Chapter 01
1. Number Series & Progression Patterns
Number Series problems present a sequence of numbers following a hidden arithmetic or algebraic rule. Common patterns include arithmetic differences, double differences, prime increments, geometric multipliers, alternating series, and cube/square offsets ($n^2 \pm k$, $n^3 \pm k$).
Problem: Find the next number in the series: $4, 11, 25, 46, 74, ?$
1
Find 1st differences: $11 - 4 = 7$; $25 - 11 = 14$; $46 - 25 = 21$; $74 - 46 = 28$.
2
Observe the pattern of 1st differences: $7, 14, 21, 28$ (Multiples of 7).
3
Next difference must be $28 + 7 = 35$.
4
Calculate next term: $74 + 35 = 109$.
Final Answer: 109
Common Mistake: Looking only for multiplicative relations when numbers grow fast. Often a combination of multiplication and addition ($\times 2 + 1, \times 2 + 2, \times 2 + 3$) or square differences is the true rule.
Chapter 02
2. Alphabet & Letter Series
Letter Series problems involve sequences of single letters, letter pairs, or alphanumeric clusters governed by alphabetical positioning (1 to 26), letter skips, reverse positioning, and vowel/consonant rotations.
Problem: What is the next cluster in the sequence: $\text{B2D}, \text{E5G}, \text{H8J}, \text{K11M}, ?$
1
Analyze 1st letter: $\text{B}(2) \xrightarrow{+3} \text{E}(5) \xrightarrow{+3} \text{H}(8) \xrightarrow{+3} \text{K}(11) \xrightarrow{+3} \text{N}(14)$.
2
Analyze middle number: $2 \xrightarrow{+3} 5 \xrightarrow{+3} 8 \xrightarrow{+3} 11 \xrightarrow{+3} 14$.
3
Analyze last letter: $\text{D}(4) \xrightarrow{+3} \text{G}(7) \xrightarrow{+3} \text{J}(10) \xrightarrow{+3} \text{M}(13) \xrightarrow{+3} \text{P}(16)$.
Final Answer: N14P
Chapter 03
3. Coding-Decoding & Letter Shifts
Coding-Decoding tests your ability to detect encryption rules applied to words, numbers, or symbols. Major types include Letter Coding (positional shifts $+k/-k$, reverse order), Number Coding (sum of position values), and Substitution Ciphers ("sky is blue" $\to$ "pa da sa").
Problem: In a certain code language, $\text{LEMON}$ is coded as $\text{PWQSR}$. How is $\text{APPLE}$ written in that code?
1
Examine letter shifts in LEMON $\to$ PWQSR:
$\text{L}(12) \to \text{P}(16) \implies +4$;
$\text{E}(5) \to \text{W}(23)$ (or reverse $+4$ on backwards);
Check reverse: $\text{L}(12) \leftrightarrow \text{O}$ (opposite), $+1 = \text{P}$.
Direct shift: $+4, +18, +4\dots$ Check position: $\text{L}(12)+4=\text{P}(16)$, $\text{E}(5)+18=\text{W}(23)$ (or $-8$), $\text{M}(13)+4=\text{Q}(17)$, $\text{O}(15)+4=\text{S}(19)$, $\text{N}(14)+4=\text{R}(18)$.
2
For word with constant $+4$ shift: $\text{A}(1)+4 = \text{E}(5)$, $\text{P}(16)+4 = \text{T}(20)$, $\text{P}(16)+4 = \text{T}(20)$, $\text{L}(12)+4 = \text{P}(16)$, $\text{E}(5)+4 = \text{I}(9)$.
Final Answer: ETTPI
Chapter 04
4. Blood Relations & Family Tree Diagrams
Blood Relations questions test your capacity to decode biological and marital generational hierarchies. Drawing a clean vertical family tree is the definitive technique for eliminating ambiguity in complex dialogue questions ("Pointing to a photograph...").
Problem: Pointing to a man in a photograph, Priya said, "His mother is the only daughter of my mother." How is Priya related to that man?
1
Break down from the speaker's perspective: "My mother" = Priya's mother.
2
"The only daughter of my mother" = Priya herself (since Priya is female and the only daughter).
3
"His mother is [Priya]" $\implies$ Priya is the mother of the man in the photograph.
Final Answer: Mother
Common Mistake: Assuming gender from names. In aptitude exams, never assume someone is male or female from names like "Kiran", "Robin", or "Alex" unless specified by pronouns ("he/she") or relational terms ("father", "sister").
Chapter 05
5. Direction Sense, Angular Rotations & Shadows
Direction Sense problems test navigational awareness across the 8 cardinal directions (N, S, E, W, NE, NW, SE, SW), right/left 90-degree turns, angular displacements ($45^\circ, 135^\circ$), and shadow orientations at sunrise/sunset.
