Each of the following is a four digit number in which the first two digits are somehow related to the last two digits. By examining the pattern between the first pair and the last pair of digits, select the number that is the odd one out.

Introduction / Context:
This is a typical odd one out question based on number patterns. The four digit numbers seem similar at first glance, but there is a hidden relationship between the first two digits and the last two digits in most of the options. Your job is to discover this relationship and then find the number that does not follow it. Such questions are widely used in aptitude tests to assess numerical pattern recognition and logical thinking.

Given Data / Assumptions:
- The given numbers are 8715, 5712, 9817, and 6812.
- Each number can be thought of as composed of two parts: the first two digits and the last two digits.
- We assume there is a simple arithmetic relation, such as addition, between the first pair of digits and the last pair of digits.

Concept / Approach:
The most natural approach is to split each four digit number into two parts and check whether the last two digits can be obtained from the first two digits by applying a simple operation. A very common pattern in such questions is that the last two digits equal the sum of the first two digits, written as a two digit number. If three numbers obey this pattern and one does not, then the one that breaks the rule is the odd one out.

Step-by-Step Solution:
Step 1: Consider 8715. Add the first two digits: 8 + 7 = 15. The last two digits are 15, so the pattern holds.Step 2: Consider 5712. Add the first two digits: 5 + 7 = 12. The last two digits are 12, so the pattern again holds.Step 3: Consider 9817. Add the first two digits: 9 + 8 = 17. The last two digits are 17, so the pattern holds here as well.Step 4: Consider 6812. Add the first two digits: 6 + 8 = 14. However, the last two digits are 12, not 14. This number does not follow the same rule.Step 5: Conclude that 6812 is the only number that breaks the pattern sum of first two digits equals the last two digits.

Verification / Alternative check:
We can double check by explicitly writing each number in the form AB and CD. For 8715, AB = 87 and CD = 15, and 8 + 7 = 15. For 5712, 5 + 7 = 12. For 9817, 9 + 8 = 17. Only for 6812 is the sum 6 + 8 equal to 14, which does not match 12. This confirms our conclusion.

Why Other Options Are Wrong:
8715 is not the odd one out because its last two digits correctly equal the sum of its first two digits. The same is true for 5712 and 9817; both strictly follow the same rule. Since those three obey the pattern, they must be considered consistent, leaving 6812 as the only inconsistent value.

Common Pitfalls:
One common mistake is to look for complicated patterns such as multiplication, division, or positional digit swaps when a very simple addition rule is sufficient. Another error is to add all four digits instead of separating the number into two parts. Candidates sometimes also miscalculate the sums, especially under time pressure, which can lead to a wrong choice. Carefully rechecking the addition for each option avoids this issue.

Final Answer:
The odd number is 6812, because it does not satisfy the rule that the last two digits equal the sum of the first two digits.