Odd Man Out & Series
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Solved Examples
Study MaterialSolved Examples – Odd Man Out & Series
Solved examples help students understand the practical application of number patterns, logical sequences, arithmetic progression, geometric progression, and reasoning concepts in competitive examinations. These examples are designed from basic to advanced level and cover important questions frequently asked in SSC, Banking, Railway, Insurance, Defence, CAT, CDS, NDA, and various aptitude examinations.
Topics Covered in Solved Examples
- Odd Man Out Questions
- Number Series Problems
- Arithmetic Progression (A.P.)
- Geometric Progression (G.P.)
- Prime Number Series
- Square and Cube Patterns
- Alphabet Series
- Alternating and Mixed Series
Example 1: Odd Man Out – Even Numbers
Question: Find the odd man out:
2, 4, 6, 9, 10, 12
Solution:
All numbers are even except 9.
Odd Man Out = 9
Example 2: Arithmetic Progression
Question: Find the next term:
3, 7, 11, 15, 19, ?
Solution:
Difference:
7 − 3 = 4
11 − 7 = 4
15 − 11 = 4
19 − 15 = 4
Next term:
19 + 4 = 23
Answer: 23
Example 3: Geometric Progression
Question: Find the next term:
2, 6, 18, 54, ?
Solution:
Each term is multiplied by 3.
54 × 3 = 162
Answer: 162
Example 4: Prime Number Series
Question: Find the next term:
2, 3, 5, 7, 11, 13, ?
Solution:
The series contains prime numbers.
Next prime number after 13 is 17.
Answer: 17
Example 5: Perfect Square Series
Question: Find the missing term:
1, 4, 9, 16, ?, 36
Solution:
The series is:
1², 2², 3², 4², 5², 6²
Missing term:
5² = 25
Answer: 25
Example 6: Perfect Cube Series
Question: Find the next term:
1, 8, 27, 64, 125, ?
Solution:
The series is:
1³, 2³, 3³, 4³, 5³
Next term:
6³ = 216
Answer: 216
Example 7: Fibonacci Series
Question: Find the next term:
2, 4, 6, 10, 16, 26, ?
Solution:
Each term is the sum of previous two terms.
16 + 26 = 42
Answer: 42
Example 8: Difference Method
Question: Find the next term:
5, 10, 17, 26, 37, ?
Solution:
Differences:
5, 7, 9, 11
Next difference = 13
Next term:
37 + 13 = 50
Answer: 50
Example 9: Odd Man Out – Prime Numbers
Question: Find the odd man out:
3, 5, 7, 9, 11, 13
Solution:
All numbers are prime except 9.
Odd Man Out = 9
Example 10: Alternating Series
Question: Find the next term:
2, 5, 4, 7, 6, 9, ?
Solution:
Odd positions:
2, 4, 6
Even positions:
5, 7, 9
Next odd-position term:
8
Answer: 8
Example 11: Alphabet Series
Question: Find the next term:
A, C, E, G, I, ?
Solution:
Skipping one letter each time:
A, C, E, G, I
Next letter:
K
Answer: K
Example 12: Power Series
Question: Find the next term:
2, 6, 12, 20, 30, ?
Solution:
Pattern:
1×2 = 2
2×3 = 6
3×4 = 12
4×5 = 20
5×6 = 30
Next:
6×7 = 42
Answer: 42
Example 13: Missing Number Problem
Question: Find the missing term:
7, 14, 28, ?, 112
Solution:
Each term × 2
28 × 2 = 56
56 × 2 = 112
Answer: 56
Example 14: Square Difference Pattern
Question: Find the next term:
1, 5, 11, 19, 29, ?
Solution:
Differences:
4, 6, 8, 10
Next difference = 12
29 + 12 = 41
Answer: 41
Example 15: Odd Man Out – Squares
Question: Find the odd man out:
16, 25, 36, 45, 49, 64
Solution:
16 = 4²
25 = 5²
36 = 6²
49 = 7²
64 = 8²
45 is not a perfect square.
Odd Man Out = 45
Example 16: Mixed Operation Series
Question: Find the next term:
3, 7, 15, 31, 63, ?
Solution:
Pattern:
×2 +1
3×2 +1 = 7
7×2 +1 = 15
15×2 +1 = 31
31×2 +1 = 63
Next:
63×2 +1 = 127
Answer: 127
Example 17: Factorial Series
Question: Find the next term:
1, 2, 6, 24, 120, ?
Solution:
The series is factorials:
1!, 2!, 3!, 4!, 5!
Next:
6! = 720
Answer: 720
Example 18: Alphabet Position Series
Question: Find the next term:
B, E, H, K, ?
Solution:
Alphabet positions:
B = 2
E = 5
H = 8
K = 11
Difference = 3
Next position:
14 = N
Answer: N
Important Exam Tips
- Always check differences first.
- Look for multiplication or division patterns.
- Memorize squares, cubes, and prime numbers.
- Practice alternating series regularly.
- Use elimination methods in MCQs.
- Observe patterns carefully before solving.
- Practice previous year reasoning questions.
Common Mistakes to Avoid
- Ignoring second-level differences.
- Missing alternating patterns.
- Confusing square and cube patterns.
- Ignoring alphabet positions.
- Using incorrect operations.
Practicing solved examples regularly improves logical thinking ability, pattern recognition skills, and calculation speed in solving Odd Man Out & Series aptitude questions in competitive examinations.