In this aptitude based odd one out question, you must select the number that does not follow the same divisibility property as the other three numbers from the set 5306, 2147, 4205 and 4308.

Introduction / Context:
This question belongs to the odd one out category within quantitative aptitude. The goal is to analyze the given four numbers and identify the one that does not satisfy a common numerical property that the other three share. Such questions often check divisibility, parity, or simple number patterns. Here, the focus is on divisibility by 5, which is an important and very basic concept used frequently in competitive exams.

Given Data / Assumptions:

• The four given numbers are 5306, 2147, 4205 and 4308.
• All numbers are positive integers.
• We assume that a simple divisibility rule or pattern is involved.

Concept / Approach:
One of the fastest approaches in odd one out problems with large integers is to first check basic divisibility rules. The divisibility rule for 5 is very straightforward: a number is divisible by 5 if and only if its last digit is 0 or 5. Therefore, we can focus only on the unit digit of each number. If one number is divisible by 5 and the others are not, that number will be the odd one out; likewise, if three numbers are divisible by 5 and one is not, then the non multiple of 5 is the odd one out.

Step-by-Step Solution:
Step 1: Check the last digit of 5306. The unit digit is 6, so 5306 is not divisible by 5.Step 2: Check the last digit of 2147. The unit digit is 7, so 2147 is not divisible by 5.Step 3: Check the last digit of 4205. The unit digit is 5, so 4205 is divisible by 5.Step 4: Check the last digit of 4308. The unit digit is 8, so 4308 is not divisible by 5.Step 5: We see that exactly one number, 4205, is divisible by 5. The other three numbers are not divisible by 5. Therefore 4205 is different from the others and is the odd one out.
Verification / Alternative check:
You can verify by direct division: 4205 / 5 = 841, which is an integer. On the other hand, 5306 / 5, 2147 / 5 and 4308 / 5 do not give integer results. Thus the pattern is confirmed: only 4205 is a multiple of 5 among the four given numbers.

Why Other Options Are Wrong:
5306 is not the odd one out because it is a non multiple of 5 and shares this property with 2147 and 4308.
2147 is also a non multiple of 5 and therefore is similar to 5306 and 4308, not unique.
4308 is again a non multiple of 5, so it follows the same divisibility pattern as 5306 and 2147.

Common Pitfalls:
Sometimes candidates may get distracted by the size or parity of the numbers, such as checking whether the numbers are even or odd. However, that does not isolate a single number here because both even and odd numbers appear more than once. The key is to look for a property that only one number possesses, such as divisibility by 5 in this case. Another common mistake is to overcomplicate the problem by seeking complex patterns instead of applying basic divisibility rules.

Final Answer:
The only number that is divisible by 5 is 4205, so 4205 is the correct odd one out.