Module 2: S4 Reasoning
Topic 4: Series, Coding, Operator Substitution & Analogy
1 Number Series (Pattern Catalog)
Series questions test pattern recognition speed. Test the series in the strict order of priority below.
Priority Hierarchy
1. Prime Series: $2, 3, 5, 7, 11, 13, 17, 19, 23 \dots$
2. Perfect Powers: $n^2 \pm k \quad \text{or} \quad n^3 \pm k$
3. Difference Series: $\Delta_1 = a_{n+1} - a_n$, then $\Delta_2$
4. Multiplicative: $a_{n+1} = a_n \times k \pm m$
5. Fibonacci: $a_n = a_{n-1} + a_{n-2}$
2. Perfect Powers: $n^2 \pm k \quad \text{or} \quad n^3 \pm k$
3. Difference Series: $\Delta_1 = a_{n+1} - a_n$, then $\Delta_2$
4. Multiplicative: $a_{n+1} = a_n \times k \pm m$
5. Fibonacci: $a_n = a_{n-1} + a_{n-2}$
Difference Tree Method
Master Alphabet Positional Chart
| Forward | 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Reverse | Z-26 | Y-25 | X-24 | W-23 | V-22 | U-21 | T-20 | S-19 | R-18 | Q-17 | P-16 | O-15 | N-14 |
2 Analogy Types & The "Multiple Logic" Trap
UPSC Rule Precedence
If two options satisfy two different rules for $6 : 30 :: 8 : \text{?}$
Rule A: $6 \times 5 = 30 \implies 8 \times 5 = \mathbf{40}$
Rule B: $6^2 - 6 = 30 \implies 8^2 - 8 = \mathbf{56}$
Hierarchy: Prime > Square/Cube > Multiplication/Division > Addition/Subtraction.
Therefore, Rule B ($n^2 - n$) takes precedence. Select 56.
Therefore, Rule B ($n^2 - n$) takes precedence. Select 56.
Operator Substitution Shortcut
When asked which two signs should be interchanged to fix an equation, focus on the Division ($\div$) sign!
Example: $12 + 6 \times 3 \div 2 - 8 = 19$
Check if $3 \div 2$ produces a fraction. Since $3/2 = 1.5$ (non-integer), the $\div$ sign MUST be moved to a position where it produces a whole number (e.g., swapping $\div$ and $+$ gives $12 \div 6 \dots = 2$).
Check if $3 \div 2$ produces a fraction. Since $3/2 = 1.5$ (non-integer), the $\div$ sign MUST be moved to a position where it produces a whole number (e.g., swapping $\div$ and $+$ gives $12 \div 6 \dots = 2$).