Select the related number from the given alternatives: 111 : 89 :: 105 : ?

Introduction / Context:
This is a number analogy where the second number is obtained from the first by a simple arithmetic operation. The pair 111 : 89 provides the pattern. You must detect that pattern and then apply it to 105 to find the missing number. Such questions test your ability to spot consistent differences rather than memorizing formulas.

Given Data / Assumptions:
- The first pair is 111 and 89.
- The second pair is 105 and an unknown number that must follow the same rule.
- We look for a simple linear transformation such as addition or subtraction by a constant number.
- One of the options 83, 95, 85, or 100 will match that rule.

Concept / Approach:
Start by computing the difference between 111 and 89. The difference 111 - 89 gives a clue to the operation. If this difference is a constant value that can be subtracted from 105 to yield one of the options, then the rule is very likely to be "subtract that constant." This approach keeps the analogy simple and consistent across pairs.

Step-by-Step Solution:
Step 1: Compute the difference between 111 and 89. 111 - 89 = 22. Step 2: Interpret the rule as: subtract 22 from the first number to get the second number. Step 3: Apply the same rule to the second pair. Start with 105 and subtract 22. Step 4: Calculate 105 - 22. This equals 83. Step 5: Check whether 83 is listed among the options. It appears as option A. Step 6: Therefore 105 is related to 83 by the same subtraction rule that connects 111 to 89.

Verification / Alternative check:
We can verify by reapplying the rule in both directions. 111 - 22 = 89 verifies the first pair. For the second pair, adding 22 to 83 gives 105, which reverses the operation and confirms consistency. None of the other given options produce a neat symmetric relationship with 105 based on subtracting 22 or any similarly simple constant that also works for 111 and 89. This supports the conclusion that 83 is the intended answer.

Why Other Options Are Wrong:
Option B "95" would require subtracting 16 from 111 to maintain the pattern, which does not match the actual difference of 22 seen in the first pair.
Option C "85" implies subtracting 20, which also fails to reproduce 89 from 111 when used as a constant rule.
Option D "100" would mean subtracting 11 from 111, again inconsistent with the requirement of a single shared transformation.

Common Pitfalls:
A common mistake is to force complicated rules involving digit sums or products when a simple constant difference explains the relationship. Another error is to look only at the second pair and try to deduce a rule separately from the first pair, which breaks the idea of analogy. Always base your pattern discovery on the first pair and insist on a single consistent operation for both pairs.

Final Answer:
The correct related number is 83.