Odd Man Out and Series questions with answers and concepts

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Odd Man Out and Series problems test your ability to identify patterns in sequences of numbers, letters, or figures. In 'Odd Man Out' questions, you must identify the element that doesn't follow the established pattern. In 'Series' questions, you need to find the next or missing term by recognising the underlying rule governing the sequence.

Key formulas and rules

7 rules

Arithmetic Progression (AP): $T_{n} = a + (n - 1) d$ , Sum $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$

Geometric Progression (GP): $T_{n} = a r^{n - 1}$ , Sum $S_{n} = \frac{a ( r ^{n} - 1 )}{r - 1}$ (for $r \neq = 1$ )

Square numbers pattern: $n^{2} \in {1, 4, 9, 16, 25, 36, 49, 64, 81, 100, \dots}$

Cube numbers pattern: $n^{3} \in {1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, \dots}$

Prime numbers sequence: ${2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, \dots}$

Fibonacci recurrence: $F_{n} = F_{n - 1} + F_{n - 2}$ with $F_{1} = 1, F_{2} = 1 ⟹ {1, 1, 2, 3, 5, 8, 13, 21, \dots}$

Differences of differences (Quadratic series): If second difference is constant $2 a$ , $T_{n} = a n^{2} + bn + c$

Key concepts

Arithmetic Series

In an arithmetic series, each term is obtained by adding or subtracting a fixed number (common difference) from the previous term. Example: 3, 7, 11, 15, 19... (common difference = 4). To identify: calculate the difference between consecutive terms. If the difference is constant, it's an AP.

Geometric Series

In a geometric series, each term is obtained by multiplying or dividing the previous term by a fixed number (common ratio). Example: 2, 6, 18, 54, 162... (common ratio = 3). To identify: divide each term by the previous term. If the ratio is constant, it's a GP.

Squares and Cubes

Many series are based on perfect squares or cubes. Recognise squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144... Recognise cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000... Some series may add/subtract a constant to squares/cubes.

Prime Numbers

Prime numbers are natural numbers greater than 1 with exactly two factors: 1 and the number itself. Series: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29... Note: 2 is the only even prime number. Composite numbers (non-primes) in a prime series are the odd one out.

Mixed and Alternating Patterns

Complex series may combine multiple patterns. Alternating series have two interleaved patterns (odd positions follow one rule, even positions follow another). Example: 2, 5, 4, 10, 6, 15... (odd positions: +2, even positions: +5). Check positions separately when the overall pattern isn't obvious.

Odd Man Out Strategy

To find the odd one out: (1) Analyse the entire set for a common property - could be divisibility, prime/composite, even/odd, or a mathematical relationship. (2) Check if all but one number share a characteristic. (3) Verify if all but one follow a sequence pattern. (4) Look for digit-based patterns (sum of digits, product of digits, reverse).

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Worked examples

Example 1

Find the odd number out in the following sequence: $8, 27, 64, 100, 125, 216$ .

Solution

Step 1: Analyze prime and power properties.
- $8 = 2^{3}$
- $27 = 3^{3}$
- $64 = 4^{3}$
- $125 = 5^{3}$
- $216 = 6^{3}$
- $100 = 1 0^{2}$ (a square, but not a perfect cube of an integer)

Answer: 100 is the odd number out.

Example 2

Find the missing next term in the series: $2, 6, 12, 20, 30, ?$

Solution

Step 1: Examine consecutive differences.

6 - 2 = 4, 12 - 6 = 6, 20 - 12 = 8, 30 - 20 = 10

Differences form an arithmetic progression $+ 2$ each step: $4, 6, 8, 10$ .

Step 2: Compute next term.

Next difference = 10 + 2 = 12

Next term = 30 + 12 = 42

Alternative formulation: $n (n + 1)$ for $n = 1, 2, 3, 4, 5 ⟹ 6 \times 7 = 42$ .

Answer: 42.

Example 3

Find the odd number out: $3, 5, 7, 12, 17, 19$ .

