Chapter 3 • Unit II • Section 3.1

Exercise 3.1: Odd Man Out

Identify and isolate anomalies, classification rules, divisibility traits, and letter patterns in numerical and semantic sets.

Core Theoretical Principles

Systematic principles and analytical strategies prescribed by the CBSE curriculum for Odd Man Out.

Numerical Classification & Divisibility:
In numerical sets, examine prime numbers, parity (even/odd), perfect squares/cubes, digit sums, and divisibility rules (especially divisibility by 11: alternating sum difference must be $0$ or a multiple of $11$).
Alphabetical Letter Groups:
Examine forward positional values (EJOTY: $E=5, J=10, O=15, T=20, Y=25$), reverse opposite pairs (summing to $27$, such as $A-Z, B-Y, C-X$), and vowel/consonant distribution.
Semantic & Real-World Classification:
Analyze taxonomic hierarchies (living organisms vs. inanimate objects), administrative geography (state capitals vs. secondary cities), or tool applications.

Solved Illustrative Examples

Example 1 (Numerical Divisibility)
Find the odd man out from the set: $5720, 6710, 2640, 4270$.
Step 1: Apply divisibility rule for 11:
• $5720: (5+2)-(7+0)=0$ (divisible by 11)
• $6710: (6+1)-(7+0)=0$ (divisible by 11)
• $2640: (2+4)-(6+0)=0$ (divisible by 11)
• $4270: (4+7)-(2+0)=9 \neq 0$ (not divisible by 11)
Answer: 4270 is the odd one out.
Example 2 (Alphabetical Pairs)
Find the odd letter cluster among: $ABYZ, CDWX, EFUV, GHTV$.
Step 1: Examine letter symmetry and opposite sum 27:
• $A(1) + Z(26) = 27, B(2) + Y(25) = 27$
• $C(3) + X(24) = 27, D(4) + W(23) = 27$
• $E(5) + V(22) = 27, F(6) + U(21) = 27$
• In $GHTV$: $G(7)+T(20)=27$, but $H(8)+V(22)=30 \neq 27$ (should be $S$).
Answer: GHTV is the odd cluster.
Example 3 (Semantic & Category Classification)
Find the odd man out: (a) Bird (b) Kite (c) Crow (d) Sparrow.
Step 1: In standard textbook classification, 'Bird' denotes the universal biological class (superordinate genus), whereas Kite, Crow, and Sparrow denote individual specific members.
Answer: (a) Bird is the general category classification.
Chapter 3 Hub Chapter 3 Hub Exercise 3.2: Syllogism