A is at extreme left ✓, C is 3rd right of A (pos 4) ✓,
B(2) is between A(1) and D(3) ✓, E at extreme right ✓
Final: A — B — D — C — E─── Basic Formulas ───
Total = Rank from Top + Rank from Bottom - 1
Rank from Top = Total - Rank from Bottom + 1
Rank from Bottom = Total - Rank from Top + 1
─── Example Problems ───
Q1: In a row of 40 students, Ram is 7th from the left.
What is his position from the right?
A1: Rank from right = 40 - 7 + 1 = 34th from right
Q2: In a class, Seema ranks 12th from the top and 28th from the bottom.
How many students are in the class?
A2: Total = 12 + 28 - 1 = 39 students
Q3: In a row, Rahul is 10th from the left and Mohan is 15th from the right.
If they interchange, Rahul becomes 20th from the left.
How many people are in the row?
A3: Mohan was 15th from right. After interchange, he is at Rahul's
original position, which is 10th from left.
Since Rahul becomes 20th from left after interchange, and he now
occupies Mohan's position:
Total = Rahul's new left + Mohan's original right - 1
Total = 20 + 15 - 1 = 34 people
Q4: A is taller than B. C is taller than D. B is taller than C.
Who is the tallest?
A4: From tallest to shortest: A > B > C > D
A is the tallest.
Q5: In a row of 50, A is 15th from left, B is 20th from right.
How many people are between A and B?
A5: B's position from left = 50 - 20 + 1 = 31st
Between A(15) and B(31): 31 - 15 - 1 = 15 people| Scenario | Formula | Example |
|---|---|---|
| Find people between two positions | |Pos1 - Pos2| - 1 | Between 8th and 15th: |8-15|-1 = 6 people |
| After interchange, find total | New left + Old right - 1 | Person A moves from 5th left to 12th left, other was 18th from right: 12+18-1 = 29 |
| Overlapping positions | If Pos(from left) + Pos(from right) - 1 > Total | Then they are the same person or data is inconsistent |
| Middle position | (Total + 1) / 2 | Middle of 21 people: (21+1)/2 = 11th position |
| After removal/insertion | Recalculate with new total | If 5 people removed from 50: new total = 45, recalculate all positions |
─── General Puzzle Approach ───
1. Read all clues completely (at least twice)
2. Identify variables: people, colors, cities, professions, etc.
3. Create a grid/table with one axis per variable type
4. Fill in DEFINITE information first (direct clues)
5. Use NEGATIVE information (X is not Y) to eliminate options
6. Use RELATIVE information (X sits next to Y, Z comes after A)
7. Combine clues to deduce new information
8. Verify final answer with ALL original clues
─── Common Puzzle Categories ───
- Floor-based: People live on floors (7-10 floors typical)
- Month-based: Activities in months (Jan-Dec)
- Day-based: Schedules (Mon-Sun)
- Box/Basket: Items placed in boxes with weights/colors
- Profession-based: People with different jobs
- City/Country: People from different places with preferences
- Family puzzles: Complex blood relations + professions
─── Key Techniques ───
- Elimination: Cross out impossible combinations
- Table/Grid: Create a matrix and fill cells
- Tree diagram: For hierarchical relationships
- Case analysis: When multiple scenarios possible, test each
- Working backwards: Start from the answer/end and work to beginning
─── Example: Floor Puzzle ───
5 people live on floors 1-5. Match person with profession.
Clues:
1. A lives on an odd-numbered floor
2. The Doctor lives immediately above the Teacher
3. B is an Engineer
4. C lives on the top floor
5. The Lawyer lives between A and B
Solution:
From clue 4: C is on floor 5
From clue 1: A is on floor 1 or 3
From clue 5: Lawyer is between A and B
If A = 1: Lawyer between 1 and B → Lawyer = 2 or 3
If A = 3: Lawyer between 3 and B → impossible (only floors 4,5 left)
So A = 1, Lawyer between A(1) and B → Lawyer on floor 2 or 3
B is Engineer (clue 3), so B is not Lawyer
From clue 2: Doctor immediately above Teacher
Try: A(1,?), Lawyer(2,?), ?, ?, C(5,?)