Solution

Step 1: Check primality of terms.
- $3, 5, 7, 17, 19$ are all prime numbers.
- $12$ is composite ( $12 = 2^{2} \times 3$ ).

Answer: 12.

Example 4

Determine the next number in the Fibonacci sequence: $1, 1, 2, 3, 5, 8, 13, ?$

Solution

Step 1: Recall the Fibonacci recurrence.

F_{n} = F_{n - 1} + F_{n - 2}

Step 2: Add the two preceding numbers.

F_{8} = 8 + 13 = 21

Answer: 21.

Representative solved questions

See the kind of question in this topic before opening the full practice set.

Question 1

Find the next term: 2, 5, 11, 23, 47, ?

Answer: B. 95

Explanation

Each term is 2 x previous term + 1:
$2 \times 2 + 1 = 5, 2 \times 5 + 1 = 11, 2 \times 11 + 1 = 23, 2 \times 23 + 1 = 47, 2 \times 47 + 1 = 95$

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 2

Find the next term: 1, 2, 6, 24, 120, ?

Answer: D. 720

Explanation

These are factorials: 1!, 2!, 3!, 4!, 5!
$1 = 1, 2 = 2 \times 1, 6 = 3 \times 2 x 1, 24 = 4 \times 3 x 2 \times 1, 120 = 5 \times 4 x 3 \times 2 x 1$
Next = 6! = 720

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 3

Find the next term: 1, 4, 10, 19, 31, ?

Answer: C. 46

Explanation

The differences increase by 3 each time:
$1 + 3 = 4, 4 + 6 = 10, 10 + 9 = 19, 19 + 12 = 31, 31 + 15 = 46$

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Common mistakes and useful habits

First check for arithmetic progression (constant difference) and geometric progression (constant ratio) - these are the most common patterns.
Memorise squares up to 20^2 (400) and cubes up to 10^3 (1000) for quick pattern recognition.
For odd man out questions, check divisibility rules - all numbers except one may be divisible by a certain number.
When no obvious pattern appears, try breaking the series into odd-positioned and even-positioned terms separately.
For letter series, convert letters to their alphabetical positions (A=1, B=2, etc.) and analyse the numeric pattern.
Check digit sums or digit products if the numbers don't form an obvious mathematical pattern.

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Next topic: General Aptitude

Odd Man Out and Series questions with answers and concepts

152 practice questionsPage updated 11 Nov 2026Review metadata pendingPractice questions

Practise this concept

Key formulas and rules

7 rules

Arithmetic Progression (AP): $T_{n} = a + (n - 1) d$ , Sum $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$

Geometric Progression (GP): $T_{n} = a r^{n - 1}$ , Sum $S_{n} = \frac{a ( r ^{n} - 1 )}{r - 1}$ (for $r \neq = 1$ )

Square numbers pattern: $n^{2} \in {1, 4, 9, 16, 25, 36, 49, 64, 81, 100, \dots}$

Cube numbers pattern: $n^{3} \in {1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, \dots}$

Prime numbers sequence: ${2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, \dots}$

Fibonacci recurrence: $F_{n} = F_{n - 1} + F_{n - 2}$ with $F_{1} = 1, F_{2} = 1 ⟹ {1, 1, 2, 3, 5, 8, 13, 21, \dots}$

Differences of differences (Quadratic series): If second difference is constant $2 a$ , $T_{n} = a n^{2} + bn + c$

Key concepts

Arithmetic Series

Geometric Series

Squares and Cubes

Prime Numbers

Mixed and Alternating Patterns

Odd Man Out Strategy

Check the idea while it is fresh.Open a focused exercise without losing this article.Practise this concept

Worked examples

Example 1

Find the odd number out in the following sequence: $8, 27, 64, 100, 125, 216$ .

