In the following question, select the odd number from the alternatives given below. Look for a common divisibility or factor pattern shared by most numbers and choose the one that does NOT follow it. (A) 253 (B) 473 (C) 143 (D) 633 (E) 583

Introduction / Context:
This odd-number question is based on a hidden factor/divisibility pattern. In many aptitude problems, three numbers share a common factor (like 11, 7, 13, etc.) and the odd number is the one that does not have that factor.

Given Data / Assumptions:

• We test each number for a common factor.
• A quick approach is to check divisibility by a likely shared prime factor.
• If several options share the same factor, that factor is the pattern.

Concept / Approach:
The key observation here is that 253, 473, and 143 are all divisible by 11 (they can be expressed as 11 * something). The odd number is the one that is not divisible by 11.

Step-by-Step Solution:

Verification / Alternative check:
Another quick check is the divisibility test for 11: take the alternating sum of digits. For 253: (2 - 5 + 3) = 0, divisible by 11. For 473: (4 - 7 + 3) = 0, divisible by 11. For 143: (1 - 4 + 3) = 0, divisible by 11. For 583: (5 - 8 + 3) = 0, divisible by 11. For 633: (6 - 3 + 3) = 6, not divisible by 11. So 633 is odd.

Why Other Options Are Wrong:

Common Pitfalls:
Students often try prime-checking randomly or look only at last digits. Another mistake is missing easy divisibility tests like 11. When multiple numbers look unrelated, testing for a shared small prime factor (2, 3, 5, 7, 11, 13) is usually a strong strategy.

Final Answer:
633