Multiples of 11 property — pick the odd one out Numbers: 385, 462, 572, 396, 427, 671, 264. Which one is different?

Introduction / Context:
One efficient technique for odd-man-out sets is to check divisibility by a common factor that most numbers share. If all but one are multiples of a particular integer (here 11), the non-multiple is the outlier.

Given Data / Assumptions:

• Candidates: 385, 462, 572, 396, 427, 671, 264.
• Hypothesis: Most of these might be divisible by 11.

Concept / Approach:
Use the 11-divisibility test or quick division to confirm whether each number is a multiple of 11. The one failing the test is the odd term.

Step-by-Step Solution:
385 = 35 * 11 ⇒ multiple of 11.462 = 42 * 11 ⇒ multiple of 11.572 = 52 * 11 ⇒ multiple of 11.396 = 36 * 11 ⇒ multiple of 11.671 = 61 * 11 ⇒ multiple of 11.264 = 24 * 11 ⇒ multiple of 11.427 ÷ 11 = 38 remainder 9 ⇒ not a multiple of 11.

Verification / Alternative check:
The alternating digit sum test for 11 confirms the same: for 427, (4 − 2 + 7) = 9, not a multiple of 11. All others pass cleanly by direct factorization shown.

Why Other Options Are Wrong:
385, 462, 572, 396, 671, and 264 are all multiples of 11 and hence share the majority property.

Common Pitfalls:
Overlooking easy divisibility patterns and instead trying complex relationships. A quick 11-check saves time here.

Final Answer:
427