In the following number analogy, 14 is related to 30 according to a simple arithmetic rule. Using the same rule, 16 will be related to which of the following numbers?

Introduction / Context:
This is a basic numerical analogy problem where the first pair 14 : 30 suggests a specific arithmetic transformation applied to 14 to produce 30. The same operation then needs to be applied to 16 to identify the correct related number from the options. Such questions test the ability to recognise simple functional relationships like doubling, scaling, and adding or subtracting fixed constants.

Given Data / Assumptions:
- First number pair: 14 and 30, written as 14 : 30.
- Second number pair: 16 : ? must follow exactly the same rule.
- Answer options are 68, 36, 34, and 56.
- The rule should be simple enough for quick mental calculation in an aptitude test environment.

Concept / Approach:
We test common transformations on 14 to obtain 30. If we double 14, we obtain 28. Adding 2 more gives 30. This suggests the rule Result = 2 * Number + 2. To confirm that this rule is likely intended, we check that no other simple transformation, such as adding a constant or using squares, yields 30 in a similarly neat way. Once we accept 2 * n + 2 as the rule, we apply it to 16 and see whether the resulting number appears among the options.

Step-by-Step Solution:
Step 1: Compute 2 * 14 = 28. Step 2: Add 2 to 28, giving 28 + 2 = 30, which matches the second number in the first pair. Step 3: Assume that the general rule is Result = 2 * Number + 2. Step 4: Apply this rule to 16. Compute 2 * 16 = 32. Step 5: Add 2 to obtain 32 + 2 = 34. Step 6: Check options and note that 34 appears as option C, so 16 : 34 matches the required pattern.

Verification / Alternative check:
To verify, test alternative patterns quickly. A simple constant difference would mean 30 minus 14 equals 16, and if applied to 16 would give 16 plus 16 equals 32, which is not an option. Using squares, 14 squared is 196 and does not relate to 30 in an obvious way. Therefore, the double plus two rule is much more reasonable. It is also linear and easy to compute, which is typical in exam style analogies.

Why Other Options Are Wrong:
Option A, 68, would imply applying a factor of more than four to 16, which does not align with the relationship between 14 and 30. Option B, 36, and option D, 56, also cannot be generated from 16 using the consistent rule 2 * n + 2, and they require different operations that do not work for 14. Because the same rule must hold across all pairs, any value that fails this test must be eliminated.

Common Pitfalls:
Some learners may spot that 14 plus 16 equals 30 and try to apply a similar sum to 16, without noticing that 16 is fixed and no second number is provided. Others might attempt to use trial and error on the options without identifying a rule first, leading to confusion. The better strategy is to derive a clear arithmetic formula from the first pair and then apply it systematically to the second, ensuring consistency throughout.

Final Answer:
Using the rule Result = 2 * Number + 2, the number corresponding to 16 is 34, so the completed analogy is 14 : 30 :: 16 : 34 and option C is correct.