In the following reasoning question, four groups of three numbers are given: (8, 23, 15), (17, 52, 33), (12, 35, 23) and (15, 44, 29). In three groups, the difference between the second and third number equals the first number, while one group does not follow this rule. Select the odd one out from the given alternatives.

Introduction / Context:
This is a number relationship and classification question. You are given four ordered triples: (8, 23, 15), (17, 52, 33), (12, 35, 23) and (15, 44, 29). In such problems, the second and third numbers are usually related to the first by some arithmetic rule. Here, in most groups, the difference between the second and third number equals the first number, while one group breaks this pattern. You must identify that exceptional group as the odd one out.

Given Data / Assumptions:

• Number triples: (8, 23, 15), (17, 52, 33), (12, 35, 23) and (15, 44, 29).
• We are looking for a simple arithmetic relation between the three numbers in each group.
• Difference between second and third numbers is a likely candidate for the pattern.
• In three groups, second number minus third number equals the first number.
• Exactly one group does not satisfy this rule.

Concept / Approach:
The easiest way to detect the pattern is to compute, for each group, the value of (second number minus third number) and compare it with the first number. If they match, the group follows the rule. If not, that group is the odd one out. This type of relationship is common in reasoning questions because it is simple but not always immediately obvious unless you systematically test it.

Step-by-Step Solution:
Step 1: Analyse (8, 23, 15).Compute 23 - 15 = 8, which exactly equals the first number. So this group follows the rule.Step 2: Analyse (12, 35, 23).Compute 35 - 23 = 12, again matching the first number. This group also follows the rule.Step 3: Analyse (15, 44, 29).Compute 44 - 29 = 15, which is equal to the first number. So this group fits the pattern.Step 4: Analyse (17, 52, 33).Compute 52 - 33 = 19, which does not equal the first number 17. So this group does not follow the same rule.Step 5: Identify the odd triple.Since three groups satisfy the condition second minus third equals first, and (17, 52, 33) does not, (17, 52, 33) is the odd one out.

Verification / Alternative check:
As an additional check, you can express the rule algebraically for the valid triples: if the group is (a, b, c), then b - c = a. Substitute values from each group to verify. For (8, 23, 15), 23 - 15 = 8. For (12, 35, 23), 35 - 23 = 12. For (15, 44, 29), 44 - 29 = 15. Only for (17, 52, 33) do we get 52 - 33 = 19 which is not equal to 17. This confirms that the second group is inconsistent with the general pattern.

Why Other Options Are Wrong:
(8, 23, 15): Follows b - c = a, so it is not the odd group.
(12, 35, 23): Also obeys b - c = a and belongs with the main pattern.
(15, 44, 29): Again satisfies the same relation and thus is not the exception.

Common Pitfalls:
Sometimes candidates try more complicated formulas like b = 3a - 1 or c = 2a - 1 and get lost in unnecessary algebra. In many triple based reasoning questions, simple operations such as addition, subtraction or doubling are sufficient. It is a good habit to check simple expressions like b + c, b - c or a + c before moving on to more complex possibilities, as that often reveals the intended pattern quickly.

Final Answer:
The odd number group is (17, 52, 33), because only in this group does the difference between the second and third numbers not equal the first number.