Problem: A person walks 12 km North, turns right and walks 9 km. How far and in which direction is he from his starting point?
1
Net Northward movement $y = 12\text{ km}$; Net Eastward movement $x = 9\text{ km}$.
2
Shortest distance: $d = \sqrt{12^2 + 9^2} = \sqrt{144 + 81} = \sqrt{225} = 15\text{ km}$.
3
Direction relative to origin is North-East.
Final Answer: 15 km North-East
Chapters 06 & 07
6 & 7. Analogy & Classification (Odd One Out)
Analogy establishes correspondence between two pairs ($A : B :: C : D$). Classification requires identifying the element that does not share a common characteristic with the rest of the group.
Problem: Select the related number: $6 : 222 :: 7 : ?$
1
Examine relationship between 6 and 222: $6^3 = 216$, $216 + 6 = 222$ (Pattern: $n^3 + n$).
2
Apply pattern to 7: $7^3 + 7 = 343 + 7 = 350$.
Final Answer: 350
Chapter 08
8. Syllogisms & Venn Deduction
Syllogisms test formal deductive logic. Given statements that must be treated as absolute truth, you determine which conclusions logically follow beyond any doubt. Drawing minimum-overlap Venn diagrams prevents false positives.
Statements: 1. All apples are fruits. 2. Some fruits are sweet.
Conclusions: I. Some apples are sweet. II. All fruits are apples.
1
Draw Venn: Place circle "Apples" entirely inside "Fruits". Draw circle "Sweet" overlapping "Fruits" without necessarily touching "Apples".
2
Test Conclusion I ("Some apples are sweet"): Apples and Sweet might overlap, but it is NOT mandatory. Definite truth fails $\implies$ Does not follow.
3
Test Conclusion II ("All fruits are apples"): Only some fruits are apples (Apples $\subset$ Fruits). Reverse is false $\implies$ Does not follow.
Final Answer: Neither Conclusion I nor II follows
Chapter 09
9. Seating Arrangement (Linear & Circular)
Seating Arrangement challenges require positioning 6 to 8 individuals along a straight line, parallel dual rows, or around circular/polygonal tables under directional constraints (facing center, facing outward, facing North/South).
Two-Case Strategy: Whenever a clue allows two possible positions for a person, instantly sketch two parallel diagrams (Case 1 & Case 2). Continue filling clues until one diagram violates a constraint and is eliminated.
Chapter 10
10. Analytical Floor & Scheduling Puzzles
Complex grid puzzles link multiple attributes (such as Name, Floor Number, Profession, City, Car Model). Systematic table grids with (+) for confirmed matches and ($\times$) for confirmed negatives prevent cognitive overload.
Chapter 11
11. Statement & Assumptions / Conclusions (Critical Reasoning)
Critical reasoning tests evaluate whether you can separate objective facts from unwarranted assumptions, evaluate argument strength, and determine if an action is a logical course of action.
Chapter 12
12. Data Sufficiency in Reasoning
Data Sufficiency questions consist of a question followed by two statements. Your goal is NOT to find the numerical answer, but to determine whether Statement 1 alone, Statement 2 alone, both combined, or neither is sufficient to answer the question uniquely.
Chapter 13
13. Non-Verbal & Spatial Reasoning
Non-verbal reasoning examines visual pattern progression, image rotations, figure matrix completeness, mirror reflections, and paper folding/cutting transformations.
How do I start solving complex floor and seating puzzles without getting stuck?
Never start by guessing. Begin by listing all definite clues that fix a person or floor immediately. If a clue gives two possibilities (e.g., A is on floor 2 or 6), draw two parallel cases side by side. As you add more clues, one of the cases will produce an impossible conflict and cancel out, leaving the single correct solution.
What is the difference between "definitely true" and "possibility" in Syllogisms?
A conclusion is definitely true only if it holds true across every possible Venn diagram you can draw without violating the premises. If there exists even one valid Venn diagram where the conclusion fails, it is not definitely true. In contrast, a possibility conclusion ("Some A being B is a possibility") is valid if it holds true in at least one permissible Venn diagram.
How can I quickly memorize reverse alphabet pairs for Coding-Decoding?
Use mnemonic pairs: AZ (Amazon), BY (Boy), CX (Crux), DW (Dew), EV (Even), FU (Fun), GT (GT Road), HS (High School), IR (Indian Railways), JQ (Jungle Queen), KP (Kurta Pajama), LO (Love), MN (Man). The sum of forward and reverse positions of these pairs always equals 27.
