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 multiplication. In most groups, the second number is twice the first and the third number is three times the first, but one group breaks this pattern. Select the odd group of numbers from the given alternatives.

Introduction / Context:
This is a numerical reasoning question involving simple multiples and proportional relationships. Each option contains three numbers, and the second and third numbers are generated from the first using some multiplication rule. Such questions test your ability to detect how numbers are scaled and to spot the one group that does not follow the same multiplication pattern as the others.

Given Data / Assumptions:
- The options are (5, 10, 15), (7, 14, 21), (6, 12, 18), (8, 16, 28), and (9, 18, 27).
- In most groups, the second number is 2 times the first number and the third number is 3 times the first number.
- Exactly one group does not obey this 2 times and 3 times rule and must be chosen as the odd one out.

Concept / Approach:
The method is to take the first number of each group and check whether the second and third numbers can be written as multiples of that first number with factors 2 and 3 respectively. When a group fits the pattern first, 2 times first, 3 times first, it follows the rule. When it does not, it breaks the pattern. This simple form of proportional reasoning is very common in aptitude tests.

Step-by-Step Solution:
Step 1: For (5, 10, 15), the second number is 2 * 5 = 10, and the third number is 3 * 5 = 15, so the pattern holds.Step 2: For (7, 14, 21), the second number is 2 * 7 = 14, and the third number is 3 * 7 = 21, so this group also fits the same rule.Step 3: For (6, 12, 18), we have 2 * 6 = 12 and 3 * 6 = 18, so this group continues the same pattern.Step 4: For (9, 18, 27), we have 2 * 9 = 18 and 3 * 9 = 27, so this group fits the rule as well.Step 5: For (8, 16, 28), the second number is 2 * 8 = 16, but the third number should be 3 * 8 = 24 to follow the rule, whereas the given number is 28.Step 6: Since only the third number in the group (8, 16, 28) does not equal 3 times the first number, this group breaks the pattern and is the odd one out.

Verification / Alternative check:
We can also think in terms of ratios. In four groups, the ratios of the three numbers are 1 : 2 : 3. In the group (8, 16, 28), the ratios simplify to 8 : 16 : 28, which is 1 : 2 : 3.5 after dividing all terms by 8. The presence of 3.5 instead of 3 makes this group inconsistent with the simple integer multiple pattern of the others.

Why Other Options Are Wrong:
The groups (5, 10, 15), (7, 14, 21), (6, 12, 18), and (9, 18, 27) all satisfy the mapping first number, twice first, and thrice first. Because they share this exact structure, they belong to one family of patterns. None of these groups can be considered the odd one out when compared with a group like (8, 16, 28) that does not match the expected ratios.

Common Pitfalls:
Under time pressure, some students may focus only on whether the second number is twice the first and forget to verify the third number. Others may miscalculate 3 times the first number in their head. To avoid these errors, always check both second and third numbers systematically. Building this careful habit will help you solve many proportional reasoning and number pattern questions accurately.

Final Answer:
(8, 16, 28)