Consider the number series 9, 17, 11, 19, 13, ... . What are the next three numbers in this series?

Introduction / Context:
This problem checks your skill with number series where two simple patterns are interleaved. Such questions appear often in aptitude tests because they test observation, pattern recognition, and the ability to separate a mixed sequence into simpler subsequences.

Given Data / Assumptions:
- The given terms are 9, 17, 11, 19, 13, ... .
- We must find the next three numbers in this sequence.
- All terms are integers and the pattern is assumed to be regular and consistent.
- The series may consist of more than one interleaved pattern.

Concept / Approach:
A common trick in such questions is that the odd position terms form one sequence and the even position terms form another. Each subsequence often follows a simple arithmetic pattern such as adding a constant. We will separate the series into odd and even positions and look for a regular increase or decrease in each subsequence.

Step-by-Step Solution:
Step 1: Mark positions of the terms. Positions: 1st = 9, 2nd = 17, 3rd = 11, 4th = 19, 5th = 13. Step 2: Form the subsequence of odd positions. Odd positions: 1st, 3rd, 5th give 9, 11, 13. This is an arithmetic progression with common difference +2. So the next odd position (7th term) will be 13 + 2 = 15. Step 3: Form the subsequence of even positions. Even positions: 2nd, 4th give 17, 19. This is also an arithmetic progression with common difference +2. So the next even positions are: 6th term = 19 + 2 = 21 and 8th term = 21 + 2 = 23. Step 4: Put the terms back into the original order. Existing: 1st 9, 2nd 17, 3rd 11, 4th 19, 5th 13. Next three: 6th = 21, 7th = 15, 8th = 23.

Verification / Alternative check:
Check the resulting series: 9, 17, 11, 19, 13, 21, 15, 23. Odd positions are 9, 11, 13, 15 (all increase by 2). Even positions are 17, 19, 21, 23 (also increase by 2). This symmetry confirms the correctness of the logic and the answer.

Why Other Options Are Wrong:
Option A (17, 10, 18) breaks both arithmetic progressions and mixes inconsistent increases and decreases.
Option B (19, 14, 23) does not maintain the steady +2 pattern in both subsequences.
Option D (19, 13, 22) introduces values that do not fit either arithmetic progression for odd or even positions.

Common Pitfalls:
Many learners try to find a single pattern across all terms and do not think about splitting the series into two subsequences. Others may misidentify the common difference due to quick mental calculation. Another common mistake is to place the new terms in the wrong positions instead of respecting the alternating sequence structure. Always write positions clearly, separate the terms, and then recombine carefully.

Final Answer:
The next three numbers in the series are 21, 15, and 23.