If Lawyer is on 2: B could be 3 or 4 (must be Engineer)
Doctor above Teacher: if Teacher=3, Doctor=4 or if Teacher=1, Doctor=2
A(1) could be Teacher → Doctor(2)=Lawyer? No, one person one profession.
Let me try:
Floor 1: A - Teacher
Floor 2: ? - Doctor (immediately above Teacher)
Floor 3: ? - Lawyer (between A and B)
Floor 4: B - Engineer
Floor 5: C - ?
Remaining profession for C: none needed if only 4 professions mentioned.
If there's a 5th: maybe Scientist.
Floor 1: A - Teacher Floor 2: D - Doctor Floor 3: E - Lawyer
Floor 4: B - Engineer Floor 5: C - Scientist─── Standard Answer Options ───
A: Statement I alone is sufficient
B: Statement II alone is sufficient
C: Both I and II together are sufficient
D: Either I or II alone is sufficient
E: Neither I nor II is sufficient; more data needed
─── Step-by-Step Approach ───
1. Read the question carefully — identify EXACTLY what is asked
2. Check Statement I ALONE — can you answer? If yes → Answer A
3. Check Statement II ALONE — can you answer? If yes → Answer B
4. Check both TOGETHER — can you answer? If yes → Answer C
5. If neither alone but either can → Answer D
6. If even together insufficient → Answer E
─── Common Traps ───
- Statement gives RATIO but question asks VALUE → Not sufficient
- Statement gives TOTAL but question asks INDIVIDUAL → May not be sufficient
- Statement gives COMPARISON but question asks EXACT → Not sufficient
- "What is the value of X?" → Need unique numerical answer, not range
- "Is X > Y?" → Need comparison, not exact values
─── Example ───
Question: What is the age of Ram?
Statement I: Ram is 5 years older than Shyam.
Statement II: Shyam is 20 years old.
Answer: C (Both needed)
From I: Ram = Shyam + 5 (but Shyam's age unknown)
From II: Shyam = 20 (but Ram's age unknown)
Together: Ram = 20 + 5 = 25 years
─── Example 2 ───
Question: In which year was Rahul born?
Statement I: Rahul is 30 years old as of 2024.
Statement II: Rahul was born after 1990.
Answer: A (Statement I alone is sufficient)
From I: 2024 - 30 = 1994 (unique answer)
Statement II alone only gives range (after 1990), not unique year.| Question Type | Example | Approach |
|---|---|---|
| Puzzle | There are 3 boxes labeled Fruits, Mix, Sweets. All labels are wrong. Pick 1 item from 1 box to fix all labels. | Pick from "Mix" box. Since all labels are wrong, "Mix" must be either all Fruits or all Sweets. If you find a fruit, it is the Fruits box. The Sweets box (wrongly labeled) must contain Mix. The remaining box is Sweets. |
| Logical Deduction | If it rains, the match is cancelled. It is raining. Is the match cancelled? | Yes. This is modus ponens: If P then Q; P is true; therefore Q is true. |
| Critical Thinking | Is it possible for a statement to be both true and false? | In classical logic, no (law of non-contradiction). In fuzzy/quantum logic, superposition allows partial truth values. |
| Pattern Recognition | What comes next: 3, 6, 18, 72, 360? | Multiply by 2, 3, 4, 5, 6: 3x2=6, 6x3=18, 18x4=72, 72x5=360, 360x6=2160 |
| Estimation | How many cricket balls fit in this room? | Estimate room volume / volume of one ball. Room: 4m x 3m x 3m = 36 cu m. Ball radius ≈ 3.6 cm, volume ≈ 0.0002 cu m. Approx 180,000 (with packing efficiency ~64%: ≈115,000). |