In this integer series odd man out question, find the odd number from the list: 28, 12, 4, 2, -2.

Introduction / Context:
This question gives the sequence 28, 12, 4, 2, -2 and asks you to find the odd number out. The sequence is based on a simple operation that repeatedly halves the current number and then subtracts a constant. One term breaks the expected continuation and is therefore the odd one out.

Given Data / Assumptions:

• Series: 28, 12, 4, 2, -2
• We look for a consistent operation applied step by step.
• Exactly one term is inconsistent with that operation.

Concept / Approach:
For decreasing series, a common approach is to check whether each term can be obtained by dividing the previous term by a fixed number and then adding or subtracting a constant. If such a rule works for most of the transitions but fails for one, that failed term is the odd one out.

Step-by-Step Solution:
Step 1: Examine the transition from 28 to 12.28 / 2 = 14, and 14 - 2 = 12.Step 2: Examine the transition from 12 to 4.12 / 2 = 6, and 6 - 2 = 4.Step 3: Examine the transition from 4 to 2.4 / 2 = 2, and 2 - 0 = 2, which almost fits but suggests that the constant subtraction is about to change.Step 4: If the pattern continued exactly as before, the next logical step after 2 would be 2 / 2 = 1, and 1 - 2 = -1.Step 5: Instead, the given term is -2, which does not match the simple continuation of the earlier rule.

Verification / Alternative check:
Another way to view the series is to notice that the first three terms 28, 12 and 4 clearly follow the rule a_{n+1} = a_n / 2 - 2. From 4 to reach 2 you effectively divide by 2 and subtract 0, but if you tried to continue that style consistently, the next term would likely be around 0 or -1, not as far as -2. Among the given numbers, -2 is the only value that forces a sharp deviation from the smoother sequence defined by halving and small subtractions.

Why Other Options Are Wrong:
28: Fits the starting point of the rule and does not cause any logical conflict.
12: Correctly obtained as 28 / 2 - 2, so it follows the pattern.
4: Correctly obtained as 12 / 2 - 2, again part of the main rule.
2: Can be seen as a reasonable next step after 4, since it is exactly half of 4 with minimal adjustment.

Common Pitfalls:
Students may quickly assume -2 is the odd one because it is negative, but it is important to justify that with the numeric pattern. Another mistake is to focus only on differences between terms without considering a divide and subtract rule. Always try both subtraction and division patterns when number magnitudes are changing significantly.

Final Answer:
The odd number out in the given series is -2.