In this odd man out reasoning question on numbers, find the odd number from the alternatives: 286, 374, 143, 279.

Introduction / Context:
This question tests your ability to recognize divisibility patterns in numbers. The options are 286, 374, 143 and 279. Three of these numbers share a special factor, while one does not. Identifying that exception is the goal of this odd man out problem.

Given Data / Assumptions:

• Numbers given: 286, 374, 143, 279
• Exactly one number fails to share a key factor with the others.
• We focus on divisibility by the prime number 11, which has a distinctive test.

Concept / Approach:
A classic reasoning trick uses divisibility by 11. For a number to be divisible by 11, the alternating sum of its digits (sum of digits in odd positions minus sum of digits in even positions) must be either 0 or a multiple of 11. We can also directly factorize small numbers to confirm this property. If three numbers are divisible by 11 and one is not, the latter is the odd one out.

Step-by-Step Solution:
Step 1: Factorize 286.286 = 2 * 11 * 13, so 286 is divisible by 11.Step 2: Factorize 374.374 = 2 * 11 * 17, again divisible by 11.Step 3: Factorize 143.143 = 11 * 13, so it is clearly divisible by 11.Step 4: Factorize 279.279 = 3 * 3 * 31 = 9 * 31, and 11 is not a factor.Step 5: Summarize the pattern.286, 374 and 143 are all multiples of 11, whereas 279 is not.

Verification / Alternative check:
We can also apply the divisibility by 11 test. For 286, (2 + 6) - 8 = 0, multiple of 11, so divisible by 11. For 374, (3 + 4) - 7 = 0, again divisible by 11. For 143, (1 + 3) - 4 = 0, so divisible by 11. For 279, (2 + 9) - 7 = 4, not a multiple of 11, so it is not divisible by 11. This confirms that only 279 fails the test.

Why Other Options Are Wrong:
286: Divisible by 11 and fits the common pattern among three numbers.
374: Also divisible by 11, so it belongs to the main group.
143: Another multiple of 11 that satisfies the same structural property.

Common Pitfalls:
Some learners focus solely on the magnitude of the numbers or their parity (odd or even), which does not isolate exactly one number. Others may attempt to examine differences between them, but that usually leads to no clear single odd term. Recognizing standard divisibility tricks, especially for 11, often turns such questions from confusing to straightforward.

Final Answer:
The odd number out among the given options is 279.