In this digit sum based odd one out question, choose the four digit number that does not share the same digit sum property as the others: 1919, 5656, 6761 and 7760.

Introduction / Context:
Number puzzles that ask you to find the odd one out often hide patterns in the sum of digits or relationships between digit groups. This problem presents four four digit numbers and expects you to identify the one whose digit sum behaves differently from the others. Learning to quickly compute and compare digit sums is useful for many aptitude questions, including divisibility tests and pattern recognition.

Given Data / Assumptions:

• The four numbers are 1919, 5656, 6761 and 7760.
• We will use simple addition of digits to compute the digit sum of each number.
• The goal is to spot the number that breaks the common pattern observed in the other three.

Concept / Approach:
A neat way to approach this is to find the sum of digits of each number and compare them. If three numbers share the same total digit sum and one number has a different total, then the number with the different digit sum can be considered the odd one out. This is a standard style in reasoning questions where entire numbers are not special, but their digit patterns are.

Step-by-Step Solution:
Step 1: For 1919, add the digits: 1 + 9 + 1 + 9 = 20. So the digit sum of 1919 is 20. Step 2: For 6761, add the digits: 6 + 7 + 6 + 1 = 20. The digit sum of 6761 is also 20. Step 3: For 7760, add the digits: 7 + 7 + 6 + 0 = 20. Again, the digit sum of 7760 is 20. Step 4: For 5656, add the digits: 5 + 6 + 5 + 6 = 22. The digit sum of 5656 is 22, which is different from 20. Step 5: Therefore three numbers (1919, 6761 and 7760) share the same digit sum of 20, while 5656 has digit sum 22. So 5656 is the odd one out.

Verification / Alternative check:
A quick verification is to observe that 1919, 6761 and 7760 all have digit sums that are multiples of 20, while 5656 gives a higher sum. Because the pattern is very clean (exact equality of digit sums for three numbers), and 5656 is the only number that breaks it, no further complex checks are needed. This confirms that 5656 is uniquely different in terms of digit sum.

Why Other Options Are Wrong:
1919 is wrong as the odd one out because its digit sum 20 matches the pattern shared with 6761 and 7760. 6761 is wrong as the odd one out because it also has digit sum 20, consistent with 1919 and 7760. 7760 is wrong as the odd one out because its digit sum 20 again follows the same rule.

Common Pitfalls:
Students may start by testing divisibility or looking for some complex arithmetic relation between the whole numbers and feel stuck. Another mistake is to check only the first or last two digits and ignore the full four digit structure. In many such questions, the digit sum is the intended pattern because it is easy to compute and provides a clear distinction, as it does here.

Final Answer:
The only number whose digit sum is different from the others, and therefore the odd one out, is 5656.