Odd one out in a digit-property set Identify the number that does not follow the common digit rule in the set: 253, 136, 352, 460, 324, 631, 244.

Introduction / Context:
This odd-man-out puzzle asks you to detect a hidden pattern across multi-digit numbers and then pick the single value that breaks that rule. Many such questions rely on simple arithmetic relations among digits (sum, difference, parity, or primality). Here, checking divisibility and compositeness often reveals the correct outlier quickly and reliably.

Given Data / Assumptions:

• Numbers to test: 253, 136, 352, 460, 324, 631, 244.
• We assume the same base-10 digit interpretation for all terms.
• We look for a common numeric property present in most items but violated by exactly one item.

Concept / Approach:
For digit-based sets where no clear arithmetic progression exists, a fast screen is to test primality or obvious factorization. If six items share “composite” status and a single one is prime, the prime is the odd one out. This method is robust when digit-relationship hypotheses (like middle digit equals sum of outer digits) do not hold uniformly across the set.

Step-by-Step Solution:
Check 253 = 11 * 23 ⇒ composite.Check 136 = 8 * 17 ⇒ composite.Check 352 = 32 * 11 ⇒ composite.Check 460 = 46 * 10 ⇒ composite.Check 324 = 18 * 18 ⇒ composite.Check 244 = 4 * 61 ⇒ composite.Check 631: test small primes (2,3,5,7,11,13,17,19,23). Not divisible by 2 or 5. Sum of digits = 10 ⇒ not divisible by 3. 631/7 ≠ integer; 631/11 ≠ integer; 631/13 ≈ 48.5; 631/17 ≈ 37.1; 631/19 ≈ 33.2; 631/23 ≈ 27.4. No small factor found; 631 is prime.

Verification / Alternative check:
Since every other number factors cleanly, and 631 resists all standard small-prime divisibility tests, 631 is the only prime in the set. That makes it the clear outlier by the “composite vs. prime” property.

Why Other Options Are Wrong:
244, 352, 136, and 460 are all composite (each has nontrivial factors), so they fit the dominant pattern and cannot be the odd one out.

Common Pitfalls:
Getting distracted by digit-sum tricks (e.g., “first + last = middle”) that do not hold consistently, or assuming a hidden sequence when the task is a classification by number type. Always test simple number-theory properties early for odd-man-out items.

Final Answer:
631