Select the related number from the given alternatives: 12.5 is to 6.25 as 7 is to which number?

Introduction / Context:
This numerical analogy uses a simple fractional relationship. You are told that 12.5 corresponds to 6.25, and must find the number that corresponds to 7 in the same way. Many decimal analogies of this type rely on halving, doubling, or simple fractions such as one half or one quarter. Here, the transformation from 12.5 to 6.25 is straightforward halving.

Given Data / Assumptions:

• The first pair is 12.5 on the left and 6.25 on the right.
• The second starting number is 7, and the related number is unknown.
• The options are 3.5, 3.25, 6.5, and 12.
• We assume the same arithmetic operation connects 12.5 to 6.25 and 7 to the missing number.
• The operation should be simple and common, such as multiplication by a fraction.

Concept / Approach:
First, observe that 6.25 is exactly half of 12.5, because 12.5 divided by 2 is 6.25. This strongly suggests that the pattern is to divide the given number by 2. Once we verify that this is correct for the example pair, we apply the same rule to 7 and check which option matches the result. This is a standard halving pattern often used in aptitude tests with decimal numbers.

Step-by-Step Solution:
Step 1: Check the relationship between 12.5 and 6.25. Step 2: Divide 12.5 by 2. The result is 12.5 / 2 = 6.25. Step 3: This confirms that the rule in the example pair is to take half of the original number. Step 4: Now apply the same rule to 7. Compute 7 / 2. Step 5: 7 divided by 2 equals 3.5. Step 6: Compare this with the options and see that 3.5 appears as option a. Step 7: Therefore, 3.5 is the correct related number for 7 in this analogy.

Verification / Alternative check:
We can quickly test alternative patterns to make sure halving is the most reasonable. If we tried subtracting a fixed amount, 12.5 minus 6.25 equals 6.25, which is not obviously useful for 7. If we tried multiplying or dividing by some less familiar fraction, it would be unnecessarily complex for this type of problem. Halving exactly reproduces the given pair and leads to 3.5, which is a simple, clean decimal that matches one of the choices.

Why Other Options Are Wrong:
3.25 is half of 6.5, not half of 7. The option 6.5 is actually greater than 7 and would correspond to 12.5 multiplied by approximately 0.52, which does not match the first pair. The option 12 is close to 12.5 but does not represent a clear fraction of 7. None of these alternative values can be produced by the straightforward halving rule that correctly explains the example pair.

Common Pitfalls:
Under time pressure, candidates sometimes miscalculate half of a decimal or confuse halving with subtracting a similar looking number. Others may jump to the visually familiar 3.25 because 12.5 and 6.25 share the digits 1, 2, 5, and 6. It is important to focus on the operation, not on superficial digit similarities. When the first pair is clearly a case of dividing by 2, apply that same operation to the second number without overcomplicating the situation.

Final Answer:
Since 6.25 is half of 12.5, the number corresponding to 7 by the same rule is half of 7, which is 3.5.