In this numerical analogy question, select the related number from the given alternatives to complete the proportion: 12.5 : 6.25 :: 7 : ?

Introduction / Context:
This numerical analogy checks whether you can detect a simple proportional relationship involving halving. The pair 12.5 and 6.25 is provided, and you must determine the corresponding number for 7 so that the analogy 12.5 : 6.25 :: 7 : ? holds true. Questions like this are common in quantitative aptitude tests and require a clear understanding of basic fraction and decimal relationships without complicated formulas.

Given Data / Assumptions:
The first pair of numbers is 12.5 and 6.25.
The second pair starts with 7, and the unknown related number must be selected from the options.
The options are 3.5, 3.25, 6.5, 12, and 14.
We assume that the numerical operation connecting 12.5 to 6.25 must be applied to 7 to find the missing value.

Concept / Approach:
The simplest way to relate 12.5 and 6.25 is to note that 6.25 is exactly half of 12.5. In fraction terms, 6.25 / 12.5 = 1/2. This strongly suggests that the transformation from the first term to the second term in each pair is division by 2. Therefore, we should divide 7 by 2 to obtain the answer. Recognising such halving or doubling patterns is a key skill in analogy questions involving numbers.

Step-by-Step Solution:
Step 1: Verify the relationship in the first pair. Compute 12.5 / 2 = 6.25.Step 2: Confirm that 6.25 is exactly half of 12.5, so the operation in the first pair is division by 2.Step 3: Apply the same operation to the second pair. Compute 7 / 2.Step 4: We know that 7 / 2 = 3.5.Step 5: Check the options and confirm that 3.5 is available.Step 6: Conclude that 3.5 is the only option that satisfies the same divide by 2 relationship as in the first pair.

Verification / Alternative check:
We can confirm the reasoning with a proportional expression. If 12.5 : 6.25 equals 7 : x, then the ratio 12.5 / 6.25 should equal 7 / x. Since 12.5 / 6.25 = 2, we have 2 = 7 / x, giving x = 7 / 2 = 3.5. This matches the earlier direct halving approach, so both methods support the same answer and reinforce the correctness of 3.5 as the missing term.

Why Other Options Are Wrong:
Option 3.25 is half of 6.5, not half of 7, so it does not follow the same relationship as the first pair.
Option 6.5 is almost equal to 7 and would correspond to dividing by a factor close to 1, which is inconsistent with the exact halving observed between 12.5 and 6.25.
Option 12 implies multiplying 7 by a factor less than 2 instead of dividing by 2, which reverses the type of operation.
Option 14 represents doubling 7, which again contradicts the divide by 2 relationship found in the first pair.

Common Pitfalls:
Some candidates may misread decimals and assume that 6.25 is a more complicated fraction of 12.5, leading them to overthink the problem. Others might be tempted by numbers that look familiar or neat, such as 14, without verifying whether the same operation is applied to both pairs. The reliable strategy is always to compute the exact numeric ratio between the first pair and then apply that ratio to the second pair. Here, that ratio is clearly 1/2, so the second term must also be half of the given number.

Final Answer:
Therefore, following the same halving relationship as in 12.5 : 6.25, the correct completion of the analogy 12.5 : 6.25 :: 7 : ? is 3.5.