Odd One Out — Among 25631, 33442, 34424, and 52163, three have the same digit sum. Find the exception and explain.

Introduction / Context:
Digit-based invariants (sum, product, parity of sum) are classic levers in classification items. We will use digit sums to isolate the odd number.

Given Data / Assumptions:

• Numbers: 25631, 33442, 34424, 52163.
• Digit sum means adding all decimal digits of the number.

Concept / Approach:
Compute each digit sum and compare. When three match and one differs, that one is the outlier.

Step-by-Step Solution:
25631: 2 + 5 + 6 + 3 + 1 = 17.33442: 3 + 3 + 4 + 4 + 2 = 16.34424: 3 + 4 + 4 + 2 + 4 = 17.52163: 5 + 2 + 1 + 6 + 3 = 17.Observation: three values share digit sum 17; one has digit sum 16.

Verification / Alternative check:
You can also check the sums modulo 3: 17 ≡ 2 (mod 3); 16 ≡ 1 (mod 3). The single residue mismatch also isolates the same item.

Why Other Options Are Wrong:

• 25631: digit sum 17; matches the majority.
• 34424: digit sum 17; matches the majority.
• 52163: digit sum 17; matches the majority.

Common Pitfalls:
Over-searching for complex prime or square properties; the neat invariant here is the digit sum.

Final Answer:
33442