What is 'Odd Man Out' in aptitude?

Odd Man Out means finding the one term in a group that does not belong to the pattern. All other terms follow a specific rule — you must identify that rule and pick the term that breaks it.

What is the fastest approach to series problems?

First check if it's a simple AP (constant difference) or GP (constant ratio). If not, compute differences between consecutive terms and look for a pattern in the differences. Also check if terms are squares, cubes, or primes.

What types of series appear most in TNPSC exams?

TNPSC commonly tests: AP/GP series, square/cube series, prime number series, alternating series (two interleaved series), and difference-based series where differences form an AP.

How do I identify a wrong term in a series?

Assume the series follows a rule, derive what each term should be, and find the one actual term that doesn't fit. The wrong term is almost always off by a small amount, often ±1 or ±2 from the correct value.

Odd Man Out and Series — Shortcuts, Patterns, and Worked Examples | TNPSC, SSC, Bank

Quick Concept Summary

Odd Man Out: Given a set of numbers/letters, find the one that doesn't belong.

Series Problems: Find the missing term, next term, or wrong term in a sequence.

Common Series Types

Type	Pattern	Example
AP (Arithmetic Progression)	Constant difference	3, 7, 11, 15, 19 (d = 4)
GP (Geometric Progression)	Constant ratio	2, 6, 18, 54 (r = 3)
Squares	n²	1, 4, 9, 16, 25, 36
Cubes	n³	1, 8, 27, 64, 125
Primes	Prime numbers	2, 3, 5, 7, 11, 13
Square + n	n² ± constant	2, 5, 10, 17, 26 (= n²+1)
Alternating	Two interleaved series	1, 2, 4, 3, 7, 4, 10...
Difference AP	Differences form AP	1, 2, 4, 7, 11, 16 (diff: 1,2,3,4,5)
Difference GP	Differences form GP	3, 4, 6, 10, 18 (diff: 1,2,4,8)
Fibonacci-type	Each term = sum of two before	1, 1, 2, 3, 5, 8, 13

Step-by-Step Approach

Compute differences between consecutive terms: d₁ = T₂−T₁, d₂ = T₃−T₂, ...
Are differences constant? → AP
Are ratios constant? → GP
Are differences themselves AP/GP? → 2nd-level pattern
Are terms perfect squares or cubes? → Square/cube series
Does every alternate term form a pattern? → Alternating two series
Can each term be expressed as f(n) = n² ± k, n³ ± k, etc.?

Worked Examples

Example 1: Find the Odd One Out (Squares)

Problem:
Find the odd one out: 2, 5, 10, 17, 26, 37, 50, 64

Step 1: Compute differences
  5−2=3, 10−5=5, 17−10=7, 26−17=9, 37−26=11, 50−37=13, 64−50=14

Step 2: Differences should be 3, 5, 7, 9, 11, 13, 15 (odd numbers)
  But the last difference is 14, not 15.

Step 3: Correct 8th term should be 50 + 15 = 65, not 64.

Pattern: T_n = n² + 1 → 1²+1=2, 2²+1=5, 3²+1=10, ..., 8²+1=65 ✓

Answer: 64 is the odd one out (should be 65)

Example 2: Find the Wrong Term (Difference Pattern)

Problem:
Find the wrong term: 1, 2, 5, 10, 17, 26, 38

Step 1: Differences
  2−1=1, 5−2=3, 10−5=5, 17−10=7, 26−17=9, 38−26=12

Step 2: Differences should be 1, 3, 5, 7, 9, 11 (odd numbers increasing by 2)
  But last difference is 12, not 11.

Step 3: Correct 7th term = 26 + 11 = 37, not 38.

Answer: 38 is the wrong term (should be 37)

Example 3: Find the Next Term (GP)

Problem:
Find the next term: 3, 9, 27, 81, 243, ?

