In this number pattern reasoning question, select the odd four digit number from the given alternatives based on divisibility by 8.

Introduction / Context:
This question is designed to test your understanding of divisibility rules for larger numbers, especially divisibility by 8. You are given four four digit numbers and asked to identify the odd one out. Three of the numbers share a common divisibility property, while one does not. Such problems appear in quantitative aptitude tests to check speed and number sense.

Given Data / Assumptions:
- The options are 4416, 8432, 4520, and 4260.- All numbers are positive and four digit.- We will use the rule for divisibility by 8 as the main test.

Concept / Approach:
A number is divisible by 8 if its last three digits form a number that is divisible by 8. This rule works because 1000 is divisible by 8, so only the last three digits affect divisibility by 8. To solve this question efficiently, we examine the last three digits of each option and check whether those three digit numbers are multiples of 8.

Step-by-Step Solution:
Step 1: For 4416, the last three digits are 416. Because 416 divided by 8 equals 52, 4416 is divisible by 8.Step 2: For 8432, the last three digits are 432. Because 432 divided by 8 equals 54, 8432 is divisible by 8.Step 3: For 4520, the last three digits are 520. Because 520 divided by 8 equals 65, 4520 is divisible by 8.Step 4: For 4260, the last three digits are 260. Because 260 divided by 8 equals 32 remainder 4, 260 is not divisible by 8, so 4260 is not divisible by 8.Step 5: Therefore, three numbers are multiples of 8, while one number is not.

Verification / Alternative check:
You may also check using direct division. 4416 divided by 8, 8432 divided by 8, and 4520 divided by 8 all give whole numbers. However, 4260 divided by 8 produces a fraction, confirming that 4260 is not a multiple of 8.

Why Other Options Are Wrong:
4416: Multiple of 8, so it fits the pattern.8432: Also divisible by 8 and belongs with 4416 and 4520.4520: Again, divisible by 8 and not the odd one.

Common Pitfalls:
Candidates sometimes test only divisibility by 2 or 4 and notice that all numbers are even, which does not help in distinguishing them. The key here is the stricter rule of divisibility by 8, which needs checking based on the last three digits.

Final Answer:
The odd number is 4260 because it is not divisible by 8, while 4416, 8432, and 4520 are all multiples of 8.