In this number analogy, select the related number from the given alternatives so that 12 : 48 :: 104 : ?

Introduction / Context:
This is a number analogy question designed to test your ability to detect a simple arithmetic pattern between pairs of numbers. The pair 12 : 48 is given, and you must apply the same relationship to 104 in order to select the correct related number. Such questions often involve basic operations like multiplication, division, or a combination of addition and subtraction.

Given Data / Assumptions:

• First pair: 12 : 48.
• Second pair: 104 : ?.
• We assume a single, consistent numerical rule applies to both pairs.
• Exactly one of the answer choices should satisfy that rule without exceptions.

Concept / Approach:
The most natural step is to compare 12 and 48 to see how one changes into the other. Here, 48 is exactly four times 12. When such a clean multiplication factor is observed, the usual approach is to apply the same factor to the second starting number, 104. We then check which option matches the product and ensure that no alternate simpler pattern exists that would contradict this reasoning.

Step-by-Step Solution:
Step 1: Consider the first pair 12 and 48.Step 2: Compute 12 * 4 = 48, which shows a direct multiplication by 4.Step 3: Assume the same rule holds for the second pair: multiply the first number by 4.Step 4: Compute 104 * 4 = 416.Step 5: Check the answer options and identify 416 as the matching value.

Verification / Alternative check:
We can test whether any alternative simple rule might exist, such as adding a fixed number or multiplying and then adding or subtracting. For example, 12 + 36 = 48 does work, but applying the same idea to 104 as 104 + 36 = 140 does not match any option. Similarly, 12 squared or other more complex transformations do not yield 48 neatly while staying consistent for 104. The cleanest and most consistent pattern is therefore multiplication by 4 for both pairs.

Why Other Options Are Wrong:
Option A (415): This is close to 416 but does not correspond to 104 multiplied by any simple factor that also maps 12 to 48.
Option B (420): This would require a different and less natural rule and does not come from 104 * 4.
Option C (480): This looks like 48 * 10 but has no consistent link to the original pair 12 : 48 when applied using the same operation.

Common Pitfalls:
Candidates sometimes get attracted to large numbers that seem roughly proportional but forget to verify the exact operation. Another pitfall is overcomplicating the pattern with unnecessary steps when a single multiplication is sufficient. In analogy questions, the rule is usually simple and elegant, so always test straightforward operations like multiplication and division first.

Final Answer:
The rule is “multiply by 4”, so 12 : 48 :: 104 : 416. The correct answer is 416.