Step 1: Ratios
  9/3=3, 27/9=3, 81/27=3, 243/81=3

Step 2: Constant ratio = 3 → GP with r = 3

Step 3: Next term = 243 × 3 = 729

Answer: 729

Example 4: Alternating Two Series

Problem:
Find the missing term: 1, 3, 3, 9, 5, 27, 7, ?, 9, 243

Step 1: Separate odd and even positions
  Odd positions: 1, 3, 5, 7, 9 (AP with d = 2)
  Even positions: 3, 9, 27, ?, 243 (GP with r = 3 → next = 81)

Answer: Missing term = 81

Full series: 1, 3, 3, 9, 5, 27, 7, 81, 9, 243

Example 5: Find Odd One Out (Prime vs Non-Prime)

Problem:
Find the odd one out: 2, 3, 7, 11, 15, 17, 19

Step 1: Check each for prime
  2 → prime ✓
  3 → prime ✓
  7 → prime ✓
  11 → prime ✓
  15 → 3 × 5 = NOT prime ✗
  17 → prime ✓
  19 → prime ✓

Answer: 15 is the odd one out (not a prime number)

Example 6: Second-Level Difference Series

Problem:
Find the next term: 4, 6, 10, 16, 24, 34, ?

Step 1: First differences
  6−4=2, 10−6=4, 16−10=6, 24−16=8, 34−24=10

Step 2: First differences: 2, 4, 6, 8, 10 → AP with d = 2

Step 3: Next first difference = 12
  Next term = 34 + 12 = 46

Answer: 46

Common Series Patterns to Memorise

Perfect Squares

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Perfect Cubes

1, 8, 27, 64, 125, 216, 343, 512, 729, 1000

Prime Numbers (first 20)

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47...

Fibonacci Sequence

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...

Triangular Numbers

1, 3, 6, 10, 15, 21, 28, 36, 45, 55... (formula: n(n+1)/2)

Tricks for Quick Solving

Trick 1: Try Differences First

Computing T₂−T₁, T₃−T₂, etc. is the fastest first step. If differences are constant → done. If they form an AP → 2nd level.

Trick 2: Ratio Check for GP

Compute T₂/T₁ and T₃/T₂. If equal → GP. Common ratios: 2, 3, 1/2, 1/3.

Trick 3: Try Square/Cube Fitting

See if terms equal n², n²+1, n²−1, n³, n³+n, etc.

Trick 4: Separate Alternating Series

If you can't find a pattern in consecutive terms, try taking every other term (positions 1,3,5,... and 2,4,6,...).

Trick 5: Wrong Term is Usually ±1 or ±2

In "find the wrong term" questions, the error is almost always small. If your derived series gives 64 but the given term is 63 or 65, check your calculation.

TNPSC Exam Pattern

Question Type	Frequency	Difficulty
Find next term in AP/GP	Very common	Easy
Find odd one out (squares/cubes/primes)	Very common	Easy
Find wrong term (difference pattern)	Common	Medium
Alternating two-series	Common	Medium
2nd-level difference series	Occasional	Medium

Practice Questions

Q1. Find the next term: 5, 10, 20, 40, 80, ? Answer: GP with r = 2 → 160

Q2. Find the odd one out: 3, 5, 7, 9, 11, 13 Answer: 9 (not a prime; all others are prime)

Q3. Find the missing term: 1, 4, 9, 16, ?, 36 Answer: 25 (series of perfect squares)

Q4. Find the next term: 2, 5, 9, 14, 20, ? Answer: Differences: 3,4,5,6 → next diff = 7 → 27

Q5. Find the wrong term: 8, 13, 21, 34, 56, 89 Answer: Each term = sum of two preceding. 8+13=21✓, 13+21=34✓, 21+34=55 (not 56) ✗. Wrong term: 56 (should be 55)

Q6. Find the odd one out: 121, 144, 169, 196, 225, 256, 288 Answer: 288 (not a perfect square; 17²=289, not 288)

Q7. Find next term: 0, 6, 24, 60, 120, ? Answer: Pattern: n³−n: 0=0, 6=2³−2, 24=3³−3, 60=4³−4, 120=5³−5 → 6³−6 = 216−6 = 210

Q8. Find the wrong term: 2, 5, 10, 17, 26, 37, 50, 64 Answer: Should be n²+1: 65 not 64. Wrong term: 64

Q9. Find missing term: 2, 3, 6, 7, 14, 15, ?, 31 Answer: Pattern: ×1+1, ×2, ×1+1, ×2... → 15×2=30, not 31. Or: pairs (2,3)(6,7)(14,15)(30,31) → missing = 30

Q10. Find the odd one out: 1, 8, 27, 64, 100, 125, 216 Answer: 100 (not a perfect cube; 4³=64, 5³=125; 100 = 10², not 10³)