Solution

Step 1: Analyze prime and power properties.
- $8 = 2^{3}$
- $27 = 3^{3}$
- $64 = 4^{3}$
- $125 = 5^{3}$
- $216 = 6^{3}$
- $100 = 1 0^{2}$ (a square, but not a perfect cube of an integer)

Answer: 100 is the odd number out.

Example 2

Find the missing next term in the series: $2, 6, 12, 20, 30, ?$

Solution

Step 1: Examine consecutive differences.

6 - 2 = 4, 12 - 6 = 6, 20 - 12 = 8, 30 - 20 = 10

Differences form an arithmetic progression $+ 2$ each step: $4, 6, 8, 10$ .

Step 2: Compute next term.

Next difference = 10 + 2 = 12

Next term = 30 + 12 = 42

Alternative formulation: $n (n + 1)$ for $n = 1, 2, 3, 4, 5 ⟹ 6 \times 7 = 42$ .

Answer: 42.

Example 3

Find the odd number out: $3, 5, 7, 12, 17, 19$ .

Solution

Step 1: Check primality of terms.
- $3, 5, 7, 17, 19$ are all prime numbers.
- $12$ is composite ( $12 = 2^{2} \times 3$ ).

Answer: 12.

Example 4

Determine the next number in the Fibonacci sequence: $1, 1, 2, 3, 5, 8, 13, ?$

Solution

Step 1: Recall the Fibonacci recurrence.

F_{n} = F_{n - 1} + F_{n - 2}

Step 2: Add the two preceding numbers.

F_{8} = 8 + 13 = 21

Answer: 21.

Representative solved questions

See the kind of question in this topic before opening the full practice set.

Question 1

Find the next term: 2, 5, 11, 23, 47, ?

Answer: B. 95

Explanation

Each term is 2 x previous term + 1:
$2 \times 2 + 1 = 5, 2 \times 5 + 1 = 11, 2 \times 11 + 1 = 23, 2 \times 23 + 1 = 47, 2 \times 47 + 1 = 95$

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 2

Find the next term: 1, 2, 6, 24, 120, ?

Answer: D. 720

Explanation

These are factorials: 1!, 2!, 3!, 4!, 5!
$1 = 1, 2 = 2 \times 1, 6 = 3 \times 2 x 1, 24 = 4 \times 3 x 2 \times 1, 120 = 5 \times 4 x 3 \times 2 x 1$
Next = 6! = 720

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 3

Find the next term: 1, 4, 10, 19, 31, ?

Answer: C. 46

Explanation

The differences increase by 3 each time:
$1 + 3 = 4, 4 + 6 = 10, 10 + 9 = 19, 19 + 12 = 31, 31 + 15 = 46$

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Common mistakes and useful habits

First check for arithmetic progression (constant difference) and geometric progression (constant ratio) - these are the most common patterns.
Memorise squares up to 20^2 (400) and cubes up to 10^3 (1000) for quick pattern recognition.
For odd man out questions, check divisibility rules - all numbers except one may be divisible by a certain number.
When no obvious pattern appears, try breaking the series into odd-positioned and even-positioned terms separately.
For letter series, convert letters to their alphabetical positions (A=1, B=2, etc.) and analyse the numeric pattern.
Check digit sums or digit products if the numbers don't form an obvious mathematical pattern.

Ready to test your understanding?

Work through 152 questions with explanations after each answer.

Start practice

Next topic: General Aptitude

Key formulas and rules

Key concepts

Arithmetic Series

Geometric Series

Squares and Cubes

Prime Numbers

Mixed and Alternating Patterns

Odd Man Out Strategy

Worked examples

Example 1

Solution

Example 2

Solution

Example 3

Solution

Example 4

Solution

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

Keep building the same skill family.

Key formulas and rules

Key concepts

Arithmetic Series

Geometric Series

Squares and Cubes

Prime Numbers

Mixed and Alternating Patterns

Odd Man Out Strategy

Worked examples

Example 1

Solution

Example 2

Solution

Example 3

Solution

Example 4

Solution

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

Keep building the same skill family.