From the following four digit numbers, select the odd one out based on the relationship between the first two digits and the last two digits considered as separate two digit numbers: 4312, 4216, 9218, 3618.

Introduction / Context:
This is an odd one out question where each option is a four digit number that can naturally be split into two two digit numbers. The task is to find a hidden numerical relationship between the first two digit block and the last two digit block. Three numbers share a similar relationship, while one stands out as different. We need to identify the exceptional number based on a clear, logical pattern involving basic arithmetic operations.

Given Data / Assumptions:

• Numbers are 4312, 4216, 9218, 3618, and 5215.
• Each number can be split into two blocks: first two digits and last two digits.
• We can consider arithmetic relationships such as divisibility or multiplication between these two blocks.
• The odd one out is the number whose pair relationship differs from that of the others.

Concept / Approach:
A useful approach is to treat each four digit number as a pair of two digit numbers and check for simple relationships such as whether the first is divisible by the second, or the second is divisible by the first. In many reasoning questions, divisibility is an important hint. Once we find a property that three numbers share, the remaining one that does not share it will be the answer. The property used here is whether the first two digit number is exactly divisible by the last two digit number.

Step-by-Step Solution:
Step 1: Consider 4312. Split it as 43 and 12. Check 43 ÷ 12 and 12 ÷ 43. Neither gives an integer, so 43 and 12 are not evenly divisible in either direction. Step 2: Consider 4216. Split it as 42 and 16. Check 42 ÷ 16 and 16 ÷ 42. Again, neither is an integer, so they are not exact multiples. Step 3: Consider 9218. Split it as 92 and 18. Check 92 ÷ 18 and 18 ÷ 92. Neither quotient is an integer, so they are also not exact multiples. Step 4: Consider 3618. Split it as 36 and 18. Now check 36 ÷ 18 = 2, which is a whole number, so 36 is exactly divisible by 18. Step 5: Consider 5215 as a distractor. Split as 52 and 15. Neither 52 ÷ 15 nor 15 ÷ 52 is an integer. Step 6: We conclude that only in 3618 is the first pair exactly divisible by the second pair, so it behaves differently from the others.

Verification / Alternative check:
We can confirm the pattern by checking for any other simple relationships such as sum or difference equalities, but these do not uniquely pick one number. The divisibility pattern is clean and unique: 36 is a multiple of 18, whereas 43, 42, 92, and 52 are not multiples of 12, 16, 18, and 15 respectively. Therefore, the pair 36 and 18 stands out, and 3618 is correctly identified as the odd one out.

Why Other Options Are Wrong:
4312: 43 and 12 do not form a multiple relationship; both directions fail to give an integer quotient.
4216: 42 and 16 are also not exact multiples in either direction, so this pair is similar to most others.
9218: 92 and 18 do not satisfy the divisibility condition as neither 92 ÷ 18 nor 18 ÷ 92 is an integer.
5215: 52 and 15 are also not exact multiples of each other, so this option fits the majority pattern.

Common Pitfalls:
A common mistake is trying to force more complicated relationships such as squares, cubes, or sum of digits, which can be confusing and may not yield a clear unique choice. Another error is not checking both directions of divisibility. To avoid this, always start by examining simple arithmetic relations like divisibility or basic sums before moving to complex patterns.

Final Answer:
The only four digit number where the first two digits form a number that is exactly divisible by the number formed by the last two digits is 3618, so it is the odd one out.