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.
Check Your Progress 3.1
Official CBSE Applied Mathematics Support Material Questions with Step-by-Step Solutions
CYP 3.1.1CBSE Textbook Question
Find the odd one out: 16-18, 56-63, 96-108, 86-99.
Reduce each ratio to simplest fractional form: • $16:18 = 8:9$ • $56:63 = 8:9$ • $96:108 = 8:9$ • $86:99 \neq 8:9$ Answer: 86-99 is the odd pair.
CYP 3.1.2CBSE Textbook Question
Find the odd man out: Bangalore, Nagpur, Bhopal, Ranchi.
Classify by administrative capital status: • Bangalore: Capital of Karnataka • Bhopal: Capital of Madhya Pradesh • Ranchi: Capital of Jharkhand • Nagpur: Not a state capital Answer: Nagpur is the odd city.
CYP 3.1.3CBSE Textbook Question
Find the odd one out: PQXZ, CQBN, ABDF, PRMN.
Analyze vowel and consonant composition: • PQXZ, CQBN, and PRMN contain only consonants. • ABDF contains the vowel 'A'. Answer: ABDF is the odd letter group.
Applied Problem-Solving Worksheet
Test your analytical mastery with graded problem sets for Odd Man Out. Work through each problem systematically.
Speed & Accuracy Drill 1:
Solve all subtopic problems under timed test conditions (15 minutes).