In this digit sum based odd one out question, you must choose the three digit number whose digit sum is different from the common digit sum of the other numbers among 863, 785, 791 and 647.

Introduction / Context:
This is a simple yet effective digit sum odd one out question in the number system category. The task is to determine which number has a different total of digits compared to the others. Digit sum patterns commonly appear in reasoning tests because they are quick to compute and highlight hidden relationships among numbers.

Given Data / Assumptions:

• The numbers are 863, 785, 791 and 647.
• We work with the base 10 representation of each number and use each of the three digits.
• The suspected pattern involves the sum of digits.

Concept / Approach:
The idea is to calculate the sum of the digits of each number and look for a common value. If three numbers share the same digit sum and one number has a different sum, the number with the different sum is the odd one out. This approach is straightforward and does not require deep numerical theory.

Step-by-Step Solution:
Step 1: For 863, digits are 8, 6 and 3. Sum = 8 + 6 + 3 = 17.Step 2: For 785, digits are 7, 8 and 5. Sum = 7 + 8 + 5 = 20.Step 3: For 791, digits are 7, 9 and 1. Sum = 7 + 9 + 1 = 17.Step 4: For 647, digits are 6, 4 and 7. Sum = 6 + 4 + 7 = 17.Step 5: We observe that 863, 791 and 647 each have a digit sum of 17, while 785 has a digit sum of 20. Therefore, 785 is the odd one out.
Verification / Alternative check:
You can recheck by adding the digits again or by grouping them differently, such as (8 + 6) + 3 for 863 and so on. The consistency of the repeated sum of 17 for three numbers and the different result of 20 for 785 confirms that 785 is unique in terms of digit sum, which is the intended pattern in this question.

Why Other Options Are Wrong:
863 is not the odd one out because its digit sum of 17 matches that of 791 and 647.
791 is also not unique since its digit sum is 17, the same as 863 and 647.
647 similarly has a digit sum of 17, aligning it with 863 and 791.

Common Pitfalls:
Students may attempt to look for more complex patterns like prime numbers or factorization and overlook the simple digit sum relation. Another common issue is careless addition, which might lead to an incorrect sum and hence a wrong choice. Being systematic and double checking simple calculations can prevent such mistakes and is a valuable habit in all numerical reasoning questions.

Final Answer:
The only three digit number with a different digit sum is 785, so 785 is the odd one out.