In the following question, four groups of three numbers are given. In each group, the second and third numbers are related to the first number by a simple arithmetic rule. Three groups follow the same pattern of equal differences, and one group breaks this pattern. Select the odd group of numbers from the given alternatives.

Introduction / Context:
This is an aptitude question based on simple number patterns and arithmetic progressions. You are given several groups of three numbers, and in each group the second and third numbers are linked to the first by a clear rule. Your task is to identify which group does not follow the same pattern as the others. Such odd one out problems test observational skills and understanding of basic arithmetic sequences.

Given Data / Assumptions:
- Options are groups: (10, 12, 14), (12, 14, 16), (18, 20, 22), (24, 26, 30), and (30, 32, 34).
- In each group there are exactly three numbers.
- We assume that in most groups the numbers follow the same simple rule based on equal differences from term to term.
- Exactly one group breaks this consistent pattern and is the odd one out.

Concept / Approach:
The most direct approach is to treat each group as a three term arithmetic progression. In an arithmetic progression, the difference between the first and second term is equal to the difference between the second and third term. If three groups show the same constant difference and one group shows a different structure, then that different group will be the required odd one out.

Step-by-Step Solution:
Step 1: For (10, 12, 14), the difference between 10 and 12 is +2, and between 12 and 14 is also +2.Step 2: For (12, 14, 16), the difference between 12 and 14 is +2, and between 14 and 16 is again +2.Step 3: For (18, 20, 22), the difference between 18 and 20 is +2, and between 20 and 22 is also +2.Step 4: For (30, 32, 34), the difference between 30 and 32 is +2, and between 32 and 34 is +2, so this group also forms an arithmetic progression with common difference 2.Step 5: For (24, 26, 30), the difference between 24 and 26 is +2, but between 26 and 30 it becomes +4, which breaks the equal difference pattern.Step 6: Therefore, (24, 26, 30) is not a proper three term arithmetic progression with common difference 2, and it is the odd group out.

Verification / Alternative check:
An alternative way is to write each group as first term plus a common difference. In four groups, the second term is first + 2 and the third term is first + 4. Only in the group (24, 26, 30) the third term is first + 6. This confirms that the pattern is broken only in this group, so the selection is correct.

Why Other Options Are Wrong:
(10, 12, 14), (12, 14, 16), (18, 20, 22), and (30, 32, 34) all have equal differences of +2 between consecutive terms. They are perfect examples of three term arithmetic progressions with common difference 2. Because they follow the same rule, these four groups cannot be considered odd ones out in this reasoning question.

Common Pitfalls:
Students sometimes look for complicated rules such as products or sums, when a simple difference pattern is enough. Another mistake is to check only the first two numbers and forget to check the difference between the second and third numbers. Always verify both gaps in each triple so that you do not accidentally select a correct progression as the odd one. Focusing on equal differences quickly reveals that (24, 26, 30) is the only inconsistent group.

Final Answer:
(24, 26, 30)