In this number analogy, 68 is related to 130 using a two step arithmetic rule. Applying the same rule, 222 is related to which of the following numbers?

Introduction / Context:
This question is a number analogy where a specific arithmetic rule connects each pair of numbers. You are told that 68 corresponds to 130 and must determine which number should be paired with 222 using the same transformation. Such questions are common in quantitative aptitude tests and help examiners see whether a student can extract a hidden rule from one example and then generalise it correctly.

Given Data / Assumptions:
- First pair: 68 and 130.
- Second given number: 222.
- The options are candidate results of applying the same rule to 222.
- We assume a single consistent arithmetic pattern, such as scaling and shifting, applies to both pairs.

Concept / Approach:
A good starting point is to check simple linear transformations. Notice that if we multiply 68 by 2 we obtain 136. If we then subtract 6, we get 130. So one neat pattern is: result = 2 * number - 6. This works exactly for the given pair 68 : 130. The next step is to verify this rule by applying it to 222 and seeing which option matches.

Step-by-Step Solution:
Step 1: Test doubling: 2 * 68 = 136. Step 2: Subtract 6 from 136: 136 - 6 = 130, which matches the given related number. Step 3: Conclude that the rule is f(n) = 2 * n - 6. Step 4: Apply the same rule to 222. Compute 2 * 222 = 444. Step 5: Subtract 6 from 444: 444 - 6 = 438. Step 6: Compare 438 with the answer options and select it as the correct related number.

Verification / Alternative check:
Test whether any other simple operation on 68, like adding a fixed constant or squaring, gives 130 in a neat way. Adding a constant would require 62, and there is no reason to prefer that over 2n minus a constant when the doubling pattern works so cleanly. Also, when the same rule is applied to 222, we obtain 438 which lies in a reasonable range and is explicitly present among the options. This double then subtract rule is simple, consistent and reproducible.

Why Other Options Are Wrong:
Option B 430, option C 444 and option D 450 cannot be obtained by the rule 2n minus 6. For instance, 2 * 222 is 444, so 444 would correspond to subtracting zero. That would break the pattern used to generate 130 from 68. Similarly, 430 or 450 would require arbitrary constants that do not match the first pair. Because a single uniform rule must apply to both pairs, these alternatives must be rejected.

Common Pitfalls:
A frequent mistake is to focus on the digits and attempt slow digit wise manipulations rather than treating the number as a whole. Others may try complicated operations such as mixing squares and cubes without noticing that a very simple linear rule fits perfectly. Always start with testing small, neat transformations like doubling, halving, adding or subtracting constants before considering more complex patterns.

Final Answer:
Using the rule result = 2 * number - 6, 68 maps to 130 and 222 maps to 438.